EFTA00285909.pdf

Praise for The Greatest Story Ever Told—So Far "In every debate I've done with theologians and religious believers, their knock-out final argument always comes in the form of two questions: Why is there something rather than nothing? and Why are we here? The presumption is that if science provides no answers then there must be a God. But God or no, we still want answers. In A Universe from Nothing Lawrence Krauss, one of the biggest thinkers of our time, addressed the first question with verve, and in The Greatest Story Ever Told he tackles the second with elegance. Both volumes should be placed in hotel rooms across America, in the drawer next to the Gideon Bible —Michael Shermer, publisher of Skeptic magazine, columnist for Scientific American, and author of The Moral Arc "Discovering the bedrock nature of physical reality ranks as one of humanity's greatest collective achievements. This book gives a fine account of the main ideas and how they emerged. Krauss is himself close to the field and can offer insights into the personalities who have led the key advances. A practiced and skilled writer, he succeeds in making the physics 'as simple as possible but no simpler: I don't know a better book on this subject? —Martin Rees, author of Just Six Numbers "It is an exhilarating experience to be led through this fascinating story, from Galileo to the Standard Model and the Higgs boson and beyond, with lucid detail and insight, illuminating vividly not only the achieve- ments themselves but also the joy of creative thought and discovery, 2P_Glealer-StoryEverTold_Atirdd I 12/16116 3:06 PIA EFTA00285909 enriched with vignettes of the remarkable individuals who paved the way. It amply demonstrates that the discovery that 'nature really follows the simple and elegant rules intuited by the twentieth- and twenty-first- century versions of Plato's philosopher? is one of the most astonishing achievements of the human intellect." —Noam Chomsky, Institute Professor & Professor of Linguistics (emeritus), MIT "Charming ... Krauss has written an account with sweep and verve that shows the full development of our ideas about the makeup of the world around us.... A great romp." —Walter Gilbert, Nobel laureate in chemistry 1 loved the fight scenes and the sex scenes were excellent." —Eric Idle 2P_GlealerASIonEverTold_Atirdd 2 1211&I6 3:06 PIA EFTA00285910 ALSO BY LAWRENCE M. KRAUSS A Universe from Nothing The Fifth Essence Fear of Physics The Physics of Star Trek Beyond Star Trek Hiding in the Mirror Quintessence Atom Quantum Man 2P_Glealer-StoryEverTold_Atirdd 3 12/1&I6 3:06 PIA EFTA00285911 1 1._ 11. 1,, EFTA00285912 THE GREATEST STORY EVER TOLD-SO FAR WHY ARE WE HERE? Lawrence M. Krauss ATRIA BOOKS NEWS YORH . . •0130,,, . ,,.NEV . \EW' DELHI EFTA00285913 ATRIA BOOKS An Imprint of Simon & Schuster, Inc. 1230 Avenue of the Americas New York, NY 10020 Copyright 0 2017 by Lawrence Krauss All rights reserved, including the right to reproduce this book or portions thereof in any form whatsoever. For information, address Atria Books Subsidiary Rights Department. 1230 Avenue of the Americas, New York, NY 10020. First Atria Books hardcover edition March 2017 ATRIA BOOKS and colophon are trademarks of Simon & Schuster, Inc. 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For more information or to book an event, contact the Simon & Schuster Speakers Bureau at 1-866-248-3049 or visit our website at Interior design by Dana Sloan Manufactured in the United States of America 109 8 7 6 543 2 1 Library of Congress Cataloging-in-Publication Data ISBN 978-1-4767-7761-0 ISBN 978-1-4767-7763-4 (ebook) 2P_Glealer-StoryEverrold_Atirdd 6 12/16116 3:06 PIA EFTA00285914 For Nancy 2P_Glealer-StoryEverTold_AC.irdd 7 128616 06 PM EFTA00285915 2P_Gtealer-StoryEverTold_Atirdd S 12/16116 3:06 PM EFTA00285916 These are the tears of things, and the stuff of our mortality cuts us to the heart. —VIRGIL 2P_Glealer-SoryEverTold_Atirdd 9 12/1&16 3:06 Pt, EFTA00285917 2P_GreatestSteryEverrold_AC.indd 10 12/16/16 3:06 PM EFTA00285918 CONTENTS Prologue 1 Part One: Genesis Chapter 1: From the Armoire to the Cave 9 Chapter 2: Seeing in the Dark 19 Chapter 3: Through a Glass, Lightly 33 Chapter 4: There, and Back Again 45 Chapter S: A Stitch in Time 55 Chapter 6: The Shadows of Reality 71 Chapter?: A Universe Stranger than Fiction 83 Chapter 8: A Wrinkle in Time 97 Chapter 9: Decay and Rubble 113 Chapter 10: From Here to Infinity: Shedding Light on the Sun 125 Part Two: Exodus Chapter 11: Desperate Times and Desperate Measures Chapter 12: March of the Titans Chapter 13: Endless Forms Most Beautiful: Symmetry Strikes Back xl 139 151 167 2P_Glealer-StoryEverrold_Atirdd 11 12/18118 3:08 MA I EFTA00285919 xi' CONTENTS Chapter 14: Cold, Stark Reality: Breaking Bad or Beautiful? 181 Chapter 15: Living inside a Superconductor 191 Chapter 16: The Bearable Heaviness of Being: Symmetry Broken, Physics Fixed 201 Part Three: Revelation Chapter 17 The Wrong Place at the Right Time 211 Chapter 18: The Fog Lifts 219 Chapter 19: Free at Last 231 Chapter 2O: Spanking the Vacuum 249 Chapter 21: Gothic Cathedrals of the Twenty-First Century 259 Chapter 22: More Questions than Answers 275 Chapter 23: From a Beer Party to the End of Time 289 Epilogue: Cosmic Humility 301 Acknowledgments 307 Index 309 2P_GrealestSloryEverTald_AC.indd 12 12/16116 3:06 PIA EFTA00285920 rgd 93:C 90141 CI Prur0Y-PRIAm3koiSaM0,0 4C LI VA OS C1101 2:13/V3 _LSA_LVAL10 '3H1 EFTA00285921 2P_Gtealer-StoryEverTold_Atincld 14 12/16116 3:06 PM EFTA00285922 PROLOGUE The hardest thing of all to see Is what Is really there. -J. A. BAKER, THE PEREGRINE L the beginning there was light. But more than this, there was gravity. After that, all hell broke loose.... This is how the story of the greatest intellectual adventure in history might properly be introduced. It is a story of science's quest to uncover the hidden realities underlying the world of our experience, which required marshaling the very pinnacle of human creativity and intellectual bravery on an unparalleled global scale. This process would not have been possible without a willingness to dispense with all kinds of beliefs and preconcep- tions and dogma, scientific and otherwise. The story is filled with drama and surprise. It spans the full arc of human history, and most remarkably, the current version isn't even the final one—just another working draft. It's a story that deserves to be shared far more broadly. Already in the first world, parts of this story are helping to slowly replace the myths and superstitions that more ignorant societies found solace in centuries or millennia ago. Nevertheless, thanks to the directors George Stevens and David Lean, the Judeo-Christian Bible is still sometimes referred 2P_Glealer-StoryEverTold_Atirdd I 12/16116 3:06 PIA EFTA00285923 2 PROLOGUE to as "the greatest story ever told." This characterization is astounding because, even allowing for the frequent sex and violence, and a bit of poetry in the Psalms, the Bible as a piece of literature arguably does not compare well to the equally racy but less violent Greek and Roman epics such as the Aeneid or the Odyssey-even if the English translation of the Bible has served as a model for many subsequent books. Either way, as a guide for understanding the world, the Bible is pathetically inconsis- tent and outdated. And one might legitimately argue that as a guide for human behavior large swaths of it border on the obscene. In science, the very word sacred is profane. No ideas, religious or otherwise, get a free pass. For this reason the pinnacle of the human story did not conclude with a prophet's sacrifice two thousand years ago, any more than it did with the death of another prophet six hundred years later. The story of our origins and our future is a tale that keeps on telling. And the story is getting more interesting all the time, not due to revelation, but due to the steady march of scientific discovery. Contrary to many popular perceptions, this scientific story also en- compasses both poetry and a deep spirituality. But this spirituality has the additional virtue of being tied to the real world—and not created in large part to appease our hopes and dreams. The lessons of our exploration into the unknown, led not by our de- sires, but by the force of experiment, are humbling. Five hundred years of science have liberated humanity from the shackles of enforced igno- rance. By this standard, what cosmic arrogance lies at the heart of the assertion that the universe was created so that we could exist? What myopia lies at the heart of the assumption that the universe of our expe- rience is characteristic of the universe throughout all of time and space? This anthropocentrism has fallen by the wayside as a result of the story of science. What replaces it? Have we lost something in the pro- cess, or as I shall argue, have we gained something even greater? I once said at a public event that the business of science is to make people uncomfortable. I briefly regretted the remark because I worried 2P_Glealer-StoryEverTold_Atincld 2 12/16116 3:06 PIA EFTA00285924 PROLOGUE 3 that it would scare people away. But being uncomfortable is a virtue, not a hindrance. Everything about our evolutionary history has primed our minds to be comfortable with concepts that helped us survive, such as the natural teleological tendency children have to assume objects exist to serve a goal, and the broader tendency to anthropomorphize, to as- sign agency to lifeless objects, because clearly it is better to mistake an inert object for a threat than a threat for an inert object. Evolution didn't prepare our minds to appreciate long or short time- scales or short or huge distances that we cannot experience directly. So it is no wonder that some of the remarkable discoveries of the scientific method, such as evolution and quantum mechanics, are nonintuitive at best, and can draw most of us well outside our myopic comfort zone. This is also what makes the greatest story ever told so worth telling. The best stories challenge us. They cause us to see ourselves differently, to re- align our picture of ourselves and our place in the cosmos. This is not only true for the greatest literature, music, and art. It is true of science as well. In this sense it is unfortunate that replacing ancient beliefs with modern scientific enlightenment is often described as a "loss of faith." How much greater is the story our children will be able to tell than the story we have told? Surely that is the greatest contribution of science to civilization: to ensure that the greatest books are not those of the past, but of the future. Every epic story has a moral. In ours, we find that letting the cosmos guide our minds through empirical discovery can produce a great rich- ness of spirit that harnesses the best of what humanity has to offer. It can give us hope for the future by allowing us to enter it with our eyes open and with the necessary tools to actively participate in it. • • • My previous book, A Universe from Nothing, described how the revolu- tionary discoveries over the past hundred years have changed the way we understand our evolving universe on its largest scales. This change has led science to begin to directly address the question Why is there something 2P_Glealer-StoryEverrold_Atirdd 3 12/16116 3:06 PIA EFTA00285925 4 PROLOGUE rather than nothing?"—which was formerly religious territory—and re- work it into something less solipsistic and operationally more useful. Like A Universe from Nothing, this story also originated in a lecture I presented, in this case at the Smithsonian Institution in Washington, DC, which generated some excitement at the time, and as a result I was once again driven to elaborate upon the ideas I started to develop there. In con- trast to A Universe from Nothing, in this book I explore the other end of the spectrum of our knowledge and its equally powerful implications for under- standing age-old questions. The profound changes over the past hundred years in the way we understand nature at its smallest scales are allowing us to similarly co-opt the equally fundamental question Why are we here?" We will find that reality is not what we think it is. Under the surface are "weird: counterintuitive, invisible inner workings that can chal- lenge our preconceptions of what makes sense as much as a universe arising from nothing might. And like the conclusion I drew in my last book, the ultimate lesson from the story I will tell here is that there is no obvious plan or purpose to the world we find ourselves living in. Our existence was not preordained, but appears to be a curious accident. We teeter on a precarious ledge with the ultimate balance determined by phenomena that lie well beneath the surface of our experience—phenomena that don't rely in any way upon our existence. In this sense, Einstein was wrong: "God" does appear to play dice with the universe, or universes. So far we have been lucky. But like playing at the craps table, our luck may not last forever. • • • Humanity took a major step toward modernity when it dawned in our ancestors' consciousness that there is more to the universe than meets the eye. This realization was probably not accidental. We appear to be hardwired to need a narrative that transcends and makes sense of our own existence, a need that was probably intimately related to the rise of religious belief in early human societies. 2P_Glealer-StoryEverTold_Atincld 4 12/16116 3:06 PIA EFTA00285926 PROLOGUE 5 By contrast, the story of the rise of modern science and its divergence from superstition is the tale of how the hidden realities of nature were uncovered by reason and experiment through a process in which seem- ingly disparate, strange, and sometimes threatening phenomena were ultimately understood to be connected just beneath the visible surface. Ultimately these connections dispelled the goblins and fairies that had earlier spawned among our ancestors. The discovery of connections between otherwise seemingly dispa- rate phenomena is, more than any other single indicator, the hallmark of progress in science. The many classic examples include Newton's connection of the orbit of the Moon to a falling apple; Galileo's recogni- tion that vastly different observed behaviors for falling objects obscure that they are actually attracted to the earth's surface at the same rate; and Darwin's epic realization that the diversity of life on Earth could arise from a single progenitor by the simple process of natural selection. None of these connections was all that obvious, at first. However, after the relationship comes to light and becomes clear, it prompts an "Ahar experience of understanding and familiarity. One feels like saying, 1 should have thought of that!" Our modern picture of nature at its most fundamental scale—the Standard Model, as it has become called—contains an embarrassment of riches, connections that are far removed from the realm of everyday experience. So far removed that it is impossible without some ground- ing to make the leap in one step to visualize them. Not surprisingly, such a single leap never occurred historically, ei- ther. A series of remarkable and unexpected and seemingly unrelated connections emerged to form the coherent picture we now have. The mathematical architecture that has resulted is so ornate that it almost seems arbitrary. "Ahar is usually the furthest thing from the lips of the noninitiated when they hear about the Higgs boson or Grand Unifica- tion of the forces of nature. To move beyond the surface layers of reality, we need a story that 2P_Glealer-StoryEverTold_Atirdd S 12/16116 3:06 PM EFTA00285927 6 PROLOGUE connects the world we know with the deepest corners of the invisible world all around us. We cannot understand that hidden world with in- tuitions based solely on direct sensation. That is the story I want to tell here. I will take you on a journey to the heart of those mysteries that lie at the edge of our understanding of space, time, and the forces that operate within them. My goal is not to unnecessarily provoke or offend, but to prod you, just as we physicists ourselves have been prodded and dragged by new discoveries into a new reality that is at once both un- comfortable and uplifting. Our most recent discoveries about nature's fundamental scales have chillingly altered our perception of the inevitability of our presence in the universe. They provide evidence too that the future will no doubt be radically different from what we might otherwise have imagined, and they too further decrease our cosmic significance. We might prefer to deny this uncomfortable, inconvenient reality, this impersonal, apparently random universe, but if we view it in an- other context, all of this need not be depressing. A universe without purpose, which is the way it is as far as I can tell, is far more exciting than one designed just for us because it means that the possibilities of existence are so much more diverse and far ranging. How invigorating it is to find ourselves with an exotic menagerie to explore, with laws and phenomena that previously seemed beyond our wildest dreams, and to attempt to untangle the knotted confusion of experience and to search for some sense of order beneath. And how fascinating it is to discover that order, and to piece together a coherent picture of the universe on scales far beyond those that we may ever directly experience—a picture woven together by our ability to predict what will happen next, and the consequent ability to control the environment around us. How lucky to have our brief moment in the Sun. Every day that we discover some- thing new and surprising, the story gets even better. 2P_Glealer-StoryEverTold_Atirdd S 12/16116 3:06 PIA EFTA00285928 Part One GENESIS EFTA00285929 2P_Gtealer-StoryEverTold_Atirdd S 12/16116 3:06 PM EFTA00285930 Chapter 1 FROM THE ARMOIRE TO THE CAVE The simple inherit folly, but the prudent are crowned with knowledge. -PROVERBS 14:18 L my beginning there was light. Surely there was light at the beginning of time, but before we can get to the beginning of time, we will need to explore our own beginnings, which also means exploring the beginning of science. And that means returning to the ultimate motive for both science and religion: the longing for some- thing else. Something beyond the universe of our experience. For many people, that longing translates into something that gives meaning and purpose to the universe and extends to a longing for some hidden place that is better than the world in which we live, where sins are forgiven, pain is absent, and death does not exist. Others, however, long for a hidden place of a very different sort, the physical world beyond our senses, the world that helps us understand how things behave the way they do, rather than why. This hidden world underlies what we ex- perience, and the understanding of it gives us the power to change our lives, our environment, and our future. 9 2P_Gtealer-StoryEverTold_Atincld 9 12/16116 3:06 PIA EFTA00285931 10 THE GREATEST STORY EVER TOLD-SO FAR The contrast between these two worlds is reflected in two very dif- ferent works of literature. The first, The Lion, the Witch and the Wardrobe, by C. S. Lewis, is a twentieth-century children's fantasy with decidedly religious overtones. It captures a childhood experience most of us have had—looking under the bed or in the closet or in the attic for hidden treasure or evidence that there is more out there than what we normally experience. In the book, several schoolchildren discover a strange new world, Narnia, by climbing into a large wardrobe in the country house outside London where they have been sequestered for their protection during the Second World War. The chil- dren help save Narnia with the aid of a lion, who lets himself be humiliated and sacrificed, Christlike, at an altar in order to conquer evil in his world. While the religious allusion in story is clear, we can also in- terpret it in another way—as an allegory, not for the existence of God or the devil, but rather for the remarkable and potentially terrifying possi- bilities of the unknown, possibilities that lie just beyond the edge of our senses, just waiting for us to be brave enough to seek them out. Possibili- ties that, once revealed, may enrich our understanding of ourselves or, for some who feel a need, provide a sense of value and purpose. The portal to a hidden world inside the wardrobe is at once safe, with the familiar smell of oft-worn clothes, and mysterious. It implies the need to move beyond classical notions of space and time. For if nothing is revealed to an observer who is in front of or behind the wardrobe, and something is revealed only to someone inside, then the space experienced inside the wardrobe must be far larger than that seen from its outside. Such a concept is characteristic of a universe in which space and time can be dynamical, as in the General Theory of Relativity, where, for ex- ample, from outside the "event horizon" of a black hole—that radius inside of which there is no escape—a black hole might appear to comprise a small volume, but for an observer inside (who has not yet been crushed to smithereens by the gravitational forces present), the volume can look quite different. Indeed, it is possible, though beyond the domain where we 2P_GrealestSloryEverTold_AC.indd 10 12/10/16 3:06 PIA EFTA00285932 From the Armoire to the Cave 11 can perform reliable calculations, that the space inside a black hole might provide a portal to another universe disconnected from our own. But the central point I want to return to is that the possibility of universes beyond our perception seems to be tied, in the literary and philosophical imagination, at least, to the possibility that space itself is not what it seems. The harbinger of this notion, the "ur" story if you will, was written twenty-three centuries before Lewis penned his fantasy. I refer to Plato's Republic, and in particular to my favorite section, the Allegory of the Cave. But in spite of its early provenance, it illuminates more directly and more clearly both the potential necessity and the potential perils of searching for understanding beyond the reach of our immediate senses. In the allegory, Plato likens our experience of reality to that of a group of individuals who live their entire lives imprisoned inside a cave, forced to face a blank wall. Their only view of the real world is that wall, which is illuminated by a fire behind them, and on which they see shad- ows moving. The shadows come from objects located behind them that the light of the fire projects on the wall. I show the drawing below, which came from the high school text in which I first read this allegory, in a 1961 translation of Plato's dialogues. 2P_Glealer-StoryEverTold_Atirdd t1 12.'1&16 3:C8 PM EFTA00285933 12 THE GREATEST STORY EVER TOLD-SO FAR The drawing is amusing because it clearly reflects as much about the time it was drawn as it does the configuration of the cave described in the dialogue. Why, for example, are the prisoners here all women, and scantily clad ones at that? In Plato's day, any sexual allusion might easily have displayed young boys. Plato argues that the prisoners will view the shadows as reality and even give them names. This is not unreasonable, and it is, in one sense, as we shall soon see, a very modern view of what reality is, namely that which we can directly measure. My favorite definition of reality still is that given by the science fiction writer Philip K. Dick, who said, "Reality is that which, when you stop believing in it, doesn't go away." For the prisoners, the shadows are what they see. They are also likely to hear only the echoes of noises made behind them as the sounds bounce off the wall. Plato likened a philosopher to a prisoner who is freed from bondage and forced, almost against his will, to not only look at the fire, but to move past it, and out to the daylight beyond. First, the poor soul will be in distress, with the glare of the fire and the sunshine beyond the cave hurting his eyes. Objects will appear completely unfamiliar; they will not resemble their shadows. Plato argues that the new freeman may still imagine the shadows that he is used to as truer representations than the objects themselves that are casting the shadows. If the individual is reluctantly dragged out into the sunshine, ulti- mately all of these sensations of confusion and pain will be multiplied. But eventually, he will become accustomed to the real world, will see the stars and Moon and sky, and his soul and mind will be liberated of the illusions that had earlier governed his life. If the person returns to the cave, Plato argues, two things would hap- pen. First, because his eyes would no longer be accustomed to the dark- ness, he would be less able to distinguish the shadows and recognize them, and his compatriots would view him as handicapped at best, and 2P_GrealestStrayE-verTold_AC.indd 12 12/18/18 3:08 PIA EFTA00285934 From the Armoire to the Cave 13 dim at worst. Second, he would no longer view the petty and myopic priorities of his former society, or the honors given to those who might best recognize the shadows and predict their future, as worthy of his respect. As Plato poetically put it, quoting from Homer: "Better to be the poor servant of a poor master, and to endure any- thing, rather than think as they do and live after their manner." So much for those whose lives are lived entirely in illusion, which Plato suggests includes most of humanity. Then, the allegory states that the journey upward—into the light—is the ascent of the soul into the intellectual world. Clearly in Plato's mind only a retreat to the purely "intellectual world," a journey reserved for the few—aka philosophers—could replace illusion with reality. Happily, that journey is far more accessible today using the techniques of science, which combine reason and reflection with empirical inquiry. Nevertheless, the same challenge remains for scientists today: to see what is behind the shadows, to see that which, when you drop your preconceptions, doesn't disappear. While Plato doesn't explicitly mention it, not only would his fellow prisoners view the poor soul who had ventured out and returned as handicapped, but they would likely think he was crazy if he talked about the wonders that he had glimpsed: the Sun, the Moon, lakes, trees, and other people and their civilizations. This idea is strikingly modern. As the frontiers of science have moved further and further away from the world of the familiar and the world of common sense as inferred from our direct experience, our picture of the reality underlying our experience is getting increasingly difficult for us to comprehend or accept. Some find it more comforting to retreat to myth and superstition for guidance. But, we have every reason to expect that "common sense," which first evolved to help us cope with predators in the savannas of Africa, might lead us astray when we attempt to think about nature on vastly differ- 2P_Glealer-StoryEverTold_Aairdd 13 12/16116 3:06 PIA EFTA00285935 14 THE GREATEST STORY EVER TOLD-SO FAR ent scales. We didn't evolve to intuitively understand the world of the very small, the very big, or the very fast. We shouldn't expect the rules we have come to rely on for our daily lives to be universal. While that myopia was useful from an evolutionary perspective, as thinking beings we can move beyond it. In this regard, I cannot resist quoting one last admonition in Plato's allegory: "In the world of knowledge the idea of good appears last of all and is seen only with an effort; and, when seen, is also inferred to be the au- thor of all things good and right, parent of light, and ... the immediate source of reason and truth." Plato further argues that this is what those who would act rationally should strive for, in both public and private life—seeking the "good" by focusing on reason and truth. He suggests that we can only do so by exploring the realities that underlie the world of our direct experience, rather than by exploring the illusions of a reality that we might want to exist. Only through rational examination of what is real, and not by faith alone, is rational action—or good—possible. Today, Plato's vision of "pure thought" has been replaced by the sci- entific method, which, based on both reason and experiment, allows us to discover the underlying realities of the world. Rational action in public and private life now requires a basis in both reason and empiri- cal investigation, and it often requires a departure from the solipsistic world of our direct experience. This principle is the source of most of my own public activism in opposition to government policies based on ideology rather than evidence, and it is also probably why I respond so negatively to the concept of the "sacred"—implying as it does some idea or admonition that is off-limits to public questioning, exploration, dis- cussion, and sometimes ridicule. It is hard to state this view more strongly than I did in a New Yorker piece: 'Whenever scientific claims are presented as unquestionable, they undermine science. Similarly, when religious actions or claims 2P_Glealer-StoryEverTold_Atirdd 14 12/16116 3:06 PIA EFTA00285936 From the Armoire to the Cave 15 about sanctity can be made with impunity in our society, we undermine the basis of modern secular democracy. We owe it to ourselves and to our children not to give a free pass to governments—totalitarian, theo- cratic, or democratic—that endorse, encourage, enforce, or otherwise legitimize the suppression of open questioning in order to protect ideas that are considered 'sacred.' Five hundred years of science have liberated humanity from the shackles of enforced ignorance! Philosophical reflections aside, the prime reason I am introducing Plato's cave here is that it can provide a concrete example of the nature of the scientific discoveries at the heart of the story I want to tell. Imagine a shadow that our prisoners might see on the wall, displayed by an evil puppeteer located on a ledge in front of the fire: This shadow displays both length and directionality, two concepts that we, who are not confined to the cave, take for granted. However, as the prisoners watch, this shadow changes: Later it looks like this: And again later like this: And later still, like this: 2P_Glealer-StoryEverTold_Atirdd 15 12/16116 3:06 PIA EFTA00285937 16 THE GREATEST STORY EVER TOLD-SO FAR What would the prisoners infer from all of this? Presumably, that concepts such as length or direction have no absolute meaning. The ob- jects in their world can change both length and directionality arbitrarily. In the reality of their direct experience, neither length nor directionality appears to have significance. What will the natural philosopher, who has escaped to the surface to explore the richer world beyond the shadows, discover? He will see that the shadow is first of all just a shadow: a two-dimensional image on the wall cast from a real, three-dimensional object located behind the pris- oners. He will see that the object has a fixed length that never changes, and that it's accompanied by an arrow that is always on the same side of the object. From a vantage point slightly above the object, he sees that the series of images results from the projection of a rotating weather vane onto the wall: When he returns to join his former colleagues, the philosopher- scientist can explain that an absolute quantity called length doesn't change over time, and that directionality can be assigned unambiguously to cer- tain objects as well. He will tell his friends that the real world is three- dimensional, not two-dimensional, and that once they understand, all of their confusion about the seemingly arbitrary changes will disappear. Would they believe him? It would be a tough sell because they won't have an intuitive idea of what a rotation is (after all, with an intuition based purely on two-dimensional experience, it would likely be difficult to "picture" mentally any rotations in a third dimension). Blank stares? Probably. The loony bin? Maybe. However, he might win over the com- munity by stressing attractive characteristics associated with his claim: behavior that on the surface appears to be complex and arbitrary can be 2P_Glealer-StoryEverTold_Atindd 18 12/16116 3:06 PIA EFTA00285938 From the Armoire to the Cave 17 shown to result from a much simpler underlying picture of nature, and seemingly disparate phenomena are actually connected and can be part of a unified whole. Better still, he could make predictions that his friends could test. First, he could argue that, if the apparent change in length of the shadows measured by the group is really due to a rotation in a third dimension, whenever the length of the object briefly vanishes, it will immediately reemerge with the arrow pointing in the opposite direction. Second, he could argue that as the length oscillates, the maximum length of the shadow when the arrow is pointing in one direction will always be ex- actly the same as the maximum length of the shadow when it is pointing in the other direction. Plato's cave thus becomes an allegory for far more than he may have intended. Plato's freed man discovers the hallmarks of the remarkable true story of our own struggle to understand nature on its most fun- damental scales of space, time, and matter. We too have had to escape the shackles of our prior experience to uncover profound and beauti- ful simplifications and predictions that can be as terrifying as they are wonderful. But just as the light beyond Plato's cave is painful to the eyes at first, with time it becomes mesmerizing. And once witnessed, there is no going back. 2P_Glealer-Storgverrold_Atirdd 17 12/16116 3:06 PIA EFTA00285939 2P_GreatestSlowEverrold_AC.indd 18 1211&18 3:06 PM EFTA00285940 Chapter 2 SEEING IN THE DARK Let there be light: and there was light -GENESIS 1:3 L the beginning there was light. It is no coincidence that the ancients imagined in Genesis that light was created on the first day. Without light, there would be little aware- ness of the vast universe surrounding us. When we nod and say, 1 see," to a friend who is trying to explain something, we convey far more than just an observation, but rather a fundamental understanding. Plato's allegory was appropriately centered on light—light from a fire to cast the shadows on the cave wall and light from the outside to temporarily blind the freed prisoner and then illuminate the real world for him. Like the prisoners in the cave, we too are prisoners of light— almost everything we learn about the world we learn from what we see. While the most significant words in the Western religious canon may be Let there be light, in the modern world this phrase now has a completely different significance from what it once did. Human beings may be prisoners of light, but so is the universe. What once appeared as a whim of a Judeo-Christian God, or other gods before that one, we now understand to be required by the very laws that allow both heaven, and 19 2P_Glealer-StoryEverTold_Atirdd 19 1211&I6 3:06 PIA EFTA00285941 20 THE GREATEST STORY EVER TOLD-SO FAR more important, Earth, to exist. You cannot have one without the other. Earth, or matter, follows light. This change in perception underlies almost every development in the edifice we call modern science. I am writing these words as I stare out from a ship at one of the Galapagos Islands, which Charles Darwin made famous, and which made him famous in return, as he changed our perception of life and its diversity with a single brilliant realiza- tion: that all living species developed through the natural selection of small inherited variations that are passed along to future generations by survivors. As surely as the understanding of evolution changed every- thing about our understanding of biology, our changing understanding of light changed everything about our physical understanding of our place in the universe. As a useful fringe benefit, this change resulted in virtually all of the technology on which the modern world is based. The extent to which our observations of the world imprison our minds, and frame our description of the fabric of the universe, remained unappreciated for more than twenty centuries following Plato. Once se- rious minds began to investigate in detail the hidden nature of the uni- verse, it took over four centuries for them to fully resolve the question What is light? Perhaps the most serious modern mind, although certainly not the first, to ask this question was also one of the most famous—and oddest—scientists in history: Isaac Newton. It is not inappropriate to classify Newton as a modern mind—after all, his seventeenth-century Principia: Mathematical Principles of Natural Philosophy uncovered the classical laws of motion and laid the basis for his theory of gravity, both of which form the foundation of much of modern physics. Never- theless, as John Maynard Keynes pointed out: Newton was not the first of the age of reason, he was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind that looked out on the visible and intellectual world 2P_Glealer-StoryEverrold_Atincld 20 12/16116 3:06 PIA EFTA00285942 Seeing in the Dark 21 with the same eyes as those who began to build our intellectual inheritance rather less than to,000 years ago. The truth of this statement reflects the revolutionary importance of Newton's work. After the Principia, no rational person could view the world the same way the ancients had viewed it. But it also reflects the character of Newton himself. He devoted far more time, and far more ink, to writing about the occult, alchemy, and searching for hidden meanings and codes in the Bible—focusing in particular on the Book of Revelation and mysteries associated with the ancient Temple of Solo- mon—than he did to writing about physics. Newton was also one in a long line of people, which extends before and after him, who felt that he had been specifically chosen by God to help reveal the true meaning of the Scriptures. To what extent his stud- ies of the universe derived from his fascination with the Bible is not clear, but it does seem reasonable to conclude that his primary interest was in theology, and that natural philosophy came in well below that, and probably below alchemy as well. Many individuals point to Newton's fascination with God as evi- dence of the compatibility between science and religion, and to assert that modern science owes its existence to Christianity. This confuses history with causality. It is undeniable that many of the early giants of modern Western natural philosophy, from Newton onward, were deeply religious, although Darwin lost much, if not all, of his reli- gious belief later in life. But remember that during much of this pe- riod there were primarily two sources of education and wealth: the Church and the Crown. The Church was the National Science Foun- dation of the fifteenth, sixteenth, and seventeenth centuries. All in- stitutions of higher learning were tied to various denominations, and it was unthinkable for any educated person to not be affiliated with the Church. And as Giordano Bruno and later Galileo discovered, it was unpleasant at best to counter its doctrine. It would have been 29_Glealer-StoryEverrold_Aairdd 21 12/16116 3:06 PIA EFTA00285943 22 THE GREATEST STORY EVER TOLD-SO FAR remarkable for any of these leading early scientific thinkers to have been anything but religious. The religiosity of the early scientific pioneers is also cited today by sophists who claim that science and religious doctrine are compatible, but who confuse science and scientists. In spite of frequent appearances to the contrary, scientists are people. And like all people they are capa- ble of holding many potentially mutually contradictory notions in their head at the same time. No correlation between divergent views held by any individual is representative of anything but human foibles. To claim that some scientists are or were religious is like saying some scientists are Republicans or some are flat-earthers or some are creationists. It doesn't imply causality or consistency. My friend Rich- ard Dawkins has told me of a professor of astrophysics who, during the day, writes papers that are published in astronomical journals assuming that the universe is more than 13 billion years old, but then goes home and privately espouses the literal biblical claim that the universe is six thousand years old. What determines intellectual consistency or lack thereof in the sci- ences is a combination of rational arguments with subsequent evidence and continued testing. It is perfectly reasonable to claim that religion, in the Western world, may be the mother of science. But as any parent knows, children rarely grow up to be models of their parents. Newton may, following tradition, have been motivated to look at light because it was a gift from God. But we remember his work not because of his motivation, but because of what he discovered. Newton was convinced that light was made of particles, which he re- ferred to as corpuscles, while Descartes, and later Newton's nemesis Robert Hooke, and still later the Dutch scientist Christiaan Huygens, all claimed that light was a wave. One of the key observations that appeared to support the wave theory was that white light, such as light from the Sun, could split into all the colors of the rainbow when passed through a prism. As was often the case during his life, Newton believed that he was 2P_Glealer-StoryEverTaid_Atirdd 22 12/16116 3:06 PIA EFTA00285944 Seeing in the Dark 23 correct and several of his most famous contemporaries (and competi- tors) were wrong. To demonstrate this, he devised a clever experiment using prisms that he first performed while at home in Woolsthorpe, to escape the bubonic plague ravaging Cambridge. As he reported at the Royal Society in 1672, on the forty-fourth try, he observed precisely what he hoped he would see. Advocates of the wave theory had argued that light waves were made of white light and that the light split into colors when it passed through a prism because of "corruption" of the rays as they traversed the glass. In this case, the more glass, the more splitting. Newton reasoned that this was not the case, but that light is made of colored particles that combine together to appear white. (With a nod to his occult fascination, Newton classified the colored particles of the spectrum-a term he coined—into seven different types: red, orange, yellow, green, blue, indigo, and violet. From the time of the Greeks, the number seven had been considered to possess mystical qualities.) To demonstrate that the wave/corruption picture was incorrect, Newton passed a beam of white light through two prisms held in opposite orien- tations. The first prism split the light into its spectrum, and the second recomposed it back into a single white light beam. This result would have been impossible if the glass had corrupted the light. A second prism would have simply made the situation worse and would not have caused the light to revert back to its original state. This result does not in fact disprove the wave theory of light (it actu- ally supports it, because light slows down as it bends upon entering the prism, just as waves would do). But since the advocates of that theory had argued (incorrectly) that the spectral splitting was due to corrup- tion, Newton's demonstration that this was not the case struck a signifi- cant blow in favor of his particle model. Newton went on to discover many other facets of light that we use today in our understanding of the wave nature of light. He showed that every color of light has a unique bend angle when passing through a 2P_Glealer-StoryEverrold_Aairdd 23 12/16116 3:06 PIA EFTA00285945 24 THE GREATEST STORY EVER TOLD-SO FAR glass prism. He also showed that all objects appear to be the same color as the color of the light beam illuminating them. And he showed that colored light will not change its color no matter how many times it is reflected by or passes through a prism. All of these results, including his original result, can be explained simply if white light is indeed composed of a collection of different col- ors—that much he got right. But they can't be explained if light is made of different-colored particles. Rather, white light is composed of waves of many different wavelengths. Newton's opponents did not give up easily, even in the face of New- ton's rising popularity and the death of his chief opponent, Hooke. They did not give up even after Newton's election as president of the Royal Society in 1703, the year he then actually published his research on light in his epic Opticks. Indeed, the debate on the nature of light continued to rage on for over a century. Part of the problem with a wave picture of light was the question ' hat is it that light is a wave of exactly?" And if it is a wave, then since all known waves require some medium, what medium does it travel in? These ques- tions were sufficiently perplexing that practitioners of the wave theory had to resurrect a new invisible substance permeating all space, the ether. The resolution of this conundrum came, as such resolutions often do, from a totally unexpected corner of the physical world, one full of sparks, and spinning wheels. When I was a young professor at Yale—in the ancient but huge office I was lucky enough to commandeer when an equally ancient colleague retired—there was left hanging for me a copy of a photograph of Mi- chael Faraday taken in 186i. I have treasured it ever since. I don't believe in hero worship, but if I did, Faraday would be up there with the best. Perhaps more than any other scientist of the nine- teenth century, he is responsible for the technology that powers our cur- rent civilization. Yet he had little formal education and at age fourteen became a bookbinder's apprentice. Later in his career, after achieving 2P_Glealer-StoryEverTold_Atirdd 24 12/18118 3:08 PIA EFTA00285946 Seeing in the Dark 25 world recognition for his scientific contributions, he insisted on keep- ing to his humble roots, turning down a knighthood and twice turning down the presidency of the Royal Society. Later on he refused to advise the British government on the production of chemical weapons for use in the Crimean War, citing ethical reasons. And for more than thirty- three years he gave a series of Christmas lectures at the Royal Institu- tion to excite young people about science. What's not to like? Much as one might admire the man, it is the scientist who matters here for our story. Faraday's first scientific lesson is one I tell my students: always suck up to your professors. At the age of twenty, after completing seven years of apprenticeship as a bookbinder, Faraday attended the lec- tures of the famous chemist Humphry Davy, then the head of the Royal Institution. Afterward Faraday presented Davy with a three-hundred- page, beautifully bound book containing the notes Faraday had taken during the lectures. Within a year, Faraday was appointed Davy's sec- retary and shortly thereafter got an appointment as chemical assistant in the Royal Institution. Later on, Faraday learned the same lesson but with the opposite result. Following his excitement over some early, quite significant experiments that he performed, Faraday accidentally forgot to acknowledge work with Davy in his published results. This acciden- tal snub probably resulted in his being reassigned to other activities by Davy and delaying his world-changing research by several years. When reassigned, Faraday had been working on the "hot" area of sci- entific research, the newly discovered connections between electricity and magnetism, driven by results of the Danish physicist Hans Christian Oersted. These two forces seem quite different, yet have odd similarities. Electric charges can attract or repel. So can magnets. Yet magnets always seem to have two poles, north and south, which cannot be isolated, while electric charges can individually be positive or negative. For some time, scientists and natural philosophers had wondered if the two forces might have some hidden connection, and the first empirical clue came to Oersted by accident In 182o, while delivering a lecture, Oersted 2P_GrealesiSleryEverTold_AC.indd 25 12/16116 3:06 PIA EFTA00285947 26 THE GREATEST STORY EVER TOLD-SO FAR saw that a compass needle was deflected when an electric current from a battery was switched on. A few months later he followed up on this ob- servation and discovered that a current of moving electric charges, which we now commonly call an electric current, produced a magnetic attraction that caused compass needles to point in a circle around the wire. He had blazed a new trail. Word spread quickly among scientists, through the Continent and across the English Channel. Moving electric charges produced a magnetic force. Could there be other connections? Could magnets in turn influence electric charges? Scientists searched for such a possibility, without success. Davy and an- other colleague tried to build an electric motor based on the connection discovered by Oersted, but failed. Faraday ultimately got a wire with a cur- rent in it to move around a magnet, which did form a crude sort of motor. It was this exciting development that he reported without citing Davy's name. Partly this was mere gamesmanship. No new fundamental phenom- enon was being uncovered. Perhaps this was the rationale for one of my favorite (likely apocryphal) stories about Faraday. It is said that William Gladstone, later to be British prime minister, heard of Faraday's labora- tory, full of weird devices, and asked in 289a what the practical value of all this study into electricity was. Faraday was purported to have replied, "Why, sir, there is every probability that you will soon be able to tax it." Apocryphal or not, both great irony and truth are in that witty comeback. Curiosity-driven research may seem self-indulgent and far from the immediate public good. However, essentially all of our cur- rent quality of life, for people living in the first world, has arisen from the fruits of such research, including all the electric power that drives almost every device we use. Two years after Davy's death in 2829, and six years after Faraday had become director of the laboratory of the Royal Institution, he made the discovery that cemented his reputation as perhaps the greatest experi- mental physicist of the nineteenth century—magnetic induction. Since 1824, he had tried to see if magnetism could alter the current flowing 2P_Glealer-StorgverTold_Atindd 28 12/16116 3:06 PIA EFTA00285948 Seeing in the Dark 27 in a nearby wire or otherwise produce some kind of electric force on charged particles. He primarily wanted to see if magnetism could in- duce electricity, just as Oersted had shown that electricity, and electric currents in particular, could produce magnetism. On October 28, 1831, Faraday recorded in his laboratory notebook a remarkable observation. While closing the switch to turn on a current in a wire wound around an iron ring to magnetize the iron, he noticed a current flow momentarily in another wire wrapped around the same iron ring. Clearly the mere presence of a nearby magnet could not cause an electric current to flow in a wire—but turning the magnet on or off could. Subsequently he showed that the same effect occurred if he moved a magnet near a wire. As the magnet came closer or moved away, a current would flow in the wire. Just as a moving charge created a mag- net, somehow a moving magnet—or a magnet of changing strength— created an electric force in the nearby wire and produced a current. If the profound theoretical implication of this simple and surprising result is not immediately apparent, you can be forgiven, because the implication is subtle, and it took the greatest theoretical mind of the nineteenth century to unravel it. To properly frame it, we need a concept that Faraday himself intro- duced. Faraday had little formal schooling and was largely self-taught and thus was never comfortable with mathematics. In another probably apocryphal story, Faraday boasted of using a mathematical equation only one time in all of his publications. Certainly, he never described the important discovery of magnetic induction in mathematical terms. Because of his lack of comfort with formal mathematics, Faraday was forced to think in pictures to gain intuition about the physics be- hind his observations. As a result he invented an idea that forms the cornerstone of all modern physics theory and resolved a conundrum that had puzzled Newton until the end of his days. Faraday asked himself, How does one electric charge "know" how to respond to the presence of another, distant electric charge? The same 2P_Glealer-StoryEverTold_Atinid 27 12/16116 3:06 PIA EFTA00285949 28 THE GREATEST STORY EVER TOLD-SO FAR question had been posed by Newton in terms of gravity, where he ear- lier wondered how the Earth "knew" to respond as it did to the gravita- tional pull of the Sun. How was the gravitational force conveyed from one body to another? To this, he gave his famous response "Hypotheses non jingo," "I frame no hypotheses," suggesting that he had worked out the force law of gravity and showed that his predictions matched obser- vations, and that was good enough. Many of us physicists have subse- quently used this defense when asked to explain various strange physics results—especially in quantum mechanics, where the mathematics works, but the physical picture often seems crazy. Faraday imagined that each electric charge would be surrounded by an electric "field," which he could picture in his head. He saw the field as a bunch of lines emanating radially outward from the charge. The field lines would have arrows on them, pointing outward if the charge was positive, and inward if it was negative: \17( \ 7Th He further imagined that the number of field lines increased as the magnitude of the charge increased: The utility of this mental picture was that Faraday could now in- tuitively understand both what would happen when another test charge 2P_Glealer-StoryEverTold_Atirdd 28 12/16116 3:06 PM EFTA00285950 Seeing in the Dark 29 was put near the first charge and why. (Whenever I use the colloquial why, I mean "how.") The test charge would feel the "field" of the first charge wherever the second charge was located, with the strength of the force being proportional to the number of field lines in the region, and the direction of the force being along the direction of the field lines. Thus, for example, the test charge in question would be pushed outward in the direction shown: \-17( 71,\ One can do more than this with Faraday's pictures. Imagine placing two charges near each other. Since field lines begin at a positive charge and end on a negative charge and can never cross, it is almost intuitive that the field lines in between two positive charges should appear to repel each other and be pushed apart, whereas between a positive and a negative charge they should connect together: Once again, if a test charge is placed anywhere near these two charges, it would feel a force in the direction of the field lines, with a strength proportional to the number of field lines in that region. Faraday thus pictured the nature of electric forces between particles 2P_Glealer-StoryEverrold_Aairdd 29 12/1006 3:06 PM EFTA00285951 90 THE GREATEST STORY EVER TOLD-SO FAR in a way that would otherwise require solving the algebraic equations that describe electrical forces. What is most amazing about these pic- tures is that they capture the mathematics exactly, not merely approxi- mately. A similar pictorial view could be applied to magnets, and magnetic fields, reproducing the magnetic force law between magnets, experi- mentally verified by Coulomb, or current-carrying wires, derived by Andth-Marie Ampere. (Up until Faraday, all the heavy lifting in discov- ering the laws of electricity and magnetism was done by the French.) Using these mental crutches, we can then reexpress Faraday's dis- covery of magnetic induction as follows: an increase or decrease in the number of magnetic field lines going through a loop of wire will cause a current to flow in the wire. Faraday recognized quickly that his discovery would allow the con- version of mechanical power into electrical power. If a loop of wire was attached to a blade that was made to rotate by, say, a flow of water, such as a waterwheel, and the whole thing was surrounded by a magnet, then as the blade turned the number of magnetic field lines going through the wire would continuously change, and a current would continuously be generated in the wire. Voila, Niagara Falls, hydroelectricity, and the modern world! This alone might be good enough to cement Faraday's reputation as the greatest experimental physicist of the nineteenth century. But tech- nology wasn't what motivated Faraday, which is why he stands so tall in my estimation; it was his deep sense of wonder and his eagerness to share his discoveries as broadly as possible that I admire most. I am convinced that he would agree that the chief benefit of science lies in its impact in changing our fundamental understanding of our place in the cosmos. And ultimately, this is what he did. I cannot help but be reminded of another more recent great experi- mental physicist, Robert R. Wilson—who, at age twenty-nine, was head of the Research Division at Los Alamos, which developed the atomic 2P_Glealer-StoryEverTold_Atirdd 30 12/16116 3:06 PIA EFTA00285952 Seeing in the Dark 31 bomb during the Manhattan Project. Many years later he was the first director of the Fermi National Accelerator Laboratory in Batavia, Il- linois. When Fermilab was being built, in 1969 Wilson was summoned before Congress to defend the expenditure of significant funds on this exotic new accelerator, which was to study the fundamental interac- tions of elementary particles. Asked if it contributed to national security (which would have easily justified the expenditure in the eyes of the congressional committee members), he bravely said no. Rather: It only has to do with the respect with which we regard one another, the dignity of men, our love of culture. . . It has to do with, are we good painters, good sculptors, great poets? I mean all the things that we really venerate and honor in our country and are patriotic about. In that sense, this new knowledge has all to do with honor and country, but it has nothing to do directly with defending our country except to help make it worth defending. Faraday's discoveries allowed us to power and create our civilization, to light up our cities and our streets, and to run our electric devices. It is hard to imagine any discovery that is more deeply ingrained in the workings of modern society. But more deeply, what makes his contribu- tion to our story so remarkable is that he discovered a missing piece of the puzzle that changed the way we think about virtually everything in the physical world today, starting with light itself. If Newton was the last of the magicians, Faraday was the last of the modern scientists to live in the dark, regarding light. After his work, the key to uncovering the true nature of our main window on the world lay in the open waiting for the right person to find it. • • • Within a decade, a young Scottish theoretical physicist, down on his luck, took the next step. 29_Glealer-StoryEverrold_Atindd 31 12/16116 3:06 PIA EFTA00285953 2P_GreatestSlowEverrold_AC.indd 32 12/16/I6 3:06 PM EFTA00285954 Chapter THROUGH A GLASS, LIGHTLY Nothing is too wonderful to be true, if it be consistent with the laws of nature; and in such things as these, experiment is the best test of such consistency. -FARADAY. LABORATORY JOURNAL ENTRY *10,040 (MARCH IS. 1849) The greatest theoretical physicist of the nineteenth century, James Clerk Maxwell, whom Einstein would later compare to Newton for his impact on physics, was coincidentally born in the same year that Mi- chael Faraday made his great experimental discovery of induction. Like Newton, Maxwell also began his scientific career fascinated by color and light. Newton had explored the spectrum of visible colors into which white light splits when traversing a prism, but Maxwell, while still a student, investigated the reverse question: What is the minimal combina- tion of primary colors that would reproduce for human perception all the visible colors contained in white light? Using a collection of colored spin- ning tops, he demonstrated that essentially all colors we perceive can result from mixtures of red, green, and blue—a fact familiar to anyone who has plugged RGB cables into a color television. Maxwell used this realization to produce the world's first, rudimentary color photograph. Later he became 33 2P_Gtealer-StoryEverrold_Atirdd 33 12/113116 3:0B PIA EFTA00285955 34 THE GREATEST STORY EVER TOLD-SO FAR fascinated with polarized light, which results from light waves whose elec- tric and magnetic fields oscillate only in certain directions. He sandwiched blocks of gelatin between polarizing prisms and shined light through them. If the two prisms allowed only light to pass that was polarized in different perpendicular directions, then if one was placed behind the other, no light would make it through. However, if stresses were present in the gelatin, then the light could have its axis of polarization rotated as it passed through the material, so that some light might then make it through the second prism. By searching for such fringes of light passing through the second prism, Maxwell could explore for stresses in the material. This has become a use- ful tool today for exploring possible material stresses in complex structures. Even these ingenious experiments do not adequately represent the power of Maxwell's voracious intellect or his mathematical ability, which were both manifest at a remarkably early age. Tragically, Maxwell died at the age of forty-eight and had precious little time to accomplish all that he did. His inquisitive nature was reflected in a passage his mother added to a letter from his father to his sister-in-law when Maxwell was only three: He is a very happy man, and has improved much since the weather got moderate; he has great work with doors, locks, keys, etc., and "show me how it loos" is ever out of his mouth. He also investigates the hidden course of streams and bell-wires, the way the water gets from the pond through the wall. After his mother's untimely death (of stomach cancer, to which Maxwell would later succumb at the same age), his education was in- terrupted, but by the age of thirteen he had hit his stride at the pres- tigious Edinburgh Academy, where he won the prize for mathematics, and also for English and poetry. He then published his first scientific paper—concerning the properties of mathematical curves—which was presented at the Royal Society of Edinburgh when he was only fourteen. After this precocious start, Maxwell thrived at university. He gradu- 2P_Glealer-StoryEverrold_Atirdd 34 12/16116 3:06 PIA EFTA00285956 Through a Glass. Lightly 35 ated from Cambridge, becoming a fellow of the college within a year after graduation, which was far sooner than average for most graduates. He left shortly thereafter and returned to his native Scotland to take up a chair in natural philosophy in Aberdeen. At only twenty-five, he was head of a department and teaching fifteen hours a week plus an extra free lecture for a nearby college for working men (something that would be unheard of for a chaired professor today, and something that I find difficult to imagine doing myself and still hav- ing any energy left for research). Yet Maxwell nevertheless found time to solve a problem that was two centuries old: How could Saturn's rings re- main stable? He concluded that the rings must be made of small particles, which garnered him a major prize that had been set up to encourage an answer to this question. His theory was confirmed more than a hundred years later when Voyager provided the first close-up view of the planet. You would think that, after his remarkable output, he would have been able to remain secure in his professorship. However, in 1860, the same year that he was awarded the Royal Society's prestigious Rumford Medal for his work on color, the college where he lectured merged with another college and had no room for two professors of natural philoso- phy. In what must surely go down in history as one of the dumbest aca- demic decisions ever made (and that is a tough list to top), Maxwell was unceremoniously laid off. He tried to get a chair in Edinburgh, but again the position was given to another candidate. Finally, he found a position down south, at King's College, London. One might expect Maxwell to have been depressed or disconsolate because of these developments, but if he was, his work reflected no signs of it. The next five years at King's were the most productive period in his life. During this time he changed the world—four times. The first three contributions were the development of the first light-fast color photograph; the development of the theory of how particles in a gas behave (which helped establish the foundations of the field now known as statistical mechanics—essential for understanding the properties of matter 2P_Glealer-StoryEverTold_Atindd 35 12/160I6 3:06 PIA EFTA00285957 36 THE GREATEST STORY EVER TOLD-SO FAR and radiation); and finally his development of "dimensional analysis: which is perhaps the tool most frequently used by modern physicists to establish deep relationships between physical quantities. I just used it last year, for example, with my colleague Frank Wilczek, to demonstrate a fundamental property of gravity relevant to understanding the creation of our universe. Each contribution on its own would have firmly established Maxwell among the greatest physicists of his day. However, his fourth contribution ultimately changed everything, including our notions of space and time. During his period at King's, Maxwell frequented the Royal Institu- tion, where he came in contact with Michael Faraday, who was forty years older but still inspirational. Perhaps these meetings encouraged Maxwell to return his focus to the exciting developments in electricity and mag- netism, a subject he had begun to investigate five years earlier. Maxwell used his considerable mathematical talents to describe and understand the phenomena explored by Faraday. He began by putting Faraday's hy- pothesized lines of force on a firmer mathematical footing, which allowed him to explore in more depth Faraday's discovery of induction. Over the dozen years between 1861 and 1873, Maxwell put the final touches on his greatest work, a complete theory of electricity and magnetism. To do this, Maxwell used Faraday's discovery as the key to revealing that the relationship between electricity and magnetism is symmetrical. Oersted's and Faraday's experiments had shown, simply, that a current of moving charges produces a magnetic field; and that a changing mag- netic field (produced by moving a magnet or simply turning on a cur- rent to produce a magnet) produces an electric field. Maxwell first expressed these results mathematically in 2861, but soon realized that his equations were incomplete. Magnetism appeared to be different from electricity. Moving charges create a magnetic field, but a magnetic field can create an electric field even without moving— just by changing. As Faraday discovered, turning on a current, which produces a changing magnetic field as the current ramps up, produces an electric force that causes a current to flow in another nearby wire. 2P_Glealer-StoryEverTold_Atirdd 38 122/18/16 3:06 PIA EFTA00285958 Through a Glass. Lightly 37 Maxwell recognized that to make a complete and consistent set of equa- tions for electricity and magnetism he had to add an extra term to the equa- tions, representing what he called a Misplacement current." He reasoned that moving charges, namely a current, produce a magnetic field, and mov- ing charges represent one way to produce a changing electric field (since the field from each charge changes in space as the charge moves along). So, maybe, a changing electric field—one that gets stronger or weaker—in a region with no charges in motion, could produce a magnetic field. Maxwell envisioned that if he hooked up two parallel plates to op- posite poles of a battery, each plate would get charged with an opposite charge as current flowed from the battery. This would produce a growing electric field between the plates and would also produce a magnetic field around the wires connected to the plates. For his equations to be com- pletely consistent, Maxwell realized, the increasing electric field between the plates should also produce a magnetic field in that empty space be- tween the plates. And that field would be the same as any magnetic field produced by a real current flowing through that space between the plates. So Maxwell altered his equations by adding a new term (displace- ment current) to produce mathematical consistency. This term effec- tively behaved like an imaginary current, flowing between the plates producing a changing electric field identical in magnitude to the actual changing electric field in the empty space between the plates. It also was the same as the magnetic field that a real current would produce if it flowed between the plates. Such a magnetic field does in fact arise when you perform the experiment with parallel plates, as undergradu- ates demonstrate every day in physics laboratories around the world. Mathematical consistency and sound physical intuition generally pay off in physics. This subtle change in the equations may not seem like much, but its physical impact is profound. Once you remove real elec- tric charges from the picture, it means that you can describe everything about electricity and magnetism entirely in terms of the hypothetical "fields" that Faraday had relied upon purely as a mental crutch. The con- 2P_GrealestSleryfverTold_AC.indd 12/16116 3:06 PIA EFTA00285959 38 THE GREATEST STORY EVER TOLD-SO FAR nections between electricity and magnetism can thus be simply stated: A changing electric field produces a magnetic field. A changing mag- netic field produces an electric field. Suddenly the fields appear in the equations as real physical objects in their own right and not merely as a way to quantify the force between charges. Electricity and magnetism became inseparable. It is impossible to talk about electrical forces alone because, as I will shortly show, one person's electric force is another person's magnetic force, depending on the circumstances of the observer, and whether the field is changing in his frame of reference. We now refer to electromagnetism to describe these phenomena, for a good reason. After Maxwell, electricity and magnetism were no longer viewed as separate forces of nature. They were different manifestations of one and the same force. Maxwell published his complete set of equations in 1865 and later simplified them in his textbook of 1873. These would become famous as the four Maxwell's Equations, which (admittedly rewritten in modern mathematical language) adorn the T-shirts of physics undergraduates around the world today. We can thus label 1873 as establishing the sec- ond great unification in physics, the first being Newton's recognition that the same force governed the motion of celestial bodies as governed falling apples on Earth. Begun with Oersted's and Faraday's experimen- tal discoveries, this towering achievement of the human intellect was completed by Maxwell, a mild-mannered young theoretical physicist from Scotland, exiled to England by the vicissitudes of academia. Gaining a new perspective on the cosmos is always—or should be— immensely satisfying. But science adds an additional and powerful ben- efit. New understanding also breeds tangible and testable consequences, and often immediately. So it was with Maxwell's unification, which now made Faraday's hy- pothetical fields literally as real as the nose on your face. Literally, be- cause it turns out you couldn't see the nose on your face without them. 2P_Glealer-StoryEverrold_Atirdd 38 12/16116 3:06 PIA EFTA00285960 Through a Glass. Lightly 39 Maxwell's genius didn't end just with codifying the principles of elec- tromagnetism in elegant mathematical form. He used the mathematics to unravel the hidden nature of that most fundamental of all physical quantities—which had eluded the great natural philosophers from Plato to Newton. The most observable thing in nature: light. Consider the following thought experiment. Take an electrically charged object and jiggle it up and down. What happens as you do this? Well, an electric field surrounds the charge, and when you move the charge, the position of the field lines changes. But, according to Max- well, this changing electric field will produce a magnetic field, which will point in and out of the paper as shown below: 0 (-; 2P_Gtealer-StoryEverrold_Atirdd 39 12111'16 3:06 PIA EFTA00285961 40 THE GREATEST STORY EVER TOLD-SO FAR Here the field line pointing into the paper has a cross (the back of an arrow), and that pointing out of the paper has a dot (the tip of an arrow). This field will flip direction as the charge changes the direction of its motion from upward to downward. But we should not stop there. If I keep jiggling the charged object, the electric field will keep changing, and so will the induced magnetic field. But a changing magnetic field will produce an electric field. Thus there are new induced electric field lines, which point vertically, chang- ing from up to down as the magnetic field reverses its sign. I display the electric field line to the right only for lack of space, but the mirror image will be induced on the left-hand side. 0 <— • —> X 0 <— • —> X But that changing electric field will in turn produce a changing mag- netic field, which would exist farther out to the right and left of the diagram, and so on. Jiggling a charge produces a succession of disturbances in both elec- tric and magnetic fields that propagate outward, with the change in each field acting as a source for the other, due to the rules of electro- magnetism as Maxwell defined them. We can extend the picture shown above to a 3-D image that captures the full nature of the changing as shown below: 2P_Glealer-StoryEverTold_Atirdd 40 12/10/16 306 PIA EFTA00285962 Through a Glass. Ughliy 41 E We see a wave of electric and magnetic disturbances, namely an electromagnetic wave moving outward, with electric and magnetic fields oscillating in space, and time, and with the two fields oscillating in directions that are perpendicular to each other and also the direction of the wave. Even before Maxwell had written down the final form of his equa- tions, he showed that oscillating charges would produce an electromag- netic wave. But he did something far more significant. He calculated the speed of that wave, in a beautiful and simple calculation that is probably my favorite derivation to show undergraduates. Here it is: We can quantify the strength of an electric force by measuring its magnitude between two charges whose magnitude we already know. The force is proportional to the product of the charges. Let's call the constant of proportionality A. Similarly we can quantify the strength of the magnetic force be- tween two electromagnets, each with a current of known magnitude. This force is proportional to the product of the currents. Let's call the constant of proportionality in this case B. Maxwell showed that the speed of an electromagnetic disturbance that emanates from an oscillating charge can be rendered precisely in terms of the measured strength of electricity and the measured strength 2P_Glealer-StoryEverTold_Atincld 41 12/16116 3:06 PM EFTA00285963 42 THE GREATEST STORY EVER TOLD-SO FAR of magnetism, which are determined by measuring the constants A and B in the laboratory. When he used the data then available for the mea- sured strength of electricity and the measured strength of magnetism and plugged in the numbers, he derived: Speed of electromagnetic waves Fac 311,000,000 meters per second A famous story claims that when Albert Einstein finished his Gen- eral Theory of Relativity and compared its predictions for the orbit of Mercury to the measured numbers, he had heart palpitations. One can only imagine, then, the excitement that Maxwell must have had when he performed his calculation. For this number, which may seem arbi- trary, was well known to him as the speed of light. In 1849, the French physicist Fizeau had measured the speed of light, an extremely difficult measurement back then, and had obtained: Speed of light 313,000,000 meters per second Given the accuracy available at the time, these two numbers are identical. (We now know this number far more precisely as 299,792,458 meters per second, which is a key part of the modern definition of the meter.) In his typical understated tone, Maxwell noted in 1862, when he first performed the calculation, We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena." In other words, light is an electromagnetic wave. Two years later, when he finally wrote his classic paper on electro- magnetism, he added somewhat more confidently, "Light is an elec- tromagnetic disturbance propagated through the field according to electromagnetic laws? With these words, Maxwell appeared to have finally put to rest the 2P_Glealer-StorgverTold_Atincld 42 1211&I6 3:06 PIA EFTA00285964 Through a Glass. Lightly 43 two-thousand-year-old mystery regarding the nature and origin of light. His result came, as great insights often do, as an unintended by-product of other fundamental investigations. In this case, it was a by-product of one of the most important theoretical advances in history, the unifica- tion of electricity and magnetism into a single beautiful mathematical theory. Before Maxwell, the chief source of wisdom came from a faith in divin- ity via Genesis. Even Newton relied upon this source for understanding the origin of light. After 1862, however, everything changed. James Clerk Maxwell was deeply religious, and like Newton before him, his faith sometimes led him to make strange assertions about na- ture. Nevertheless, like the mythical character Prometheus before him, who stole fire from the gods and gave it to humans to use as a tool to forever change their civilization, so too Maxwell stole fire from the Judeo-Christian God's first words and forever changed their meaning. Since 1873, generations of physics students have proudly proclaimed: "Maxwell wrote down his four equations and said, Let there be lights" 2P_Glealer-StoryEverTold_Atindd 43 12/16116 3:06 PIA EFTA00285965 2P_Gtealer-StoryEverTold_Atirdd 44 12/16116 3:06 PM EFTA00285966 Chapter 4 THERE, AND BACK AGAIN He set the earth on its foundations; it can never be moved. -PSALMS 104:5 Wen Galileo Galilei was being tried in 1633 for heresy for "holding as true the false doctrine taught by some that the Sun is the center of the world," he allegedly muttered under his breath in front of his Church inquisitors, And yet it moves:' With these words, his revo- lutionary nature once again sprang forth, in spite of his having been forced to publicly adhere to the archaic position that the Earth was fixed. While the Vatican eventually capitulated on Earth's motion, the poor God of the Psalms never got the news. This is somewhat perplexing since, as Galileo showed a year before the trial, a state of absolute rest is impossible to verify experimentally. Any experiment that you perform at rest, such as throwing a ball up in the air and catching it, will have an identical result if performed while moving at a constant speed, as, say, might happen while riding on an airplane in the absence of turbulence. No experiment you can perform on the plane, if its windows are closed, will tell you whether the plane is moving or standing still. While Galileo started the ball rolling, both literally and metaphori- 45 2P_Gtealer-StoryEverrold_Atirdd 45 12/16116 3:06 PIA EFTA00285967 48 THE GREATEST STORY EVER TOLD-SO FAR cally, in 1632, it took another 273 years to fully lay to rest this issue (issues, unlike objects, can be laid to rest). It would take Albert Einstein to do so. Einstein was not a revolutionary in the same sense as Galileo, if by this term one describes those who tear down the dictates of the authorities who came before, as Galileo had for Aristotle. Einstein did just the opposite. He knew that rules that had been established on the basis of experiment could not easily be tossed aside, and it was a mark of his genius that he didn't. This is so important I want to repeat it for the benefit of those people who write to me every week or so telling me that they have discovered a new theory that demonstrates everything we now think we know about the universe is wrong—and using Einstein as their exemplar to justify this possibility. Not only is your theory wrong, but you are doing Ein- stein a huge disservice: rules that have been established on the basis of experiment cannot easily be tossed aside. • • • Albert Einstein was born in 1879, the same year that James Clerk Maxwell died. It is tempting to suggest that their combined brilliance was too much for one simple planet to house at the same time. But it was just a coincidence, albeit a fortuitous one. If Maxwell hadn't preceded him, Ein- stein couldn't have been Einstein. He came from the first generation of young scientists who grew up wrestling with the new knowledge about light and electromagnetism that Faraday and Maxwell had generated. This was the true forefront of physics for young Turks such as Einstein near the end of the nineteenth century. Light was on everyone's mind. Even as a teenager, Einstein was astute enough to realize that Max- well's beautiful results regarding the existence of electromagnetic waves presented a fundamental problem: they were inconsistent with the equally beautiful and well-established results of Galileo regarding the basic properties of motion, produced three centuries earlier. Even before his epic battle with the Catholic Church over the motion of Earth, Galileo had argued that no experiment exists that can be performed 2P_Glealer-StoryEverTold_Atincld 48 12/18118 308 PIA EFTA00285968 There, and Back Again 47 by anyone to determine whether he or she is moving uniformly or stand- ing still. But up until Galileo, a state of absolute rest was considered special. Aristotle had decided that all objects sought out the state of rest, and the Church decided that rest was so special that it should be the state of the center of the universe, namely the planet on which God had placed us. Like a number of Aristotle's assertions, although by no means all, this notion that a state of rest is special is quite intuitive. (For those who like to quote Aristotle's wisdom when appealing to his "Prime Mover" argument for the existence of God, let us remember that he also claimed that women had a different number of teeth than men, presumably without bothering to check.) Everything we see in our daily lives comes to rest. Everything, that is, except the Moon and the planets, which is perhaps one reason that these were felt to be special in antiquity, guided by angels or gods. However, every sense that we have that we are at rest is an illusion. In the example I gave earlier of throwing a ball up and catching it while in a moving plane, you will eventually be able to tell that your plane is moving when you feel the bouncing of turbulence. But even when the plane is on the tarmac, it is not at rest. The airport is moving with the Earth at about 3o km/sec around the Sun, and the Sun is moving about zoo km/sec around the galaxy, and so on. Galileo codified this with his famous assertion that the laws of phys- ics are the same for all observers moving in a uniform state of motion, i.e., at a constant velocity in a straight line. (Observers at rest are simply a special case, when velocity is zero.) By this he meant that there is no experiment you can perform on such an object that can tell you it is not at rest. When you look up in the air at an airplane, it is easy to see that it is moving relative to you. But, there is no experiment you can perform on the ground or on the plane that will distinguish whether the ground on which you are standing is moving past the plane, or vice versa. While it seems remarkable that it took so long for anyone to rec- ognize this fundamental fact about the world, it does defy most of our 2P_Glealer-StoryEverTold_Atirdd 4? 12/16116 3:06 PIA EFTA00285969 48 THE GREATEST STORY EVER TOLD-SO FAR experience. Most, but not all. Galileo used examples of balls rolling down inclined planes to demonstrate that what previous philosophers thought was fundamental about the world—the retarding force of fric- tion that makes things eventually settle at rest—was not fundamental at all but rather masked an underlying reality. When balls roll down one plane and up another, Galileo noted, on smooth surfaces the balls would rise back to the same height at which they started. But by considering balls rolling up planes of ever-decreasing incline, he showed that the balls would have to roll farther to reach their same original height. He then reasoned that if the second incline disappeared entirely, the balls would continue rolling at the same speed forever. This realization was profoundly important and fundamentally changed much about the way we think about the world. It is often sim- ply called the Law of Inertia, and it set up Newton's law of motion, relat- ing the magnitude of an external force to the observed acceleration of an object. Once Galileo recognized that it took no force to keep some- thing moving at a constant velocity, Newton could make the natural leap to propose that it took a force to change its velocity. The heavens and the Earth were no longer fundamentally different. The hidden reality underlying the motion of everyday objects also made clear that the unending motion of astronomical objects was not super- natural, setting the stage for Newton's Universal Law of Gravity, further demoting the need for angels or other entities to play a role in the cosmos. Galileo's discovery was thus fundamental to establishing physics as we know it today. But so was Maxwell's later brilliant unification of elec- tric and magnetic forces, which established the mathematical frame- work on which all of current theoretical physics is built. As Albert Einstein began his journey in this rich intellectual landscape, he quickly spied a deep and irreconcilable chasm running through it: both Galileo and Maxwell could not be right at the same time. 2P_Glealer-StoryEverTold_Atincld J8 12/16116 3:06 PIA EFTA00285970 There, and Back Again 49 More than twenty years ago, when my daughter was an infant, I first began to think about how to explain the paradox that young Einstein struggled with, and a good example literally hit me on the head while driving her in my car when she was an infant. Galileo had demonstrated that as long as I am driving safely and at a constant speed and not accelerating suddenly, the laws of physics in our car should be indistinguishable from the laws of physics that would be measured in the laboratories in the physics building to which I was driving to work. If my daughter was playing with a toy in the backseat, she could throw the toy up in the air and expect to catch it without any surprises. The intuition her body had built up to play at home would have served her well in the car. However, riding in the car did not lull her to sleep like many young chil- dren, but rather made her anxious and uncomfortable. During our trip, she got sick and projectile-vomited, and the vomit followed a trajectory well described by Newton, with an initial speed of, say, fifteen miles per hour, and a nice parabolic trajectory in the air, ending on the back of my head. Say my car was coasting to a red light at this time at a relatively slow speed, say, ten miles per hour. Someone on the ground watching all of this would see the vomit traveling at 2.5 miles per hour, the speed of the car relative to them (io mph) plus the speed of the vomit (is mph), and its trajectory would be well described by Newton again, with this higher speed (zs mph) as it traveled toward my (now moving) head. So far so good. Here's the problem, however. Now that my daughter is older, she loves to drive. Say she is driving behind a friend's car and dials him on her cell phone (hands-free, for safety) to tell him to turn right to get to the place they are both going. As she talks into the phone, elec- trons in the phone jiggle back and forth producing an electromagnetic wave (in the microwave band). That wave travels to the cell phone of her friend at the speed of light (actually it travels up to a satellite and then gets beamed down to her friend, but let's ignore that complication for the moment) and is received in time for him to make the correct turn. 2P_Glealer-StoryEverTold_Atirdd 49 12/16116 3:06 PIA EFTA00285971 50 THE GREATEST STORY EVER TOLD-SO FAR Now, what would a person on the ground measure? Common sense would suggest that the microwave signal would travel from my daugh- ter's car to her friend's car at a speed equal to the speed of light, as might be measured by a detector in my daughter's car (label it with the symbol c), plus the speed of the car. But common sense is deceptive precisely because it is based on com- mon experience. In everyday life we do not measure the time it takes light, or microwaves, to travel from one side of the room to another or from one phone to a nearby phone. If common sense applied here, that would mean someone on the ground (with a sophisticated measuring apparatus) would measure the electrons in my daughter's phone jiggling back and forth and observe the emanation of a microwave signal, which would be traveling at a speed c plus, say, ten miles per hour. However, the great triumph of Maxwell was to show that he could calculate the speed of electromagnetic waves emanated by an oscillat- ing charge purely by measuring the strength of electricity and magne- tism. Therefore if the person on the ground observed the waves having speed c plus io mph, then for that person the strength of electricity and magnetism would have to be different from the values that my daughter would observe, for whom the waves were moving at a speed c. But Galileo tells us this is impossible. If the measured strengths of electricity and magnetism differed between the two observers, then it would be possible to know who was moving and who was not, because the laws of physics—in this case electromagnetism—would take on dif- ferent values for each observer. So, either Galileo or Maxwell had to be right, but not both of them. Perhaps because Galileo had been working when physics was more primitive, most physicists came down closer to the side of Maxwell. They decided that the universe must have some absolute rest frame and that Maxwell's calculations applied in that frame only. All observ- ers moving with respect to that frame would measure electromagnetic 2P_Glealer-StoryEverTold_Atind0 50 12/16116 3:06 PIA EFTA00285972 There, and Back Again 51 waves to have a different speed relative to themselves than Maxwell had calculated. A long scientific tradition gave physical support to this idea. After all, if light was an electromagnetic disturbance, what was it a distur- bance of? For thousands of years, philosophers had speculated about an "ether," some invisible background material filling all of space, and it became natural to suspect that electromagnetic waves were traveling in this medium, just as sound waves travel in water or air. Electromag- netic waves would travel with some fixed, characteristic speed in this medium (the speed calculated by Maxwell), and observers moving with respect to this background would observe the waves as faster or slower, depending on their relative motion. While intuitively sensible, this notion was a cop-out, because if you think back to Maxwell's analysis, it would mean that these different ob- servers in relative motion would measure the strength of electricity and magnetism to be different. Perhaps it was deemed to be acceptable be- cause all speeds obtainable at the time were so small compared to the speed of light that any such differences would have been minute at best and would certainly have escaped detection. The actor Alan Alda once turned the tables on conventional wisdom at a public event I attended by saying that art requires hard work, and science requires creativity. While both require both, what I like about his version is that it stresses the creative, artistic side of science. I would add to this statement that both endeavors require intellectual bravery. Creativity alone amounts to nothing if it is not implemented. Novel ideas generally stagnate and die without the courage to implement them. I bring this up here because perhaps the true mark of Einstein's ge- nius was not his mathematical prowess (although, contrary to conven- tional wisdom, he was mathematically talented), but his creativity and his intellectual confidence, which fueled his persistence. The challenge that faced Einstein was how to accommodate two con- 2P_Glealer-StoryEverrold_AC.irdd Si 12/16116 3:06 PIA EFTA00285973 52 THE GREATEST STORY EVER TOLD-SO FAR tradictory ideas. Throwing one out is the easy way. Figuring out a way to remove the contradiction required creativity. Einstein's solution was not complex, but that does not mean it was easy. I am reminded of an apocryphal story about Christopher Colum- bus, who got a free drink in a bar before departing to find the New World by claiming he could balance an egg upright on top of the bar. After the barman accepted the bet, Columbus broke the tip off the egg and placed it easily upright on the counter. He never mentioned not cracking it, after all. Einstein's resolution of the Galileo-Maxwell paradox was not that different. Because, if both Maxwell and Galileo were right, then some- thing else had to be broken to fix the picture. But what could it be? For both Maxwell and Galileo to be right re- quired something that was clearly crazy: in the example I gave, both observers would have to measure the velocity of the microwave emitted by my daughter's cell phone to be the same relative to them, instead of measuring values differing by the speed of the car. However, Einstein asked himself an interesting question, What does it mean to measure the velocity of light, after all? Velocity is determined by measuring the distance something travels in a certain time. So Ein- stein reasoned as follows: it is possible for two observers to measure the same speed for the microwave relative to each of them, as long as the distance each measures the ray to travel relative to themselves during a fixed time interval (e.g., say, one second, as measured by each of them in their own frame of reference) is the same. But this too is a little crazy. Consider the simpler example of the projectile vomit. Remember that in my frame it travels from her mouth in the backseat to hit my head, say, three feet away, in about one-quarter second. But for someone on the ground the car is traveling at 10 miles per hour during this period, which is about 14.5 feet per second. Thus for the person on the ground, in one-quarter second the vomit travels about 3.6 feet plus 3 feet, or a total 6.6 feet. 2P_Glealer-StoryEverTold_Aairdd 52 12/16116 3:06 PIA EFTA00285974 There, and Back Again 53 Hence for the two observers, the distances traveled by the vomit in the same time is noticeably different. How could it be that for the micro- wave the distances both observers measure could be the same? The first hint that perhaps such craziness is possible is that electro- magnetic waves travel so fast that in the time it takes the microwaves to get from one car to another, each car has moved hardly at all. Thus any possible difference in measured distance traveled during this time for the two observers would be essentially imperceptible. But Einstein turned this argument around. He realized that both observers had not actually measured the distances traveled by the mi- crowaves over human-scale distances, because the relevant times ap- propriate for light to travel over human-scale distances were so short that no one could have measured them at the time. And similarly, on human timescales light would travel such large distances that no one could measure those distances directly either. Thus, who was to say that such crazy behavior couldn't really happen? The question then became, What is required for it to actually occur? Einstein reasoned that for this seemingly impossible result to be pos- sible, the two different observers must measure distances and/or times differently from each other in just such a way that light, at least, would traverse the same measured distance in the same measured time for both observers. Thus, for example, it would be as if the observer on the ground in the vomit case were to measure the vomit traversing 6.6 feet, but would somehow also infer the time interval over which this hap- pened to be larger than I would measure it inside my car, so that the in- ferred speed of the vomit would be the same relative to him as I measure it to be relative to me. Einstein then made the bold assertion that something like this does happen, that both Maxwell and Galileo were correct, and that all ob- servers, regardless of their relative state of motion, would measure any light ray to travel at the same speed, c, relative to them. Of course, Einstein was a scientist, not a prophet, so he didn't just 2P_Glealer-StoryEverTold_Aairdd 53 12/16116 3:06 PIA EFTA00285975 54 THE GREATEST STORY EVER TOLD-SO FAR claim something outlandish on the basis of authority. He explored the consequences of his claim and made predictions that could be tested to verify it. In doing so he moved the playing field of our story from the domain of light to the domain of intimate human experience. He not only for- ever changed the meaning of space and time, but also the very events that govern our lives. 2P_Glealer-StoryEverTold_Atirdd 54 12/16116 3:06 PIA EFTA00285976 Chapter 5 A STITCH IN TIME He stretcheth out the north over the empty place, and hangeth the earth upon nothing. -JOB 26:7 The great epic stories of ancient Greece and Rome revolve around heroes such as Odysseus and Aeneas, who challenged the gods and often outwitted them. Things have not changed that much for more modern epic heroes. Einstein overcame thousands of years of misplaced human percep- tion by showing that even the God of Spinoza could not impose his absolute will on space and time, and that each of us evades those imagi- nary shackles every time we look around us and view new wonders amid the stars above. Einstein emulated artistic geniuses such as Vincent van Gogh and reasoned with the parsimony of Ernest Hemingway. Van Gogh died fifteen years before Einstein developed his ideas on space and time, but his paintings make it clear that our perceptions of the world are subjective. Picasso may have had the chutzpah to claim that he painted what he saw, even as he produced representations of disjointed people with body parts pointing in different directions, but van Gogh's 55 2P_Glealer-StoryEverrold_Aairdd 55 12/16116 3:06 PIA EFTA00285977 56 THE GREATEST STORY EVER TOLD-SO FAR masterpieces demonstrate that the world can look very different to dif- ferent people. So too, Einstein explicitly argued, for the first time as far as I know in the history of physics, that "here" and "now" are observer-dependent concepts and not universal ones. His argument was simple, based on the equally simple fact that we cannot be in two places at once. We are accustomed to feeling that we share the same reality with those around us because we appear to share the same experiences as we look about together. But that is an illusion created by the fast speed of light. When I observe something happening now, say, a car crash down the street or two lovers kissing under a lamppost as I walk nearby, neither of these events happened now, but rather then. The light that enters my eye was reflected off the car or the people just a little bit earlier. Similarly when I take a photo of a beautiful landscape, as I just did in Northern Ireland where I began writing this chapter, the scene I captured is not a scene merely spread out in space, but rather in space and time. The light from the distant pillared cliffs at Giant's Causeway perhaps a kilometer away left those cliffs well before (perhaps thirty-millionths of a second before) the light from the people in the foreground scrambling over the hexagonal lava pods left to reach my camera at the same time. With this realization, Einstein asked himself what two events that one observer views as happening at the same time in two different loca- tions would look like for another observer moving with respect to the first observer while the observations were being made. The example he considered involved a train, because he lived in Switzerland at a time when a train was leaving about every five minutes for somewhere in the country from virtually any other place in the country. Imagine the picture shown below in which lightning hits two points beside either end of a train that are equidistant from observer A, who is at rest with respect to those points, and observer B on a moving train, who passes by A at the instant A later determines the lightning bolts struck: 2P_Glealer-StoryEverTold_Atirdd 58 122/18/16 3:06 PIA EFTA00285978 A Shich in Time 57 lightning hits B A a little while later A little while later A will see both lightning flashes reaching him at the same time. B, however, will have moved during this time. Therefore the light wave bringing the information that a flash occurred on the right will already have passed B, and the light bringing the information about the flash on the left will not yet have reached him. B sees the light coming from either end of his train, and indeed the flash at the front end occurs before the flash at the rear end. Since he measures the light as traveling toward him at speed c, and since he is in the middle of his train, he concludes therefore that the right-hand flash must have occurred before the left-hand flash. Who is right here? Einstein had the temerity to suggest that both ob- servers were right. If the speed of light were like other speeds, then B would of course see one wave before the other, but he would see them traveling toward him at different speeds (the one he was moving toward would be faster and the one from which he was moving away would be slower), and he would therefore infer that the events happened at the same time. But because both light rays are measured by B to be traveling toward him at the same speed, c, the reality he infers is completely different. As Einstein pointed out, when defining what we mean by different physical quantities, measurement is everything. Imagining a reality that is independent of measurement might be an interesting philosophical ex- ercise, but from a scientific perspective it is a sterile line of inquiry. If both A and B are located at the same place at the same time, they must both measure the same thing at that instant, but if they are in remote locations, almost all bets are off. Every measurement that B can make tells him that 2P_Glealer-StoryEverrold_Atirdd Si 12/16116 3:06 PIA EFTA00285979 58 THE GREATEST STORY EVER TOLD-SO FAR the event at the forward end of his train happened before the next, while every measurement that A makes tells him the events were simultaneous. Since neither A nor B can be at both places at the same time, their mea- surement of time at remote locations depends upon remote observations, and if those remote observations are built on interpreting what light from those events reveals, they will differ on their determination of which re- mote events are simultaneous, and they will both be correct. Here and now is only universal for here and now, not there and then. • • • I wrote "almost all" bets are off for a reason. For as strange as the example I just gave might seem, it can actually be far stranger. Another observer, C, traveling on a train moving in the opposite direction from B on a third track beside A and B will infer that the event on the left side (the forward part of his train) occurred before the event on the right-hand side. In other words, the order of the events seen by the two observers B and C will be completely reversed. One person's "before" will be the other's "after." This presents a big apparent problem. In the world in which most of us believe we live, causes happen before effects. But if "before" and "after" can be observer dependent, then what happens to cause and effect? Remarkably, the universe has a sort of built-in catch-n, which ends up ensuring that while we need to keep an open mind about reality, we don't have to keep it so open that our brains fall out, as the publisher of the New York Times used to say. In this case, Einstein demonstrated that a reversal of the time ordering of distant events brought about by the constancy of light is only possible if the events are far enough apart so that a light ray will take longer to travel between them than the inferred time differ- ence between the two events. Then, if nothing can travel faster than light (which turns out to be another consequence of Einstein's effort to coordi- nate Galileo and Maxwell), no signal from one event could ever arrive in time to affect the other, so one event could not be the cause of the other. But what about two different events that occur some time apart at 2P_Glealer-Storgverrold_Atirdd 58 12/16116 3:06 PIA EFTA00285980 A Stitch in Time 59 the same place. Will different observers disagree about them? To ana- lyze this situation Einstein imagined an idealized clock on a train. The ticks of the clock occur each time a light ray sent from a clock on one side of the train reflects off a mirror located on the other side and re- turns to the clock on the original side of the train (see below). minor clock Let us say each round-trip (tick) is a millionth of a second. Now con- sider an observer on the ground watching the same round-trip. Because the train is moving, the light ray travels on the trajectory shown below, with the clock and mirror having moved between the time of emission and reception. mirror 4 clock clock Clearly this light ray traverses a greater distance relative to the observer on the ground than it does relative to the clock on the train. However, the light ray is measured to be traveling at the same speed, c. Thus, the round- trip takes longer. As a result, the one-millionth-of-a-second click of the clock on the train is observed on the ground to take, say, two-millionths of a second. The clock on the train is therefore ticking at half the rate of a clock on the ground. Time has slowed down for the clock on the train. Stranger still, the effect is completely reciprocal. Someone aboard the train will observe a clock on the ground as ticking at half the rate of their 2P_Glealer-StoryEverTold_Atincld 59 12/16116 3:06 PIA EFTA00285981 60 THE GREATEST STORY EVER TOLD-SO FAR clock on the train, as the figure would look identical for someone on the train watching a light travel between mirrors placed on the ground. This may make it seem like the slowing of clocks is merely an illusion, but once again, measurement equals reality, although in this case a little more subtly than for the case of simultaneity. To compare clocks later to see which, if any, of the observers clocks has really slowed down, at least one of the observers will have to return to join the other. That observer will have to change his or her uniform motion, either by slowing down and reversing, or by speeding up from (apparent) rest and catching up with the other observer. This makes the two observers no longer equivalent. It turns out that the observer who does the accelerating or the decelerating will find, when she arrives back at the starting position, that she has actually aged far less than her counterpart, who has been in uniform motion during the whole time. This sounds like science fiction, and indeed it has provided the fod- der for a great deal of science fiction, both good and bad, because in principle it allows for precisely the kind of space travel around the gal- axy that is envisaged in so many movies. There are a few rather signifi- cant glitches, however. While it does make it possible in principle for a spacecraft to travel around the galaxy in a single human lifetime, so that Jean-Luc Picard could have his Star Trek adventures, those back at Star Fleet command would have a hard time exerting command and control over any sort of federation. The mission of ships such as the USS Enter- prise might be five years long for the crew on board, but each round-trip from Earth to the center of the galaxy of a ship at near light speed would take sixty thousand years or so as experienced by society back home. To make matters worse, it would take more fuel than there is mass in the galaxy to power a single such voyage, at least using conventional rockets of the type now in use. Nevertheless, science fiction woes aside, "time dilation"—as the rel- ativistic slowing of clocks is called with regard to moving objects—is very much real, and very much experienced every day here on Earth. 2P_Glealer-StoryEverTold_Atirdd 60 12/16116 3:06 PIA EFTA00285982 A Stitch in Time 61 At high-energy particle accelerators such as the Large Hadron Collider, for example, we regularly accelerate elementary particles to speeds of 99.9999 percent of the speed of light and rely on the effects of relativity when exploring what happens. But even closer to home, relativistic time dilation has an impact. We on Earth are all bombarded every day by cosmic rays from space. If you had a Geiger counter and stood out in a field, the counter would click at a regular rate every few seconds, as it recorded the impact of high-energy particles called muons. These particles are produced where high-energy protons in cosmic rays smash into the atmosphere, produc- ing a shower of other, lighter particles—including muons—which are unstable, with a lifetime of about one-millionth of a second, and decay into electrons (and my favorite particles, neutrinos). If it weren't for time dilation, we would never detect these muon cosmic rays on Earth. Because a muon traveling at close to the speed of light for a millionth of a second would cover about three hundred meters before decaying. But the muons raining down on Earth make it twenty kilometers, or about twelve and a half miles or so, from the upper atmosphere, in which they are produced, down to our Geiger counter. This is possible only if the muons internal "clocks" (which prompt them to decay after one-millionth of a second or so) are ticking slowly relative to our clocks on Earth, ten to one hundred times more slowly than they would be if they were produced at rest here in a laboratory on Earth. The last implication of Einstein's realization that the speed of light must be constant for all observers appears even more paradoxical than the others—in part because it involves changing the physical behavior of objects we can see and touch. But it also will help carry us back to our beginnings to glimpse a new world beyond the confines of our normal earthbound imagination. The result is simply stated, even if the consequences may take some 2P_Glealer-StoryEverTold_Atirdd SI 12/16116 3:06 PIA EFTA00285983 82 THE GREATEST STORY EVER TOLD-SO FAR time to digest. When I am carrying an object such as a ruler, and mov- ing fast compared to you, my ruler will be measured by you to be smaller than it is for me. I might measure it to be to cm, say: But to you, it might appear to be merely 6 cm: Surely, this is an illusion, you might say, because how could the same object have two different lengths? The atoms can't be compressed to- gether for you, but not for me. Once again, we return to the question of what is "real." If every mea- surement you can perform on my ruler tells you it is 6 cm long, then it is 6 cm long. "Length" is not an abstract quantity but requires a mea- surement. Since measurement is observer dependent, so is length. To see this is possible while illuminating another of relativity's slippery catch-2zs, consider one of my favorite examples. Say I have a car that is twelve feet long, and you have a garage that is eight feet deep. My car will clearly not fit in your garage: car But, relativity implies that if I am driving fast, you will measure my car to be only, say, six feet long, and so it should fit in your garage, at least while the car is moving: car 4 garage 2P_Glealer-StoryEverTold_Atincld 62 12/16116 3:06 PIA EFTA00285984 A Stitch in Time 63 However, let's view this from my vantage point. For me, my car is twelve feet long, and your garage is moving toward me fast, and it now is measured by me to be not eight feet deep, but rather four feet deep: car garage Thus, my car clearly cannot fit in your garage. So which is true? Clearly my car cannot both be inside the garage and not inside the garage. Or can it? Let's first consider your vantage point, and imagine that you have fixed big doors on the front of your garage and the back of your garage. So that I don't get killed while driving into it, you perform the following. You have the back door closed but open the front door so my car can drive in. When it is inside, you close the front door: However, you then quickly open the back door before the front of my car crashes, letting me safely drive out the back: Thus, you have demonstrated that my car was inside your garage, which of course it was, because it is small enough to fit in it. However, remember that, for me, the time ordering of distant events can be different. Here is what I will observe. I will see your tiny garage heading toward me, and I will see you open the front door of the garage in time for the front of my car to pass through. 2P_Glealer-StoryEverTold_Atirdd S3 12,1&I6 3:06 PIA EFTA00285985 84 THE GREATEST STORY EVER TOLD-SO FAR I will then see you kindly open the back door before I crash: After that, and after the back of my car is inside the garage, I will see you close the front door of your garage: As will be clear to me, my car was never inside your garage with both doors closed at the same time because that is impossible. Your garage is too small. "Reality" for each of us is simply based on what we can measure. In my frame the car is bigger than the garage. In your frame the garage is bigger than my car. Period. The point is that we can only be in one place at one time, and reality where we are is unambiguous. But what we infer about the real world in other places is based on remote measurements, which are observer dependent. But the virtue of careful measurement does not stop there. The new reality that Einstein unveiled, based as it was on the em- pirical validity of Galileo's law, and Maxwell's remarkable unification 2P_Glealer-StoryEverTold_Atincld S4 12116116 3:06 PM EFTA00285986 A Stitch in Time 66 of electricity and magnetism, appears on its face to replace any last vestige of objective reality with subjective measurement. As Plato reminds us, however, the job of the natural philosopher is to probe deeper than this. It is said that fortune favors the prepared mind. In some sense, Plato's cave prepared our minds for Einstein's relativity, though it remained for Einstein's former mathematics professor Hermann Minkowski to com- plete the task. Minkowski was a brilliant mathematician, eventually holding a chair at the University of Gottingen. But in Zurich, where he was one of Einstein's professors, he was a brilliant mathematician whose classes Einstein skipped, because while he was a student, Einstein appeared to have a great disdain for the significance of pure mathematics. Time would change that view. Recall that the prisoners in Plato's cave also saw from shadows on their wall that length apparently had no objective constancy. The shadow of a ruler might at one time look like this, at io cm: and, at another time like this, at 6 cm: The similarity with the example I presented when discussing relativ- ity is intentional. In the case of Plato's cave dwellers, however, we rec- ognized that this length contraction occurred because the cave dwellers were merely seeing two-dimensional shadows of an underlying three- dimensional object. Viewed from above, it can easily be seen that the shorter shadow projected on the wall results because the ruler has been rotated at an angle to the wall: 2P_Glealer-StoryEverTold_Atincld 65 12/16116 3:06 PIA EFTA00285987 BB THE GREATEST STORY EVER TOLD-SO FAR shadow And as another Greek philosopher, Pythagoras, taught us, when seen this way, the length of the ruler is fixed, but the projections onto the wall and a line perpendicular to the wall always combine together to give the same length, as shown below: shadow N This yields the famous Pythagorean theorem, L a = + y2, which high school students have been subjected to for as long as high schools have taught geometry. In three dimensions, this becomes L a = + ya + z1. Two years after Einstein wrote his first paper on relativity Minkowski recognized that perhaps the unexpected implications of the constancy of the speed of light, and the new relations between space and time unveiled by Einstein, might also reflect a deeper connection between the two. Knowing that a photograph, which we usually picture as a two-dimensional representation of three-dimensional space, is really an image spread out in both space and time, Minkowski reasoned that observers who were moving relative to each other might be observing different three-dimensional slices of a four-dimensional universe, one in which space and time are treated on an equal footing. 29_GlealerASIoryEverTold_Atirdd 88 1'2/1&16 3:06 PIA EFTA00285988 A Stitch in Time 67 If we return to the ruler example in the case of relativity, where the ruler of the moving observer is measured to be shorter by the other observer than it would be in the frame in which it is at rest, we should also remember that for this observer the ruler is also `spread out" in time—events at either end that are simultaneous to the observer at rest with respect to the ruler are not simultaneous for the second ob- server. Minkowski recognized that one could accommodate this fact, and all the others, by considering that the different three-dimensional perspectives probed by each observer were in some sense different "rotated" projections of a four-dimensional "space-time," where there exists an invariant four-dimensional space-time length" that would be the same for all observers. The four-dimensional space, which we now call Minkowski space, is a little different from its 3-D counterpart, in that time as a fourth dimension is treated slightly differently from the three dimensions of space, x, y, and z. The four-dimensional `space-time length," which we can label as S, is not written, in analogy to the three- dimensional length, which we denoted by L, above, as S2=X2+y2+22+t2 but rather as S2 = X2 + y2 + 22 - The minus sign that appears in front of t2 in the definition of space- time length, S, gives Minkowski space its special characteristics, and it is the reason our different perspectives of space and time when we are moving relative to one another are not simple rotations, as in the case of Plato's cave, but something a little more complicated. Nevertheless, in one fell swoop, the very nature of our universe had changed. As Minkowski poetically put it in 1908: "Henceforth space by 2P_Glealer-StoryEverTold_Atincld 67 12/16116 3:06 PIA EFTA00285989 68 THE GREATEST STORY EVER TOLD-SO FAR itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." Thus, on the surface, Einstein's Special Theory of Relativity appears to make physical reality subjective and observer dependent, but rela- tivity is in this sense a misnomer. The Theory of Relativity is instead a theory of absolutes. Space and time measurements may be subjective, but `space-time" measurements are universal and absolute. The speed of light is universal and absolute. And four-dimensional Minkowski space is the field on which the game of nature is played. The depth of the radical change in perspective brought about by Minkowski's reframing of Einstein's theory can perhaps best be under- stood by considering Einstein's own reactions to Minkowski's picture. Initially Einstein called it `superfluous learnedness," suggesting that it was simply fancy mathematics, devoid of physical significance. Shortly thereafter he emphasized this by saying, "Since the mathematicians have invaded relativity theory, I do not understand it myself anymore." Ultimately, however, as happened several times in his lifetime, Ein- stein came around and recognized that this insight was essential to understand the true nature of space and time, and he later built his General Theory of Relativity on the foundation that Minkowski had laid. It would have been difficult if not impossible to guess that Faraday's spinning wheels and magnets would eventually lead to such a profound revision in our understanding of space and time. With the spectacles of hindsight, however, we could have had at least an inkling that the unifi- cation of electricity and magnetism could have heralded a world where motion would reveal a new underlying reality. Returning to Faraday and Maxwell, one of the important discoveries that started the ball rolling was that a magnet acts on a moving elec- tric charge with an odd force. Instead of pushing the charge forward or backward, the magnet exerts a force always at right angles to the motion of the electric charge. This force, now called the Lorentz force—after 2P_Glealer-StoryEverTold_Atincld 88 12/18/18 3:06 PIA EFTA00285990 A Stitch in Time 69 Hendrik Lorentz, a physicist who came close to discovering relativity himself—can be pictured as follows: force on particle The charge moving between the poles of the magnet gets pushed upward. But now consider how things would look from the frame of the par- ticle. In its frame, the magnet would be moving past it. force on particle But by convention we think of an electrically charged particle at rest as being affected only by electric forces. Thus, since the particle is at rest in this frame, the force pushing the particle upward in this picture would be interpreted as an electric force. 2P_Gtealer-StoryEverTaid_Atirdd 89 12/16116 3:06 PIA EFTA00285991 70 THE GREATEST STORY EVER TOLD-SO FAR One person's magnetism is therefore another person's electricity, and what connects the two is motion. The unification of electricity and mag- netism reflects at its heart that uniform relative motion gives observers different perspectives of reality. Motion, a subject first explored by Galileo, ultimately provided, three centuries later, a key to a new reality—one in which not only electric- ity and magnetism were unified, but also space and time. No one could have anticipated this saga at its beginning. But that is the beauty of the greatest story ever told. 2P_Gtealer-SlowEverTaid_Atindd 10 12/16116 3:06 PIA EFTA00285992 Chapter 6 THE SHADOWS OF REALITY As they were walking along and talking together, suddenly a chariot of fire and horses of fire appeared and separated the two of them. -2 KINGS 2:11 One might have thought that, in 1908, following the after- shock of the discovery of an unexpected hidden connection between space and time, nature couldn't have gotten much stranger. But the cos- mos doesn't care about our sensibilities. And once again, light provided the key to the door of the rabbit hole to a world that makes Alice's expe- riences seem tame. While they may be strange, the connections unearthed by Einstein and Minkowski can be intuitively understood—given the constancy of the speed of light—as I have tried to demonstrate. Far less intuitive was the next discovery, which was that on very small scales, nature behaves in a way that human intuition cannot ever fully embrace, because we cannot directly experience the behavior itself. As Richard Feynman once argued, no one understands quantum mechanics—if by under- stand one means developing a concrete physical picture that appears fully intuitive. 71 29_Glealer-StoryEverTold_Atincld 71 12/16/16 3:OB PM EFTA00285993 72 THE GREATEST STORY EVER TOLD-SO FAR Even many years after the rules of quantum mechanics were dis- covered, the discipline would keep yielding surprises. For example, in 19s2 the astrophysicist Hanbury Brown built an apparatus to measure the angular size of large radio sources in the sky. It worked so well that he and a colleague, Richard Twiss, applied the same idea to try to mea- sure the optical light from individual stars and determine their angular size. Many physicists claimed that their instrument, called an intensity interferometer, could not possibly work. Quantum mechanics, they ar- gued, would rule it out. But it worked. It wasn't the first time physicists had been wrong about quantum mechanics, and it wouldn't be the last.... Coming to grips with the strange behavior of quantum mechanics means often accepting the seemingly impossible. As Brown himself amusingly put it when trying to explain the theory of his intensity in- terferometer, he and Twiss were expounding the "paradoxical nature of light, or if you like, explaining the incomprehensible—an activity closely, and interestingly, analogous to preaching the Athanasian Creed." In- deed, like many of the stranger effects in quantum mechanics, the Holy Trinity—Father, Son, and Holy Ghost all embodied at the same time in a single being—is also seemingly impossible. The similarity ends there, however. Common sense also tells us that light cannot be both a wave and a particle at the same time. However, in spite of what common sense suggests, and whether we like it or not, experiments tell us it is so. Un- like the Creed, developed in the fifth century, this fact is not a matter of semantics or choice or belief. So we don't need to recite quantum mechanics creeds every week to make them seem less bizarre or more believable. One hears about the interpretation of quantum mechanic? for good reason, because the "classical" picture of reality—namely the pic- ture given by Newton's laws of classical motion of the world as we ex- 2P_GlealerASIonEverTold_Atincld 72 12/16116 3:06 PIA EFTA00285994 The Shadows of Reality 73 perience it on human scales—is inadequate to capture the full picture. The surface world we experience hides key aspects of the processes that underlie the phenomena we observe. So too Plato's philosophers could not discover the biological processes that govern humans by observing just the shadows of humans on the wall. No level of analysis would be likely to allow them to intuit the full reality underlying the dark forms. The quantum world defies our notion of what is sensible—or even possible. It implies that at small scales and for short times, the simple classical behavior of macroscopic objects—baseballs thrown from pitcher to catcher, for example—simply breaks down. Instead, on small scales, objects are undergoing many different classical behaviors—as well as classically forbidden behaviors—at the same time. Quantum mechanics, like almost all of physics since Plato, began with scientists thinking about light. So it is appropriate to begin to ex- plore quantum craziness by starting with light, in this case by return- ing to an important experiment first reported by the British polymath Thomas Young around iitoo—the famous "double-slit experiment." Young lived in an era that is hard to appreciate today, when a bril- liant and hardworking individual could make breakthroughs in a host of different fields. But Young was not just any brilliant hardworking in- dividual. He was a prodigy, reading at two, and by the age of thirteen he had read the major Greek and Latin epic poems, had built a micro- scope and a telescope, and was learning four different languages. Later, trained as a medical doctor, Young was the first to propose, in 2806, the modern concept of energy, which now permeates every field of scientific endeavor. That alone would have made him memorable, but in his spare time he also was one of the first to help decipher the hieroglyphics on the Rosetta stone. He developed the physics of elastic materials, associ- ated with what is now called Young's modulus, and helped first elucidate the physiology of color vision. And his brave demonstration of the wave nature of light (which argued against Isaac Newton's powerful claim 2P_Glealer-StoryEverTold_Atirdd 73 12/16116 3:06 PIA EFTA00285995 74 THE GREATEST STORY EVER TOLD-SO FAR that light was made of particles) was so compelling that it helped lay the basis of Maxwell's discovery of electromagnetic waves. Young's experiment is simple. Let's return to Plato's cave and con- sider a screen placed in front of the back wall of the cave. Place two slits in the screen as shown below (as seen from above): wall screen HITTIMInghtraYs If the light is made of particles, then those light rays that pierce the slits would form two bright lines on the wall behind these two slits: 'I` However, it was well known that waves, unlike particles, diffract around barriers and narrow slits and would produce a very different pattern on the wall. If waves impinge on the barrier, and if each slit is narrow, a circular pattern of waves is generated at each slit, and the patterns from the two slits can "interfere" with each other, sometimes constructively and sometimes destructively. The result is a pattern of bright and dark regions on the back wall, as shown below: 2P_GreafestSioniEverrold_Atincld 74 12/18/18 3:06 PIA EFTA00285996 The Shadows of 75 light waves barrier a Interference pattern Using just such an apparatus, with narrow slits, Young reported this interference pattern, characteristic of waves, and so definitively dem- onstrated the wave nature of light. In 1804, this was a milestone in the history of physics. One can try the same experiment that Young tried for light on el- ementary particles such as electrons. If we send a beam of electrons toward a phosphorescent screen, like the screen in old-fashioned televi- sion sets, you will see a bright dot where the beam hits the screen. Now imagine that we put two slits in front of the screen, as Young did for light, and aim a wide stream of electrons at the screen: Here, based on the reasoning I gave when I discussed the behavior of light, you would expect to see a bright line behind each of the two slits, where the electrons could pass through to the screen. However, as you have probably already guessed, this is not what you would see, at least if the slits are narrow enough and close enough. Instead, you see an interfer- 2P_Glealer-StoryEverrold_Atirdd 75 12/16116 306 PIA EFTA00285997 76 THE GREATEST STORY EVER TOLD-SO FAR ence pattern similar to that which Young observed for light waves. Elec- trons, which are particles, seem to behave in this case just like waves of light. In quantum mechanics, particles have wavelike properties. That the electron "waves" emanating from one slit can interfere with electron "waves" emanating from the other slit is unexpected and strange, but not nearly as strange as what happens if we send a stream of electrons toward the screen one at a time. Even in this case, the pat- tern that builds up on the screen is identical to the interference pattern. Somehow, each electron interferes with itself. Electrons are not billiard balls. We can understand this as follows: The probability of an electron's hitting the screen at each point is determined by treating each electron as not taking a single trajectory, but rather following many different tra- jectories at once, some of which go through one slit and some of which go through the other. Those that go through one slit then interfere with those that go through the other slit—producing the observed interfer- ence pattern at the screen. Put more bluntly, one cannot say the electron goes through either one slit or the other, as a billiard ball would. Rather it goes through nei- ther and at the same time it goes through both. Nonsense, you insist. So you propose a variant of the experiment to prove it. Put an electron-measuring device at each slit that clicks when an electron passes through that slit. Sure enough, as each electron makes its way to the screen, only one device clicks each time. So each electron apparently does go through one and only one slit, not both. However, if you now look at the pattern of electrons accumulating at the screen behind the slits, the pattern will have changed from the original interference pattern to the originally expected pattern—with a bright region behind each of the two slits, just as if one were shooting billiard balls or bullets and not waves toward the screen. In other words, in attempting to verify your classical intuition, you 2P_Glealer-StoryEverTold_Atindd 18 12/16116 3:06 PIA EFTA00285998 The Shadows of Reality 77 changed the behavior of the electrons. Or, as more commonly asserted in quantum mechanics, measurement of a system can alter its behavior. One of the many seemingly impossible aspects of quantum mechan- ics is that there is no experiment you can perform that demonstrates that in the absence of measurement the electrons behave in a sensible classical way. This strange wavelike nature of objects that would otherwise be con- sidered to be particles—such as electrons—is mathematically expressed by assigning to each electron a "wave function," which describes the probability of finding that electron at any given point. If the wave func- tion takes on non-zero values at many different points, then the elec- tron's position cannot be isolated in advance of accurately measuring its position. In other words there is a non-zero probability that the electron is not actually localized at just some specific point in space in advance of making a measurement. While you might imagine that this is a simple problem of not hav- ing access to all the information we need to locate the particle until we make a measurement, Young's double-slit experiment, when updated for electrons, demonstrated that this is most certainly not the case. Any "sensible" classical picture of what is happening between measurements is inconsistent with the data. • • • The strange behavior of electrons was not the first evidence that the microscopic world could not be understood by intuitive classical logic. Once again, in keeping with the revolutionary developments in our un- derstanding of nature since Plato, the discovery of quantum mechanics began with a consideration of light. Recall that if we perform Young's double-slit experiment in Plato's cave with light rays, we get the interference pattern on the wall that Young discovered, which demonstrated that light was indeed a wave. So far, so good. However, if the light source is sufficiently weak, then if we 2P_Glealer-StoryEverrold_AC.inid 17 12/16116 3:06 PIA EFTA00285999 78 THE GREATEST STORY EVER TOLD-SO FAR try to detect the light as it passes through either of the slits, something strange happens. We will measure the light beam as traveling through one slit or the other, not both. And as with electrons, in this case the pattern on the wall will now change, looking as it would if light were particles and not waves. In fact, light also behaves like both a particle and a wave, depending on the circumstances under which you choose to measure it. The indi- vidual particles of light, which we now call photons, were first labeled quanta by the German theoretical physicist Max Planck, who suggested in 1900 that light might be admitted or absorbed in some smallest bun- dle (although the idea that light might come in discrete packets had earlier been floated by the great Ludwig Boltzmann in 1877). I have come to admire Planck even more as I have learned about his life. Like Einstein, he was an unpaid lecturer and was not offered an academic position after completing his thesis. During this time he spent his career trying to understand the nature of heat and developed several important pieces of work in thermodynamics. Five years after defend- ing his thesis, he was finally offered a university position, and he then quickly rose up the ranks and became a full professor at the prestigious University of Berlin in 1892. In 1894 he turned to the question of the nature of light emitted by hot objects, in part driven by commercial considerations (the first example I know of in the story I have been telling where fundamental physics was commercially motivated). He was commissioned to explore how to get the maximum amount of light out of the newly invented lightbulbs while using the minimum amount of energy. We all know that when we heat up an oven element it first glows red, and then, when it gets hotter, it begins to glow blue. But why? Sur- prisingly, the conventional approaches to this problem were unable to reproduce these observations. After struggling with the problem for six years, Planck presented a revolutionary proposal about radiation that agreed with observations. 2P_Glealer-StoryEverTold_Atirdd 78 12/16116 3:06 PIA EFTA00286000 The Shadows of Reality 79 Originally there was nothing revolutionary about his derivation, but within two months he had revised his analysis to accommodate ideas about what was happening at a fundamental level. In a quote that has endeared him to me since I first read it, he wrote that his new approach arose as "an act of despair.... I was ready to sacrifice any of my previous convictions about physics." This reflects to me the fundamental quality that makes the scientific process so effective, and which is so clearly represented in the rise of quantum mechanics. "Previous convictions" are just convictions wait- ing to be overturned—by empirical data, if necessary. We throw out cherished old notions like yesterday's newspaper if they don't work. And they didn't work in explaining the nature of radiation emitted by matter. Planck derived his law of radiation from the fundamental assump- tion that light, which was a wave, nevertheless was emitted only in "packets" of some minimum energy—proportional to the frequency of the radiation in question. He labeled the constant that related the energy to the frequency the "action quantum," which is now called Planck's constant. This may not sound so revolutionary, and as Faraday did with elec- tric fields, Planck viewed his assumption as merely a formal mathemati- cal crutch to aid in his analysis. He later stated, "Actually I did not think much about it." Nevertheless, this proposal that light was emitted in particle-like packets is clearly difficult to reconcile with the classical pic- ture of light as a wave. The energy carried by a wave is simply related to the magnitude of its oscillations, which can change continuously from zero. However, according to Planck, the amount of energy that could be emitted in a light wave of a given frequency had an absolute minimum. This minimum was termed an "energy quantum." Planck subsequently tried to develop a classical physical understand- ing of these energy quanta, but failed—causing him, as he put it, "much trouble." Still, unlike a number of his colleagues, he recognized that the 2P_Glealer-StoryEverTold_Atirdd 79 12/16116 3:06 PIA EFTA00286001 80 THE GREATEST STORY EVER TOLD-SO FAR universe didn't exist to make his life easier. Referring to the physicist and astronomer Sir James Jeans, who was unwilling to give up classical notions in the face of the evidence provided by radiation, Planck stated, 1 am unable to understand Jeans's stubbornness—he is an example of a theoretician as should never be existing, the same as Hegel was for philosophy. So much the worse for the facts if they don't fit" (Just to be clear, in case readers are moved to write me letters, Planck cast this aspersion on Hegel, not me!) Planck later became friends with another physicist who had let the facts drive him toward another revolutionary idea, Albert Einstein. In 1914, when Planck had become dean at Berlin University, he established a new professorship for Einstein there. At first Planck could not accept Einstein's remarkable proposal—made in 19O5, the same year in which he proposed the Special Theory of Relativity—that not only was light emitted by matter in quantum packets, but that light beams themselves existed as bunches of these quanta—that light itself was made up of particle-like objects, which we now call photons. Einstein was driven to this proposal to explain a phenomenon called the photoelectric effect, discovered by Philipp Lenard in 19oz—a physi- cist whose anti-Semitism would later play a key role in delaying Ein- stein's Nobel Prize, and ensuring, curiously, if perhaps poetically, that it would be not for Einstein's work on relativity, but rather on the photo- electric effect. In the photoelectric effect, light shining on a metal sur- face can knock electrons out of atoms and produce a current. However, no matter how intense the light, no electrons would be emitted if the frequency of the light was below some threshold. The moment the fre- quency was raised above that threshold, a photoelectric current would be generated. Einstein realized, correctly, that this could be explained if the light came in minimum packets of energy, with the energy proportional to the frequency of light—as Planck had postulated for light emitted by mat- ter. In this case, only light with frequencies greater than some threshold 2P_GlealerASIonEverTold_Atirdd 80 12/18/18 306 PIA EFTA00286002 The Shadows of Reality 81 frequency could contain quanta energetic enough to kick electrons out of atoms. Planck could accept the quantized emission of radiation as explaining his radiation law, but the assumption that light itself was quantumlike (i.e., particle-like) was so foreign to the common understanding of light as an electromagnetic wave that Planck balked. Only six years later, at a con- ference in Belgium, the Solvay Conference, which later became famous, was Einstein finally able to convince Planck that the classical picture of light had to be abandoned, and that quanta—aka photons—were real. Einstein was also the first to actually use a fact that he later de- nounced in his famous statement deriding the probabilistic essence of quantum mechanics and reality: "God does not play dice with the uni- verse." He showed that if atoms spontaneously (i.e., without direct cause) absorb and emit finite packets of radiation as electrons jump between discrete energy levels in atoms, then he could rederive the Planck radia- tion law. It is ironic that Einstein, who started the quantum revolution but never joined it, was also perhaps the first to use probabilistic arguments to describe the nature of matter—a strategy that the subsequent physi- cists who turned quantum mechanics into a full theory would place front and center. As a result, Einstein was one of the first physicists to demonstrate that God does play dice with the universe. To take the analogy a little further, Einstein was one of the first phys- icists to demonstrate that the classical notion of causation begins to break down in the quantum realm. Many people have taken exception to my proposal that the universe needed no cause but simply popped into existence from nothing. Yet this is precisely what happens with the light you are using to read this page. Electrons in hot atoms emit pho- tons—photons that didn't exist before they were emitted—which are emitted spontaneously and without specific cause. Why is it that we have grown at least somewhat comfortable with the idea that photons can be created from nothing without cause, but not whole universes? 2P_Glealer-StoryEverTold_Atirdd SI 12/16116 3:06 PM EFTA00286003 82 THE GREATEST STORY EVER TOLD-SO FAR The realization that electromagnetic waves were also particles began a quantum revolution that would change everything about the way we view nature. To be a particle and a wave at the same time is impossible classically—as should be clear from the earlier discussion in this chap- ter—but it is possible in the quantum world. As should also be clear, this was just the beginning. 2P_GlealestStoryEverTold_Atincld B2 12/16116 3:06 PIA EFTA00286004 Chapter 7 A UNIVERSE STRANGER THAN FICTION Therefore do not throw away your confidence, which has a great reward. -HEBREWS 10:35 Conventional wisdom might suggest that physicists love to invent crazy esoterica to explain the universe around us, either be- cause we have nothing better to do, or because we are particularly per- verse. However, as the unveiling of the quantum world demonstrates, more often than not it is nature that drags us scientists, kicking and screaming, away from the safety of what is familiar. Nevertheless, to say that the pioneers who pushed us forward into the quantum world lacked confidence would be a profound misstatement. The voyage they embarked upon was without precedent and without guides. The world they were entering defied all common sense, and classical logic, and they had to be prepared at every turn for a change in the rules. Imagine taking a road trip to another country, where the inhabitants all speak a foreign language, and the laws are not based on experiences that compare to any you have ever had in your life. Moreover imagine the traffic signals are hidden and can change from place to place. Then 83 2P_Glealer-StoryEverTaid_Atindd 03 12/16116 3:06 PIA EFTA00286005 84 THE GREATEST STORY EVER TOLD-SO FAR you can get a sense of where the young Turks who overturned our under- standing of nature in the first half of the twentieth century were heading. The analogy between exploring strange new quantum worlds and embarking on a trek through a new landscape may seemed strained, but exactly such a relationship between the two was paralleled in the life of none other than Werner Heisenberg, one of the founders of quantum mechanics, who once reminisced about an evening in the summer of 1926 on the island of Helgoland, a lovely oasis in the North Sea, when he realized he had discovered the theory: It was almost three o'clock in the morning before the final result of my computations lay before me. The energy principle had held for all the terms, and I could no longer doubt the mathematical consistency and coherence of the kind of quantum mechanics to which my calculations pointed. At first, 1 was deeply alarmed. I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior and felt almost giddy at the thought that I now had to probe this wealth of mathematical structures nature had so generously spread out before me. I was far too excited to sleep, and so, as a new day dawned, I made for the southern tip of the island, where I had been longing to climb a rock jutting out into the sea. I now did so without too much trouble and waited for the sun to rise. Heisenberg, fresh from obtaining his PhD, had moved to the distin- guished German university in Gottingen to work with Max Born to try to come up with a consistent theory of quantum mechanics (a term first used in the paper "On Quantum Mechanics" by Born in 1924). However, spring hay fever had laid Heisenberg low, and he escaped the green coun- tryside for the sea. There, he polished off his ideas about the quantum behavior of atoms and sent it off to Born, who submitted it for publication. You may be familiar with Heisenberg's name, not least because of the 2P_Glealer-StoryEverTold_Atirdd B4 12/16116 3:06 PIA EFTA00286006 A Universe Stranger than fiction 85 famous principle associated with it. The Heisenberg uncertainty principle has gained a New Age aura, providing fuel for many a charlatan to take advantage of people for whom quantum mechanics seems to offer hope of a world where any dream, no matter how outlandish, is realizable. Other familiar names, Bohr, Schrodinger, Dirac, and later Feynman and Dyson, each made great leaps into the unknown. But they weren't alone. Physics is a collaborative discipline. Too often science stories are written as if the protagonists had a sudden Aha! experience alone late at night. Heisenberg had been working on quantum mechanics for sev- eral years with his PhD supervisor, the brilliant German scientist Arnold Sommerfeld (whose students would win four Nobel Prizes, and whose postdoctoral research assistants would win three), and later with Born (who was finally recognized with a Nobel almost thirty years later), as well as a young colleague, Pascual Jordan. Every major triumph we cel- ebrate with a name and a prize is accompanied by a legion of hardwork- ing, often less heralded, individuals, each of whom moves forward the line of scrimmage by a little bit. Baby steps are the norm, not the exception. The most remarkable leaps into the unknown are often not fully ap- preciated, even by their developers, until much later. Thus Einstein, for example, never trusted his beautiful General Relativity enough to believe its prediction that the universe cannot be static but must be expanding or contracting—until observations demonstrated the expansion. And the world didn't stand on its head when Heisenberg's paper appeared. Heisenberg's friend and contemporary the brilliant and irascible physi- cist Wolfgang Pauli (another future Nobel laureate assistant to Som- merfeld) thought the work to be essentially mathematical masturbation, leading Heisenberg to respond in jocular form: You have to allow that, in any case, we are not seeking to ruin physics out of malicious intent. When you reproach us that we are such big donkeys that we have never produced anything new in physics, it may well be true. But then, you are also an equally big 2P_Glealer-StoryEverTold_Atirdd BS 12/16116 3:06 PIA EFTA00286007 86 THE GREATEST STORY EVER TOLD-SO FAR jackass because you have not accomplished it either . . . Do not think badly of me and many greetings. Physics doesn't proceed in the linear fashion that textbooks recount. In real life, as in many good mystery stories, there are false leads, mispercep- tions, and wrong turns at every step. The story of the development of quan- tum mechanics is full of them. But I want to cut to the chase here, and so I will skip over Niels Bohr, whose ideas laid out the first fundamental atomic rules of the quantum world as well as the basis for much of modern chemis- try. We'll also skip Erwin Schrtidinger, who was a remarkably colorful char- acter, fathering at least three children with various mistresses, and whose wave equation is the most famous icon of quantum mechanics. Instead I will focus first on Heisenberg, or rather not Heisenberg himself, but instead the result that made his name famous: the Heisen- berg uncertainty principle. This is often interpreted to mean that the observations of quantum systems affect their properties—which was manifest in our earlier discussions of electrons or photons passing through two slits and impinging on a screen behind them. Unfortunately this leads to the misimpression that somehow observers, in particular human observers, play a key role in quantum mechanics—a confusion that has been exploited by my Twitter combatant Deepak Cho- pra, who, in his various ramblings, somehow seems to think the universe wouldn't exist if our consciousness weren't here to measure and frame its properties. Happily the universe predates Chopra's consciousness and was proceeding pretty nicely before the advent of all life on Earth. However, the Heisenberg uncertainty principle at its heart has noth- ing to do with observers at all, even though it does limit their ability to perform measurements. It is instead a fundamental property of quan- tum systems, and it can be derived relatively straightforwardly and mathematically, based on the wave properties of these systems. Consider for example a simple wavelike disturbance with a single frequency (wavelength) oscillating as it moves along the x direction: 2P_Glealer-StoryEverTold_Atirdd 88 122/18/18 308 PIA EFTA00286008 A Universe Stranger than Fiction 87 As I have noted, in quantum mechanics particles have a wavelike character. Thanks to Max Born we recognize that the square of the am- plitude of the wave associated with a particle at any point—what we now call the wave function of the particle, following Schthdinger— determines the probability of finding the particle at that point. Because the amplitude of the oscillating wave above is more or less constant at all the peaks, such a wave, if it corresponded to the probability ampli- tude of finding an electron, would imply a more or less uniform prob- ability for finding the electron anywhere along the path. Now consider what a disturbance would look like if it was the sum of two waves of slightly different frequencies (wavelengths), moving along the x axis: When we combine the two waves, the resulting disturbance will look 2P_Glealer-StoryEverTold_Atincld 87 12/18116 3:06 PIA EFTA00286009 88 THE GREATEST STORY EVER TOLD-SO FAR Because of the slightly different wavelengths of the two waves, the peaks and troughs will tend to cancel out, or "negatively interfere" with each other everywhere except for the rare places where the two peaks occur at the same point (one of these locations is shown in the figure above). This is reminiscent of the wave interference phenomenon in the Young double-slit experiment I described earlier. If we add yet another wave of slightly different wavelength the resulting wave then looks like this: The interference washes out more of the oscillations aside from the position where the two waves line up, making the amplitude of the wave at the peak much higher there than elsewhere. You can imagine what would happen if I continue this process, con- tinuing to add just the right amount of waves with slightly different fre- quencies to the original wave. Eventually the resulting wave amplitudes will cancel out more and more at all places except for some small re- gion around the center of the figure, and at faraway places where all the peaks might again line up: 2P_Gtealer-StorgverTold_Atirdd 88 12118116 3:06 PIA EFTA00286010 A Universe Stranger than Fiction 89 The greater the number of slightly different frequencies that I add to- gether, the narrower will be the width of the largest central peak. Now, imagine that this represents the wave function of some particle. The larger the amplitude of the central peak, the greater the probability of finding the particle somewhere within the width of that peak. But the width of that central peak is still never quite zero, so the disturbance remains spread out over some small, if increasingly narrow, region. Now recall that Planck and Einstein told us that, for light waves, at least, the energy of each quantum of radiation, i.e., each photon, is di- rectly related to its frequency. Not surprisingly, a similar relation holds for the probability waves associated with massive particles, but in this case it is the momentum of the particle that is related to the frequency of the probability wave associated with the particle. Hence, Heisenberg's uncertainty relation: If we want to localize a particle over a small region, i.e., have the width of the highest peak in its wave function as narrow as possible, then we must consider that the wave function is made up by adding lots of different waves of slightly different frequencies together. But this means that the momentum of the particle, which is associated with the frequency of its wave func- tion, must be spread out somewhat. The narrower the dominant peak in space in the particle's wave function, the greater the number of different 2P_GlealerASIonEverrold_Atirdd B9 12/16116 3:06 PIA EFTA00286011 90 THE GREATEST STORY EVER TOLD-SO FAR frequencies (i.e., momenta) that must be added together to make up the final wave function. Put in a more familiar way, the more accurately we wish to determine the specific position of a particle, the greater the uncertainty in its momentum. As you can see, there is no restriction here related to actual obser- vations, or consciousness, or the specific technology associated with any observation. It is an inherent property of the fact that, in the quantum world, a wave function is associated with each particle, and for particles of a fixed specific momentum, the wave function has one specific frequency. After discovering this relation, Heisenberg was the first to provide a heuristic picture of why this might be the case, which he posed in terms of a thought experiment. To measure the position of a particle you have to bounce light off the particle, and to resolve the position with great precision requires light of a wavelength small enough to resolve this position. But the smaller the wavelength, the bigger the frequency and the higher the energy associated with the quanta of that radiation. But bouncing light with a higher and higher energy off the particle clearly changes the particle's energy and momentum. Thus, after the measure- ment is made, you may know the position of the particle at the time of the measurement, but the range of possible energies and momenta you have imparted to the particle by scattering light off it is now large. For this reason, many people confuse the Heisenberg uncertainty relation with the "observer effect," as it has become known, in quan- tum mechanics. But, as the example l have given should demonstrate, inherently the Heisenberg uncertainty principle has nothing to do with observation at all. To paraphrase a friend of mine, if consciousness had anything to do with determining the results of quantum physics experi- ments, then in reporting the results of physics experiments we would have to discuss what the experimenter was thinking about—for exam- ple, sex—when performing the experiment. But we don't. The supernova explosions that produced the atoms that make up your body and mine occurred quite nicely long before our consciousness existed. 2P_Glealer-StoryEverTold_Atirdd 90 12/16116 3:06 PIA EFTA00286012 A Universe Stranger than Fiction 91 The Heisenberg uncertainty principle epitomizes in many ways the complete demise of our classical worldview of nature. Independent of any technology we might someday develop, nature puts an absolute limit on our ability to know, with any degree of certainty, both the mo- mentum and position of any particle. But the issue is even more extreme than this statement implies. Knowing has nothing to do with it. As I described in the earlier double- slit experiment example, there is no sense in which the particle has at any time both a specific position and a specific momentum. It possesses a wide range of both, at the same time, until we measure it and thereby fix at least one of them within some small range determined by our measurement apparatus. Following Heisenberg, the next step in unveiling the quantum craziness of reality was taken by an unlikely explorer, Paul Adrien Maurice Dirac. In one sense, Dirac was the perfect man for the job. As Einstein is re- puted to have later said of him, "This balancing on the dizzying path between genius and madness is awful! When I think of Dirac, an old joke comes to mind. A young child has never spoken and his parents go to see numerous doctors to seek help, to no avail. Finally, on his fourth birthday he comes down for breakfast and looks up at his parents and says, This toast is cold!" His parents nearly burst with happiness, hug each other, and ask the child why he has never before spoken. He answers, "Up to now, everything was fine! Dirac was notoriously laconic, and a host of stories exist about his unwillingness to engage in any sort of repartee, and also about how he seemed to take everything that was said to him literally. Once, while Dirac was writing on a blackboard during one of his lectures, some- one in the audience was reputed to have raised his hand and said, 1 don't understand that particular step you have just written down? Dirac stood silent for the longest while until the audience member asked if 2P_Glealer-StoryEverTold_Atirdd 91 12/16116 3:06 PIA EFTA00286013 92 THE GREATEST STORY EVER TOLD-SO FAR Dirac was going to answer the question. To which Dirac said, "There was no question." I actually spoke to Dirac, one day, on the phone—and I was terrified. I was still an undergraduate and wanted to invite him to a meeting I was organizing for undergraduates around the country. I made the mistake of calling him right after my quantum mechanics class, which made me even more terrified. After a rambling request that I blurted out, he was silent for a moment, then gave a simple one-line response: sNo, I don't think I have anything to say to undergraduates? Personality aside, Dirac was anything but timid in his pursuit of a new Holy Grail: a mathematical formulation that might unify the two new revolutionary developments of the twentieth century, quantum mechanics and relativity. In spite of numerous efforts since Schthdinger (who derived his famous wave equation during a two-week tryst in the mountains with several of his girlfriends), and since Heisenberg had re- vealed the basic underpinning of quantum mechanics, no one had been successful at fully explaining the behavior of electrons bound deep in- side atoms. These electrons have, on average, velocities that are a fair fraction of the speed of light, and to describe them, we must use Special Relativity. Schrodinger's equation worked well to describe the energy levels of elec- trons in the outer parts of simple atoms such as hydrogen, where it pro- vided a quantum extension of Newtonian physics. It was not the proper description when relativistic effects needed to be taken into account. Ultimately Dirac succeeded where all others had failed, and the equation he discovered, one of the most important in modern particle physics, is, not surprisingly, called the Dirac equation. (Some years later, when Dirac first met the physicist Richard Feynman, whom we shall come to shortly, Dirac said after another awkward silence, "I have an equation. Do you?") Dirac's equation was beautiful, and as the first relativistic treatment of the electron, it allowed correct and precise predictions for the energy 2P_GlealerASIonEverTold_Atindd 92 12/16116 3:06 PIA EFTA00286014 A Universe Stranger than Fiction 93 levels of all electrons in atoms, the frequencies of light they emit, and thus the nature of all atomic spectra. But the equation had a fundamen- tal problem. It seemed to predict new particles that didn't exist. To establish the mathematics necessary to describe an electron mov- ing at relativistic speeds, Dirac had to introduce a totally new formalism that used four different quantities to describe electrons. As far as we physicists can discern, electrons are microscopic point particles of essentially zero radius. Yet in quantum mechanics they nev- ertheless behave like spinning tops and therefore have what physicists call angular momentum. Angular momentum reflects that once objects start spinning, they will not stop unless you apply some force as a brake. The faster they are spinning, or the more massive they are, the greater the angular momentum. There is, alas, no classical way of picturing a pointlike object such as an electron spinning around an axis. Spin is thus one of the areas where quantum mechanics simply has no intuitive classical analogue. In Dirac's relativistic extension of Schthdinger's equation, electrons can possess only two possible values for their angular momentum, which we simply call their spin. Think of electrons as either spinning around one direction, which we can call up, or spinning around the opposite direc- tion, which we can call down. Because of this, two quantities are needed to describe the configurations of electrons, one for spin-up electrons and one for spin-down electrons. After some initial confusion, it became clear that the other two quantities that Dirac needed to describe electrons in his relativistic for- mulation of quantum mechanics seemed to describe something crazy— another version of electrons with the same mass and spin but with the opposite electric charge. If, by convention, electrons have a negative charge, then these new particles would have a positive charge. Dirac was flummoxed. No such particle had ever been observed. In a moment of desperation, Dirac supposed that perhaps the positively charged particle described by his theory was actually the proton, which, 2P_Glealer-StoryEverrold_Atindd 98 12/16116 3:06 PIA EFTA00286015 94 THE GREATEST STORY EVER TOLD-SO FAR however, has a mass two thousand times larger than that of the electron. He gave some hand-waving arguments for why the positively charged particle might get a heavier mass. The larger weight could be caused by different possible electromagnetic interactions it had with otherwise empty space, which he envisaged might be populated with a possibly infinite sea of unobservable particles. This is actually not as crazy as it sounds, but to describe why would force us toward one of those twists and turns that we want to avoid here. In any case, it was quickly shown that this idea didn't hold water—first, because the mathematics didn't support this argument, and the new particles would have to have the same mass as electrons. Second, if the proton and the electron were in some sense mirror images, then they could annihilate each other so that neutral matter could not be stable. Dirac had to admit that if his theory was true, some new positive version of the electron had to exist in nature. Fortunately for Dirac, within a year of his resigned capitulation, Carl Anderson found particles in cosmic rays that are identical to electrons but have the opposite charge. The positron was born, and Dirac was heard to say, in response to his unwillingness to accept the implications of his own mathematics, "My equation was smarter than I was!" Much later he reportedly gave another reason for not acknowledging the pos- sibility of a new particle: `Pure cowardice." Dirac's "prediction," even if reluctant, was a remarkable milestone. It was the first time that, purely on the basis of theoretical notions arising from mathematics, a new particle was predicted. Think about that. Maxwell had spostdicted" the existence of light as a result of his unification of electricity and magnetism. Le Verrier had predicted the existence of Neptune by using observations of anomalies in the orbit of Uranus. But here was a prediction of a new basic feature of the universe based purely on theoretical arguments about nature at its most funda- mental scales, with no direct experimental motivation in advance. It may have seemed like a matter of faith, but it wasn't—after all, the pro- 2P_Glealer-StoryEverTold_Atirdd 94 12/16116 3:06 PIA EFTA00286016 A Universe Stranger than fiction 95 poser didn't actually believe it—and while like faith it proposed an un- observed reality, unlike faith it proposed a reality that could be tested, and it could have been wrong. The discovery of relativity by Einstein revolutionized our ideas of space and time, and the discoveries by Schthdinger and Heisenberg of the laws of quantum mechanics revolutionized our picture of atoms. Dirac's first combination of the two provided a new window on the hid- den nature of matter at much smaller scales. It heralded the beginning of the modern era in particle physics, setting a trend that has continued for almost a century. First, if the Dirac equation was applied more generally to other par- ticles, and there was no reason to believe it shouldn't be, then not only would electrons have "antiparticles," as they later became known, so would all the other known particles in nature. Antimatter has become the stuff of science fiction. Starships such as the USS Enterprise in Star Trek are invariably powered by antimatter, and the possibility of an antimatter bomb was the silliest part of the plot in the recent mystery thriller Angels & Demons. But antimatter is real. Not only was the positron discovered in cosmic rays, but antiprotons and antineutrons were discovered later as well. At a fundamental level, antimatter is not so strange. Positrons are just like electrons, after all, only with the opposite charge. They do not, as many people think, fall sup" in a gravitational field. Matter and an- timatter can interact and completely annihilate into pure radiation, which seems sinister. But particle-antiparticle annihilation is just one in a host of new possible interactions of elementary particles that can occur once we enter the subatomic realm. Moreover, one would need a large amount of antimatter to actually annihilate enough matter to even light a lightbulb with the energy produced. Ultimately, that is why antimatter is strange. It is strange because the universe we live in is full of matter, and not antimatter. A universe made of antimatter would seem identical to ours. And a universe made of 2P_Glealer-StoryEverTold_Atirdd 96 12/16116 3:06 PIA EFTA00286017 96 THE GREATEST STORY EVER TOLD-SO FAR equal amounts of matter and antimatter—which would surely seem the most sensible universe to begin with—would, unless something hap- pened in the meantime, be boring because the matter and antimatter would have long ago annihilated each other and the universe would now contain nothing but radiation. Why our world is full of matter and not antimatter remains one of the most interesting issues in modern physics. But recognizing that the real reason why antimatter is strange is simply because you never en- counter it once caused me to suggest the following analogy. Antimatter is strange in the same sense that Belgians are strange. They are certainly not intrinsically strange, but if you ever ask in a big auditorium full of people, as I have, for the Belgians to raise their hands, almost no one ever does. Except when I lectured in Belgium, as I did recently, and where I learned my analogy was not appreciated. 2P_Gtealer-StoryEverTold_Atird6 98 12/16116 3:06 PIA EFTA00286018 Chapter 8 A WRINKLE IN TIME For you are a mist that appears for a little time and then vanishes. -JAMES 4:14 Each hidden connection in nature revealed by science since the time of Galileo has led physics in new and unexpected direc- tions. The unification of electricity and magnetism revealed the hidden nature of light. Unifying light with Galileo's laws of motion revealed the hidden connections between space and time embodied in relativity. The unification of light and matter revealed the strange quantum universe. And the unification of quantum mechanics and relativity revealed the existence of antiparticles. Dirac's discovery of antiparticles came as a result of his "guessing" the correct equation to describe the relativistic quantum interactions of electrons with electromagnetic fields. He had little physical intuition to back it up, which is one reason why Dirac himself and others were initially so skeptical of his result. Clarifying the physical imperative for antimatter came through the work of one of the most important physi- cists of the latter half of the twentieth century, Richard Feynman. Feynman could not have been more different from Dirac. While 97 2P_Glealer-StoryEverrold_Atindd 97 12/1006 3:06 PM EFTA00286019 98 THE GREATEST STORY EVER TOLD-SO FAR Dirac was taciturn in the extreme, Feynman was gregarious and a charming storyteller. While Dirac rarely, if ever, intentionally joked, Feynman was a prankster who openly enjoyed every aspect of life. While Dirac was too shy to meet women, Feynman, after the death of his first wife, sought out female companions of every sort. Yet, physics breeds strange bedfellows, and Feynman and Dirac will forever be intel- lectually linked—once again by light. Together they helped complete the description of the long-sought quantum theory of radiation. Coming a generation after Dirac, Feynman was in awe of him and spoke of him as one of his physics heroes. Therefore, appropriately, a short 1939 paper that Dirac wrote, in which he suggested a new ap- proach to quantum mechanics, would inspire the work that ultimately won Feynman a Nobel Prize. Heisenberg and Schrodinger had explained how systems behave quantum mechanically starting with some initial state of the system and calculating how it evolves over time. But, once again, light provides the key to another way to think about quantum systems. We are accustomed to thinking of light as always going in straight lines. But it doesn't. This is manifest when you view a mirage on a long straight highway on a hot day. The road looks wet way up ahead because light from the sky refracts, bending as it crosses the many successive layers of warm air near the surface of the road, until it heads back up to your eye. The French mathematician Pierre de Fermat showed in ikso another way to understand this phenomenon. Light travels faster in warmer, less dense air than it does in colder air. Because the warmest air is near the surface, the light takes less time to get to your eye if it travels down near 2P_Glealer-StoryEverTold_Atirdd 98 12/18/18 3:08 PIA EFTA00286020 A Wrinkle in Time 99 the ground and then returns up to your eye than it would if it came di- rectly in a straight line to your eye. Fermat formulated a principle, called the Principle of Least Time, which says that, to determine the ultimate trajectory of any light ray, you simply need to examine all possible paths from A to B and find the one that takes the least time. This makes it sound as if light has intentionality, and I resisted the temptation to say light considers all paths and chooses the one that takes the least time because I fully expect that Deepak Chopra would later quote me as implying that light has consciousness. Light does not have consciousness, but the mathematical result makes it appear as if light chooses the shortest distance. Now, recall that in quantum mechanics, light rays and electrons do not act as if they take a single trajectory to go from one place to an- other—they take all possible trajectories at the same time. Each trajec- tory has a specific probability of being measured, and the classical, least time, trajectory has the largest probability of all. In 1939, Dirac suggested a way of calculating all such probabilities and summing them to determine the quantum mechanical likelihood that a particle that starts out at A will end up at B. Richard Feynman, as a gradu- ate student, after learning about Dirac's paper at a beer party, mathemati- cally derived a specific example demonstrating that this idea worked. By taking Dirac's hint as a starting point, Feynman derived results that were identical to those that one would derive using the Schrodinger or Heisen- berg pictures, at least in simple cases. More important, Feynman could use this new `sum over paths" formula to handle quantum systems that couldn't easily be described or analyzed by the other methods. Eventually Feynman refined his mathematical technique to help push forward Dirac's relativistic equation for the quantum behavior of electrons and to produce a fully consistent quantum mechanical theory of the interaction between electrons and light. For that work, establish- ing the theory known as quantum electrodynamics (QED), he shared the Nobel Prize in 1963 with Julian Schwinger and Sin-Itiro Tomonaga. 2P_Glealer-StoryEverTold_Atindd 99 12/16116 3:06 PIA EFTA00286021 100 THE GREATEST STORY EVER TOLD-SO FAR Even before completing this work, however, Feynman described an intuitive physical reason why relativity, when combined with quantum mechanics, requires the existence of antiparticles. Consider an electron moving along on a possible "quantum" trajec- tory. What does this mean? An electron takes all possible trajectories between two points as long as I am not measuring it while it travels. Among these are trajectories that are classically not allowed because they would violate rules such as the limitation that objects cannot travel faster than light (arising from relativity). Now the Heisenberg uncer- tainty principle says that even if I try to measure the electron along its trajectory over some short time interval, some intrinsic uncertainty in the velocity of the electron remains that can never be overcome. Thus even if I measure the trajectory at various points, I cannot rule out some weird nonclassical behavior during these intervals. Now, imagine the trajectory shown below: time For the short time in the middle of the time interval shown the elec- tron is traveling faster than the speed of light. But Einstein tells us that time is relative, and different observers will measure different intervals between events. And if a particle is travel- ing faster than light in one reference frame, in another reference frame it will appear to be traveling backward in time, as shown below (this is one of the reasons relativity restricts all observed particles to travel at speeds less than or equal to the speed of light: 2P_Glealer-StoryEverTold_Atird0 100 12/16116 3:06 PIA EFTA00286022 A Wrinkle in Time 101 Ttime Feynman recognized that in the latter frame this would look like an electron moving forward in time for a little while, then moving back- ward in time, then moving forward in time. But what does an electron moving backward in time appear like? Since the electron is negatively charged, a negative charge moving backward in time to the right is equivalent to a positive charge moving forward in time to the left. Thus, the picture is equivalent to the following.. 7% 7 In this picture one starts with an electron moving forward in time, and then sometime later an electron and a particle that appears like an electron but has the opposite charge suddenly appear out of empty space, and the positively charged particle moves to the left, again for- ward in time, until it encounters the original electron and the two an- nihilate, leaving only one electron left over to continue moving. All of this happens on a timescale that cannot be observed directly, for if it could be, then this strange behavior, violating the tenets of rela- tivity, would be impossible. Nevertheless, you can be assured that inside 2P_Glealer-StoryEverrold_Atirdd 101 12/16116 3:06 PIA EFTA00286023 102 THE GREATEST STORY EVER TOLD-SO FAR the paper in the book you are now reading, or behind the screen of your ebook, these kinds of processes are happening all the time. Nevertheless, if such a trajectory is possible in the invisible quan- tum world, then antiparticles must exist in the visible world—particles identical to known particles but with opposite electric charge (which appear in the equations of this theory as if they were particles going backward in time). This also makes it possible for particle-antiparticle pairs to spontaneously appear out of empty space, as long as they an- nihilate in a time period quickly enough so that their brief existence cannot be measured. With this line of reasoning, not only did Feynman give a physical argument for the existence of antiparticles required by the unification of relativity and quantum mechanics, he also demonstrated that at any time we cannot say that only one or two particles are in some region. A potentially infinite number of "virtual" particle-antiparticle pairs— pairs of particles whose existence is so fleeting that they cannot be di- rectly observed—can be appearing and disappearing spontaneously on timescales so short that we cannot measure them. This picture sounds so outrageous that you should be incredulous. After all, if we cannot measure these virtual particles directly, how can we claim that they exist? The answer is that while we cannot detect the effects of these virtual particle-antiparticle pairs directly, we can indirectly infer their presence because they can indirectly affect the properties of systems we can observe. The theory in which these virtual particles are incorporated, along with the electromagnetic interactions of electrons and positrons, called quantum electrodynamics, is the best scientific theory we have so far. Predictions based on the theory have been compared with observations, and they agree to more than ten decimal places. In no other area of sci- ence can this level of accuracy be obtained in the comparison between observation and prediction, based on the direct applications of funda- mental principles on the most basic scales we can describe. 2P_Glealer-StoryEverrold_Atirdd 102 12/16116 3:06 PIA EFTA00286024 A Wrinkle in Time 103 But the agreement between theory and observation is only possible if the effects of virtual particles are included. Indeed, the very phenome- non of virtual particles implies that, in quantum theory, forces between particles are always conveyed by the exchange of virtual particles, in a way I shall now describe. In quantum electrodynamics, electromagnetic interactions occur by the absorption or emission of the quanta of electromagnetism, namely photons. Following Feynman, we can diagram this interaction as an electron emitting a wavy "virtual" photon (y) and changing direction: Then, the electric interaction between two electrons can be dia- grammed as: 2P_Glealer/StorgverTold_Atind0 103 1216116 306 PIA EFTA00286025 104 THE GREATEST STORY EVER TOLD-SO FAR In this case, the electrons interact with each other by exchanging a virtual photon, one that is spontaneously emitted by the electron on the left and absorbed by the other in so short a time that the photon cannot be observed. The two electrons repel each other and move apart after the interaction. This also explains why electromagnetism is a long-range force. The Heisenberg uncertainty principle tells us that if we measure a system for some time interval, then there is an associated uncertainty in the mea- sured energy of the system. Moreover, as the time interval gets bigger, the associated uncertainty in energy gets smaller. Because the photon is massless, a virtual massless photon, using Einstein's relation between mass and energy, can carry an arbitrarily small amount of energy when it is created. This means that it can travel an arbitrarily long time— and therefore an arbitrarily long distance—before being absorbed, and it will still be protected by the uncertainty principle, as the energy it can carry is so small that no visible violation of the conservation of en- ergy will occur. Thus, an electron on Earth can emit a virtual photon that could travel to Alpha Centauri, four light-years away, and that pho- ton can still produce a force on an electron there that absorbs it. If the photon weren't massless, however, but had some rest mass, m, it would carry with it a minimum energy, given by E = mo, and could therefore only travel a finite distance (i.e., over a finite time interval) before it would have to be absorbed without producing any visible violation of the conservation of energy. These virtual particles have a potential problem, however. If one particle can be exchanged or one virtual particle-antiparticle pair can spontaneously appear out of the vacuum, then why not two or three or even an infinite number? Moreover, if virtual particles must disap- pear in a time that is inversely proportional to the energy they carry, then what stops particles from popping out of empty space carrying an arbitrarily large amount of energy and existing for an arbitrarily small time? 2P_Glealer-StoryEverTold_Atincld 104 12/16116 3:06 PIA EFTA00286026 A Wrinkle in Time 106 When physicists tried to take into account these effects, they en- countered infinite results in their calculations. The solution? Ignore them. Actually not ignore them, but systematically sweep the infinite pieces of calculations under the rug, leaving only finite bits left over. This begs the questions of how one knows which finite parts to keep, and why the whole procedure is justified. The answer took quite a few years to get straight, and Feynman was one of the group who figured it out. But for many years after, including up to the time he won the Nobel Prize in 1965, he viewed the whole ef- fort as a kind of trick and figured that at some point a more fundamental solution would arise. Nevertheless, a good reason exists for ignoring the infinities intro- duced by virtual particles with arbitrarily high energies. Because of the Heisenberg uncertainty principle, these energetic particles can propa- gate only over short distances before disappearing. So how can we be sure that our physical theories, which are designed to explain phenom- ena at scales we can currently measure, actually operate the same way at these very small scales? Maybe new physics, new forces, and new el- ementary particles become relevant at very small scales? If we had to know all the laws of physics down to infinitesimally small scales in order to explain phenomena at the much larger scales we experience, then physics would be hopeless. We would need a theory of everything before we could ever have a theory of something. Instead, reasonable physical theories should be ones that are insensi- tive to any possible new physics occurring at much smaller scales than the scales that the original theories were developed to describe. We call these theories renormalizable, since we "renormalize" the otherwise in- finite predictions, getting rid of the infinities and leaving only finite, sensible answers. Saying that this is required is one thing, but proving that it can be done is something else entirely. This procedure took a long time to get 2P_Glealer-StoryEverTold_Atirdd 'OS 12/18/18 3:08 PIA EFTA00286027 106 THE GREATEST STORY EVER TOLD-SO FAR straight. In the first concrete example demonstrating that it made sense, the energy levels of hydrogen atoms were precisely calculated, which allowed a correct prediction of the spectrum of light emitted and ab- sorbed by these atoms as measured in the laboratory. Although Feynman and his Nobel colleagues elucidated the mecha- nism to mathematically implement this technique of renormalization, the proof that quantum electrodynamics (QED) was a "renormalizable" theory, allowing precise predictions of all physical quantities one could possibly measure in the theory, was completed by Freeman Dyson. His proof gave QED an unprecedented status in physics. QED provided a complete theory of the quantum interactions of electrons and light, with predictions that could be compared with observations to arbitrarily high orders of precision, limited only by the energy and determination of the theorists doing the calculations. As a result, we can predict the spectra of light emitted by atoms to exquisite precision and design laser systems and atomic clocks that have redefined accuracy in measuring distance and time. The predictions of QED are so precise that we can search in experiments for even minuscule departures from them and probe for possible new physics that might emerge as we explore smaller and smaller scales of distance and time. With fifty years of hindsight, we now also understand that quantum electrodynamics is such a notable physical theory in part because of a "symmetry" associated with it. Symmetries in physics probe deep char- acteristics of physical reality. From here on into the foreseeable future, the search for symmetries is what governs the progress of physics. Symmetries reflect that a change in the fundamental mathematical quantities describing the physical world produce no change in the way the world works or looks. For example, a sphere can be rotated in any direction by any angle, and it still looks precisely the same. Nothing about the physics of the sphere depends on its orientation. That the laws of physics do not change from place to place, or time to time, is of deep significance. The symmetry of physical law with time—that nothing 2P_Glealer-StoryEverTold_Atincld t06 12/16116 3:06 PIA EFTA00286028 A Wrinkle in Time 107 about the laws of physics appears to change with time—results in the conservation of energy in the physical universe. In quantum electrodynamics, one fundamental symmetry is in the nature of electric charges. What we call "positive" and "negative" are clearly arbitrary. We could change every positive charge in the universe to negative, and vice versa, and the universe would look and behave pre- cisely the same. Imagine, for example, that the world is one giant chessboard, with black and white squares. Nothing about the game of chess would be changed if I changed black into white, and white into black. The white pieces would become black pieces and vice versa, and otherwise the board would look identical. Now, precisely because of this symmetry of nature, the electric charge is conserved: no positive or negative charge can spontaneously appear in any process, even due to quantum mechanics, without an equal and opposite charge appearing at the same time. For this rea- son, virtual particles are only produced spontaneously in empty space in combination with antiparticles. It is also why lightning storms occur on Earth. Electric charges build up on Earth's surface because storm clouds build up large negative charges at their base. The only way to get rid of this charge is to have large currents flow from the ground upward into the sky. The conservation of charge resulting from this symmetry can be un- derstood using my chessboard analogy. That every white square must be located next to a black square means that whenever I switch black and white, the board ultimately looks the same. If I had two black squares in a row, which would mean the board had some net "blackness," then "black" and "white" would no longer be equivalent arbitrary labels. Black would be physically different from white. In short, the symmetry be- tween black and white on the board would be violated. Bear with me now, because I am about to introduce a concept that is much more subtle, but much more important. It's so important that 2P_Glealer-StoryEverTold_AC.incld 107 12/16116 3:06 PIA EFTA00286029 108 THE GREATEST STORY EVER TOLD-SO FAR essentially all of modern physical theory is based on it. But it's so subtle that without using mathematics, it is hard to describe. It is so subtle that its ramifications are still being unraveled today, more than a hundred years since it was first suggested. So, don't be surprised if it takes one or two readings to fully get your head around the idea. It has taken physi- cists much of the past century to get their heads around it. This symmetry is called gauge symmetry for an obscure historical reason I shall describe a bit later. But the strange name is irrelevant. It is what the symmetry implies that is important: Gauge symmetry in electromagnetism says that I can actually change my definition of what a positive charge is locally at each point of space without changing the fundamental laws associated with electric charge, as long as I also somehow introduce some quantity that helps keep track of this change of definition from point to point. This quantity turns out to be the electromagnetic field. Let's try to parse this using my chessboard analogy. The global sym- metry I described before changes black to white everywhere, so when the chessboard is turned by 180 degrees, it looks the same as it did be- fore and the game of chess is clearly not affected. Now, imagine instead that I change black to white in one square, and I don't change white to black in the neighboring square. Then the board will have two adjacent white squares. This board, with two ad- jacent white squares, clearly won't look the same as it did before. The game cannot be played as it was before. But hold on for a moment. What if I have a guidebook that tells me what game pieces should do every time they encounter adjacent squares where one color has been changed but not the next. Then the rules of the game can remain the same, as long as I consult the guidebook each time I move. This guidebook therefore allows the game to proceed as if nothing were changed. 2P_Glealer-StoryEverTold_Atind0 108 12/18116 3:06 PIA EFTA00286030 A Wrinkle in Time 109 In mathematics, a quantity that ascribes some rule associated with each point on a surface like a chessboard is called a function. In physics, a function defined at every point in our physical space is called a field, such as, for example, the electromagnetic field, which describes how strong electric and magnetic forces are at each point in space. Now here's the kicker. The properties that must characterize the form of the necessary function (which allows us to change our definition of electric charge from place to place without changing the underlying phys- ics governing the interaction of electric charges) are precisely those that characterize the form of the rules governing electromagnetic fields. Put another way, the requirement that the laws of nature remain in- variant under a gauge transformation—namely some transformation that locally changes what I call positive or negative charge—identically requires the existence of an electromagnetic field that is governed by precisely by Maxwell's equations. Gauge invariance, as it is called, com- pletely determines the nature of electromagnetism. This presents us with an interesting philosophical question. Which is more fundamental, the symmetry or the physical equations that man- ifest the symmetry? In the former case, where this gauge symmetry of nature requires the existence of photons, light, and all the equations and phenomena first discovered by Maxwell and Faraday, then God's appar- ent command "Let there be light" becomes identical with the command "Let electromagnetism have a gauge symmetry." It is less catchy, per- haps, but nevertheless true. Alternatively, one could say that the theory is what it is, and the dis- covery of a mathematical symmetry in the underlying equations is a happy accident. The difference between these two viewpoints seems primarily se- mantic, which is why it might interest philosophers. But nature does provide some guidance. If quantum electrodynamics were the only theory in nature that respected such a symmetry, the latter view might seem more reasonable. 2P_Glealer-StoryEverTold_Atind0 109 12/16116 3:06 PIA EFTA00286031 110 THE GREATEST STORY EVER TOLD-SO FAR But every known theory describing nature at a fundamental scale reflects some type of gauge symmetry. As a result, physicists now tend to think of symmetries of nature as fundamental, and the theories that then describe nature as being restricted in form to respect these sym- metries, which in turn then reflect some key underlying mathematical features of the physical universe. Whatever one might think of regarding this epistemological issue, what matters in the end to physicists is that the discovery and applica- tion of this mathematical symmetry, gauge symmetry, has allowed us to discover more about the nature of reality at its smallest scales than any other idea in science. As a result, all attempts to go beyond our current understanding of the four forces of nature, electromagnetism, the two forces associated with atomic nuclei, the strong and weak forces, which we shall meet shortly, and gravity—including the attempt to create a quantum theory of gravity—are built on the mathematical underpin- nings of gauge symmetry. • • • That gauge symmetry has such a strange name has little to do with quantum electrodynamics and is an anachronism, related to a property of Einstein's General Theory of Relativity, which, like all other funda- mental theories, also possesses gauge symmetry. Einstein showed that we are free to choose any local coordinate system we want to describe the space around us, but the function, or field, that tells us how to con- nect these coordinate systems from point to point is related to the un- derlying curvature of space, determined by the energy and momentum of material in space. The coupling of this field, which we recognize as the gravitational field, to matter, is precisely determined by the invari- ance of the geometry of space under the choice of different coordinate systems. The mathematician Hermann Weyl was inspired by this symmetry of General Relativity to suggest that the form of electromagnetism might 2P_Glealer-StoryEverTold_Aairdd 110 12/16116 3:06 PIA EFTA00286032 A Wrinkle in Time 111 also reflect an underlying symmetry associated with physical changes in length scales. He called these different "gauges," inspired by the various track gauges of railroads. (Einstein, and Sheldon on The Big Bang The- ory, aren't the only physicists who have been inspired by trains.) While Weyl's guess turned out to be incorrect, the symmetry that does apply to electromagnetism became known as gauge symmetry. Whatever the etymology of the name, gauge symmetry has become the most important symmetry we know of in nature. From a quantum perspective—in the quantum theory of electromagnetism, quantum electrodynamics—the existence of gauge symmetry becomes even more important. It is the essential feature that ensures that QED is sensible. If you think about the nature of symmetry, then it begins to make sense that such a symmetry might ensure that quantum electrodynam- ics makes sense. Symmetries tell us, for example, that different parts of the natural world are related, and that certain quantities remain the same under various types of transformations. A square looks the same when we rotate it ninety degrees because the sides are all the same length and the angles at each corner are the same. So, symmetry can tell us that different mathematical quantities that result from physical calculations, such as the effects of many virtual particles, and many vir- tual antiparticles, for example, can have the same magnitude. They may also have opposite signs so that they might cancel exactly. The existence of this symmetry is what can require such exact cancellations. In this way, one might imagine that in quantum electrodynamics the nasty terms that might otherwise give infinite results can cancel with other potentially nasty terms, and all the nastiness can disappear. And this is precisely what happens in QED. The gauge symmetry en- sures that any infinities that might otherwise arise in deriving physical predictions can be isolated in a few nasty terms that can be shown by the symmetry to either disappear or to be decoupled from all physically measurable quantities. This profoundly important result, proven by decades of work by some 2P_Glealer-StoryEverTold_Atindd 111 12/16116 3:06 PIA EFTA00286033 112 THE GREATEST STORY EVER TOLD-SO FAR of the most creative and talented theoretical physicists in the world, es- tablished QED as the most precise and preeminent quantum theory of the twentieth century. Which made it all the more upsetting to discover that, while this mathematical beauty indeed allowed a sensible understanding of one of nature's fundamental forces—electromagnetism—other nastiness began when considering the forces that govern the behavior of atomic nuclei. 2P_Glealer-Storgverrold_Atirdd 112 12/16116 3:06 PIA EFTA00286034 Chapter 9 DECAY AND RUBBLE There is no new thing under the sun. -ECCLESIASTES 1:9 When I first learned that we human beings are radioac- tive, it shocked me. I was in high school listening to a lecture by the re- markable polymath and astrophysicist Tommy Gold, who had done pioneering work in cosmology, pulsars, and lunar science, and he in- formed us that the particles that made up most of the mass of our bod- ies, neutrons, are unstable, with a mean lifetime of about ten minutes. Given, I hope, that you have been reading this book for longer than ten minutes, this may surprise you too. The resolution of this seeming paradox is one of the first and most wonderful of the gorgeous accidents of nature that make our existence possible. As we continue to explore more deeply the question "Why are we here?," this accident will loom large on the horizon. While the neutron may seem far removed from light, which has been the centerpiece of our story thus far, we shall see that the two are ultimately deeply connected. The decay of neutrons— responsible for the "beta decay" of unstable nuclei—required physicists to move beyond their simple and elegant theories of light and open up new fundamental areas of the universe for investigation. 113 2P_Glealer-StoryEverrold_Atindd 113 12/16116 3:06 PIA EFTA00286035 114 THE GREATEST STORY EVER TOLD-SO FAR But I am getting ahead of myself. In 1929, when Dirac first wrote down his theory of electrons and radiation, it looked as if it might end up being a theory of almost every- thing. Aside from electromagnetism, the only other force in town was gravity, and Einstein had just made great strides in understanding it. Elementary particles consisted of electrons, photons, and protons, to- gether comprising all the objects that appeared necessary to understand atoms, chemistry, life, and the universe. The discovery of antiparticles upset the applecart somewhat, but since Dirac's theory had effectively predicted them (even if Dirac him- self had to catch up with the theory), this was more like a speed bump on the road to reality than a roadblock or detour. Then came 1932. Up to that time, scientists had presumed that atoms were composed entirely of protons and electrons. This posed a bit of a problem, however, because the masses of atoms didn't quite add up. In 1911 Rutherford discovered the existence of the atomic nucleus, contain- ing almost all the mass of atoms in a small region one hundred thou- sand times smaller than the size of the orbits of the electrons. Following that discovery, it became clear that the mass of heavy nuclei was just a bit more than twice the mass that could be accounted for if the number of protons in the nucleus equaled the number of electrons orbiting the nucleus, ensuring that atoms would be electrically neutral. The proposed solution to this conundrum was simple. Actually twice as many protons were in the nucleus as electrons surrounding it, but just the right number of electrons were trapped inside the nucleus, so that again the total electric charge of the atom would be equal to zero. However, quantum mechanics implied that the electrons couldn't be confined within the nucleus. The argument is a bit technical, but it goes something like this: If elementary particles have a wavelike character, then if one is going to confine them to a small distance, the magnitude of their wavelength must be smaller than the confinement scale. But the wavelength associated with a particle is, in quantum mechanics, 2P_Glealer-StoryEverTold_Atincld 114 12/16116 306 PIA EFTA00286036 Decay and Rubble 115 inversely proportional to the momentum carried by the particle, and hence also inversely proportional to the energy carried by the particle. If electrons were confined to a region the size of an atomic nucleus, the energy they would need to possess would be about a million times the energy associated with the characteristic energies released by electrons as they jump between energy levels in their atomic orbits. How could they achieve such energies? They couldn't. For, even if electrons were tightly bound to protons within nuclei by electronic forces, the binding energy that would be released in this process as they "fell" into the nucleus would be more than ten times smaller than the energy needed to confine the quantum mechanical electron wave func- tion to a region contained within the nucleus. Here too the numbers just didn't add up. Physicists at the time were aware of the problem, but lived with it. I suspect that an agnostic approach was deemed prudent, and physi- cists were willing to suspend disbelief until they knew more, because the issues involved the cutting-edge physics of quantum mechanics and atomic nuclei. Instead of proposing exotic new theories (there were probably some at the margins that I am not aware of), the community was eventually driven by experiments to overcome its natural hesitation to take the logical next step: to assume nature was more complicated than had thus far been revealed. In 1930, about the time that Dirac was coming to grips with the pos- sibility that his antiparticles weren't really protons, a series of experi- ments provided just the clues that were needed to unravel the nuclear paradox. The poetry of the discoveries was rivaled only by the drama in the private lives of the researchers. Max Planck had helped pioneer the quantum revolution by resolving the paradox of the spectrum of radiation emitted by atomic systems. So it was fitting that Planck should indirectly help resolve the paradoxical makeup of the nucleus. While he didn't himself spearhead the relevant research, he recognized the talents of a young student of mathemat- 2P_Glealer-StoryEverTold_Atindd vIS 12/16116 3:06 PIA EFTA00286037 116 THE GREATEST STORY EVER TOLD-SO FAR ics, physics, chemistry, and music at the University of Berlin, Walther Bothe, and in 1912 Planck accepted him as a doctoral student and men- tored him throughout the rest of his career. Bothe was spectacularly lucky to be mentored by Planck and, shortly thereafter, by Hans Geiger, of Geiger counter fame. Geiger, in my mind, is one of the most talented experimental physicists to have been over- looked for a Nobel Prize. Geiger had begun his career by doing the experiments, with Ernest Marsden, that Ernest Rutherford utilized to discover the existence of the atomic nucleus. Geiger had just returned from England, where ■ worked with Rutherford, to direct a new labo- ratory in Berlin, and one of his first acts was to hire Bothe as an as- sistant. There Bothe learned to focus on important experiments, using simple approaches that yielded immediate results. After an "involuntary vacation" of five years, as a prisoner of war in Siberia during the First World War, Bothe returned and built a remark- able collaboration with Geiger, eventually succeeding him as director of the laboratory. During their time together they pioneered the use of "coincidence methods" to explore atomic, and eventually nuclear, phys- ics. Using different detectors located around a target, and using care- ful timing, they could look for simultaneous events, signaling that the source had to be a single atomic or nuclear decay. In 1930 Bothe and his assistant Herbert Becker observed something completely new and unexpected. While bombarding beryllium nuclei with products of nuclear decay called alpha particles (already known to be the nuclei of helium), the two observed the emission of a completely new form of high-energy radiation. This radiation had two unique fea- tures. It was more penetrating than the most energetic gamma rays, but like gamma rays, the radiation was composed of electrically neutral particles so that it did not ionize atoms as it passed through matter. News of this surprising discovery made its way to other physics labo- ratories throughout Europe. Bothe and Becker had initially proposed that this radiation was some new sort of gamma ray. In Paris, Irene 2P_Glealer-StoryEverTold_Atindd US 12116116 306 PIA EFTA00286038 Decay and Rubble 117 Joliot-Curie, the daughter of famed physicist Marie Curie, and Irene's husband, Frederic, replicated Bothe and Becker's results and explored the radiation in more detail. In particular, they found that when it bom- barded a paraffin target, it knocked out protons with incredible energy. This observation made it clear that the radiation couldn't be a gamma ray. Why? The answer is relatively simple. If you throw a piece of popcorn at an oncoming truck, you are unlikely to stop the truck or even break a win- dow. That is because the popcorn, even if you throw it with great energy, carries little momentum because the popcorn is light. To stop a truck you have to change its momentum by a large amount because, even if it is moving slowly, it is heavy. To stop a truck or knock a heavy object off the truck, you have to throw a big rock. Similarly, to knock out a heavy particle such as a proton from paraf- fin, a gamma ray, made of massless photons, would have to carry great energy (so that the momentum carried by the individual photons was large enough to kick out a heavy proton), and not enough energy was available, by an order of magnitude at least, in any known nuclear-decay processes for this. Surprisingly, the Joliot-Curies (they were modern and both adopted the same hyphenated last name) were probably loath, like Dirac, to pro- pose new elementary particles to explain data—since protons, electrons, and photons were not only familiar, but sufficient up to that time to ex- plain everything known, including exotic quantum phenomena associ- ated with atoms. So, Irene and Fr€deric didn't make the now-obvious proposal that maybe a new neutral massive particle was being produced in the decays that Bothe and Becker had discovered. Unfortunately, a similar timidity caused the Joliot-Curies to fail to claim discovery of the positron—in spite of having actually observed it in their experiments before Carl Anderson reported his own discovery somewhat later. It fell to the physicist James Chadwick to push things further. Chad- wick clearly had a great nose for physics, but his political acumen was 2P_Glealer-StorgverTold_Atirdd 117 12/16116 3:06 PIA EFTA00286039 118 THE GREATEST STORY EVER TOLD-SO FAR not so sharp. After graduation from the University of Manchester with a master's degree in 1913, working with Rutherford, he obtained a fel- lowship that would allow him to study anywhere. So he went to Berlin to work with Geiger. He couldn't have picked a better mentor, and he began to do important studies of radioactive decays. Unfortunately, the First World War broke out while Chadwick was in Germany, and he spent the next four years in an internment camp. Eventually he returned to Cambridge, where Rutherford had since moved, to complete his PhD under Rutherford's direction. Following this Chadwick stayed on to work with Rutherford and help direct the Caven- dish laboratory there. While he was aware of Bothe and Becker's results and even reproduced them, only when one of his students informed him of the Joliot-Curies results did Chadwick became convinced, using the energy argument I mentioned above, that the radiation that had been observed had to result from a new neutral particle—of mass comparable to that of the proton—that might reside in atomic nuclei, an idea he and Rutherford had been germinating for years. Chadwick reproduced and extended the Joliot-Curies' experiments, bombarding targets other than paraffin to explore the outgoing protons. He confirmed not only that the energetics of the collisions made it im- possible for the source to be gamma rays, but also that the interaction strength of the new particles with nuclei was far greater than would be predicted for gamma rays. Chadwick didn't dawdle. Within two weeks of beginning his experi- ments in 1932, he sent a letter to Nature entitled "Possible Existence of a Neutron" and followed this up with a more detailed article sent to the Royal Society. The neutron, which we now know makes up most of the mass of heavier nuclei, and thus most of the mass in our bodies, had been discovered. For his discovery he was awarded the Nobel Prize in Physics three years later, in 1935. In a kind of poetic justice, three of the people whose experiments had made Chadwick's results possible—but who missed 2P_Glealer-StoryEverTold_Atindd 118 12/16116 3:06 PIA EFTA00286040 Decay and Rubble 119 out on identifying the neutron—were awarded Nobel Prizes for other work. Bothe won the Nobel Prize in 1954 for his work on using coinci- dences between observed events in different detectors to explore the de- tailed nature of nuclear and atomic phenomena. Both Irene and Frederic Joliot-Curie, who barely missed out on two other Nobel Prize—winning discoveries, won the Nobel Prize in Chemistry in 193s for their discov- ery of artificial radioactivity—which was later an essential ingredient in the development of both nuclear power and nuclear weapons. Interest- ingly, only after winning the Nobel Prize was Irene awarded a profes- sorship in France. With the two Nobel Prizes for her mother, Marie, the Curie family garnered a total of five Nobel Prizes, the most that have ever been received by a single family. After his discovery Chadwick set out to measure the mass of the neutron. His first estimate, in 1933, suggested a mass of slightly less than the sum of the masses of a proton and an electron. This reinforced the idea that perhaps the neutron was a bound state of these two particles, and the mass difference, using Einstein's relation E = mca, was due to the energy lost in binding them together. However, after several conflicting measurements by other groups, further analysis a year later by Chad- wick using a nuclear reaction induced by gamma rays—which allowed all energies to be measured with great precision—definitely indicated that the neutron was heavier than the sum of the proton and electron masses, even if barely so, with the mass difference being less than 0.1 percent. It is said that `close only matters when tossing horseshoes or hand grenades, but the closeness in mass between the proton and the neutron matters a great deal. It is one of the key reasons we exist today. Henri Becquerel discovered radioactivity in uranium in 1896, and only three years later Ernest Rutherford discerned that radioactivity oc- curred in two different types, which he labeled alpha and beta rays. A year later gamma rays were discovered, and Rutherford confirmed them as a new form of radiation in 1903, when he gave them their name. Bec- 2P_Glealer-StoryEverTold_Atirdd 119 12/16116 3:06 PIA EFTA00286041 120 THE GREATEST STORY EVER TOLD-SO FAR querel determined in 1900 that the "rays" in beta decay were actually electrons, which we now know arise from the decay of the neutron. In beta decay a neutron splits into a proton and an electron, which, as I describe below, would not be possible if the neutron weren't slightly heavier than protons. What is surprising about this neutron decay is not that it occurs, but that it takes so long. Normally the decay of unstable elementary particles occurs in millionths or billionths of a second. Iso- lated neutrons live, on average, more than ten minutes. One of the chief reasons that neutrons live so long is that the mass of the neutron is only slightly more than the sum of the masses of a proton plus an electron. Thus, there is only barely enough energy available, via the neutron's rest mass, to allow it to decay into these particles and still conserve energy. (The other reason is that a neutron doesn't decay into only a proton plus an electron. It decays into three particles ... stay tuned!) While ten minutes may be an eternity on atomic timescales, it is pretty short compared to a human life or the lifetime of atoms on Earth. Returning to the puzzle I mentioned at the beginning of this chapter, what gives? How can we be largely made up of neutrons if they decay before the first commercial break in a thirty-minute TV show? The answer again lies in the extreme closeness of the neutron and proton masses. A free neutron decays in ten minutes or so. But consider a neutron bound inside an atomic nucleus. Being bound means that it takes energy to kick it out of the nucleus. But that means that it loses energy when it gets bound to the nucleus in the first place. But, Einstein told us that the total energy of a massive particle is proportional to its mass, via E = me. That means that, if the neutron loses energy when it gets bound in a nucleus, its mass gets smaller. But since its mass when it is isolated is just a smidgen more than the sum of the masses of a proton and an electron, when it loses mass, it no longer has sufficient energy to decay into a proton and an electron. If it were to decay into a proton, it would have to either release enough energy to also eject the proton from the nucleus, which, given standard nuclear-binding energies, it would 2P_GrealesiSleryfverTold_AC.indd 120 12/10/16 306 PIA EFTA00286042 Decay and Rubble 121 not have, or else release enough energy to allow the new proton to re- main in a new stable nucleus. Since the new nucleus would be that of a different element, adding one additional positive charge to the nucleus also generally requires more energy than the minute amount available when a neutron decays. As a result, the neutron and most atomic nuclei containing neutrons remain stable. The entire stability of the nuclei that make up everything we see, in- cluding most of the atoms in our body, is an accidental consequence of the fact that the neutron and proton differ in mass by only o.i percent, so that a small shift in the mass of the former, when embedded in nuclei, means it can no longer decay into the latter. That is what I learned from Tommy Gold. It still amazes me when I think about it. The existence of complex matter, the periodic table, everything we see, from distant stars to the keyboard I am typing this on—hinges on such a remarkable coinci- dence. Why? Is it an accident, or do the laws of physics require it for some unknown reason? Questions such as these drive us physicists to search deeper for possible answers. The discovery of the neutron, and the subsequent observation of its decay, introduced more than one new particle into the subatomic zoo. It suggested that perhaps two of the most fundamental properties of nature—the conservation of energy and the conservation of momen- tum—might break down on the microscopic-distance scales of nuclei. Almost twenty years before discovering the neutron, James Chadwick had observed something strange about beta rays, well before he or anyone else knew that they originated from decaying neutrons. The spectrum of energy carried by electrons emitted in neutron decay is continuous, going from essentially zero energy up to a maximum energy, which de- pends on the energy available after the neutron has decayed—for a free neutron this maximum energy is the energy difference between the mass of the neutron and the sum of the masses of the proton and electron. There is a problem with this, however. It is easiest to see the problem 2P_GrealestStenC-verTald_AC.indd 121 12/18/16 3:06 PIA EFTA00286043 122 THE GREATEST STORY EVER TOLD-SO FAR if we imagine for the moment that the proton and the electron have equal masses. Then, if the proton carries off more energy than the elec- tron after the decay, it would be moving faster than the electron. But if they have the same mass, then the proton would also have more mo- mentum than the electron. But if the neutron decays at rest, then its momentum before the decay would be zero, so the momentum of the outgoing proton would have to cancel that of the outgoing electron. But that is impossible unless they have equal momenta, going in opposite directions. So the magnitude of the proton's momentum could never be greater than that of the electron. In short, there is only one value for the energy and the momentum of the two particles after the decay if they have equal masses. The same reasoning, though mathematically a bit more involved, applies even if the proton and electron have different masses. If they are the only two particles produced in the decay of the neutron, their speeds, and hence their energy and momenta, would be required to each have unique, fixed values that depend on the ratio of their respective masses. As a result, if electrons from beta decay of neutrons come off with a range of different energies, this would violate the conservation of energy and momentum. But, as I subtly suggested above, this is only true if the electron and proton are the only particles produced as products of the neutron decay. Again, in 1930, only a few years before the discovery of the neutron, the remarkable Austrian theoretical physicist Wolfgang Pauli wrote a letter to colleagues at the Swiss Federal Institute of Technology, begin- ning with the immortal header "Dear radioactive ladies and gentlemen," in which he outlined a proposal to resolve this problem, which he also said he didn't "feel secure enough to publish anything about! He pro- posed that a new electrically neutral elementary particle existed, which he called a neutron, and that in addition to the electron and the proton this new neutral particle was produced in beta decay so that the elec- 2P_Glealer-StoryEverTold_Atirdd 122 12/16116 3:06 PIA EFTA00286044 Decay and Rubble 123 tron, proton, and this particle together could share the energy available in the decay, allowing a continuous spectrum. Pauli, who later won the Nobel Prize for his "exclusion principle" in quantum mechanics, was no fool. In fact, he had no patience for fools. He was famous for supposedly rushing up to the blackboard during lec- tures and removing the chalk from the speaker's hand if he felt nonsense was being spouted. He could be scathingly critical of theories he didn't like, and his worst criticism was reserved for any idea that was so vague, as he put it, "it isn't even wrong." (A dear old colleague of mine when I taught at Yale, the distinguished mathematical physicist Feza Gursey, once responded to a reporter who asked what was the significance of an announcement of some overhyped idea proposed by some scientists seeking publicity by saying, "It means Pauli must be dead.") Pauli realized that proposing a new elementary particle that hadn't been observed was speculative in the extreme, and he argued in his letter that such a particle was unlikely both because it had never been seen and would therefore have to interact weakly with matter, and also because it would have to be very light to be produced along with an electron, given that the energies available in beta decay were so small compared to the proton's mass. The first problem that arose with his idea was the name he chose. After Chadwick's 1932 experimental discovery of the particle we now call the neutron, appropriate for a neutral cousin of the proton with comparable mass, Pauli's hypothesized particle needed another name. The brilliant Italian physicist and colleague of Pauli's—Enrico Fermi— came up with a solution in 1934, changing its name to neutrino, an Ital- ian pun for "little neutron." It would take twenty-six years for Pauli's neutrino to be discovered, enough time for the little particle, and its heavier cousin, the neutron, to force physicists to totally revamp their views on the forces that govern the cosmos, the nature of light, and even the nature of empty space. 2P_Glealer-StoryEverTold_Atindd 123 12/16116 3:06 PIA EFTA00286045 29_Gtealer-StoryEverTold_AC.irdd 124 12/16116 3:06 PM EFTA00286046 Chapter 10 FROM HERE TO INFINITY: SHEDDING LIGHT ON THE SUN I have fought a good fight, I have finished my course, I have kept the faith. -2 TIMOTHY 4:7 The physicist Enrico Fermi is largely unsung in the public's eyes, but he remains one of the greatest twentieth-century physicists. He, together with Richard Feynman, more than any of the other remark- able figures from that equally remarkable period in physics, most influ- enced my own attitude and approach to the field, as well as my own understanding of it. I only wish I were as talented as either of them. Born in 1901, Fermi died at the age of fifty-three of cancer, perhaps brought on by his work on radioactivity. In 1954, when he died, he was nine years younger than I am as I write this. But in his short life he pushed forward the frontiers of both experimental and theoretical physics in a way that no one has since repeated, and no one is ever likely to do again. The complexity of the array of theoretical tools now used to develop phys- ical models, and the complexity of machinery now used to test them, are separately too sophisticated to allow any single individual today, no mat- 125 2P_Glealer-StoryEverrold_Atirdd 125 12/16116 3:06 PIA EFTA00286047 126 THE GREATEST STORY EVER TOLD-SO FAR ter how talented, to remain on the vanguard of both endeavors at the level Fermi achieved in his time. In 1918, when Fermi graduated from high school in Rome, the possi- bilities open to a brilliant young scientific mind were far less constrained. Quantum mechanics had just been born, new ideas were everywhere, and the rigorous mathematics necessary to deal with these ideas had not yet been developed or applied. Experimental physics had yet to enter the domain of "big science"; experiments could be performed by individual researchers in makeshift laboratories, and they could be completed in weeks instead of months. Fermi applied to the prestigious Scuola Normale Superiore in Pisa, which required an essay as part of the entrance exam. The theme that year was "specific characteristics of sounds." Fermi submitted an "essay" that included solving partial differential equations for a vibrating rod and applying a technique called Fourier analysis. Even today, these mathematical techniques are not normally encountered until maybe the third year of an undergraduate degree, and for some students not until graduate school. But as a seventeen-year-old, Fermi sufficiently im- pressed the examiners to receive first place in the exam. At the university, Fermi first majored in mathematics but switched to physics and largely taught himself General Relativity—which Einstein had only developed a few years earlier—as well as quantum mechan- ics and atomic physics, which were then emerging fields of research. Within three years of arriving at the university he published theoretical papers in major physics journals on subjects from General Relativity to electromagnetism. At the age of twenty-one, four years after beginning his university studies, he received his doctoral degree for a thesis ex- ploring the applications of probability to X-ray diffraction. At the time a thesis on purely theoretical issues was not acceptable for a physics doctorate in Italy, so this encouraged Fermi to ensure his competence in the laboratory as well as with pen and paper. Fermi moved to Germany, the center of the emerging research on 2P_Glealer-StoryEverTold_Atindd 126 12/16116 3:06 PIA EFTA00286048 From Here to infinity: Shedding Light on the Sun 127 quantum mechanics, and then to Leiden, Holland, where he met with the most famous physicists of the day—Born, Heisenberg, Pauli, Lo- rentz, and Einstein, to name a few—before returning to Italy to teach. In 192s, Wolfgang Pauli proposed the `exclusion principle," which dis- closed that two electrons could not occupy exactly the same quantum state at the same time and place, and which laid the basis of all of atomic physics. Within a year, Fermi applied this idea to systems of many such identical particles that, like electrons, have two possible values of spin, angular momentum, which we call spin up, and spin down. He thus established the modern form of the field called statistical mechanics, which is at the basis of almost all materials science, semiconductors, and those areas of physics that led to the creation of modern electronic components such as computers. As I earlier emphasized, there is no intuitive way to picture a point particle as spinning around some axis. It is simply one of the ways that quantum mechanics evades our notions of common sense. Electrons are called spin 34 particles because the magnitude of their spin angular mo- mentum turns out to be half as big as the lowest value of angular momen- tum associated with the orbital motion of electrons in atoms. Any spin 1/2 particle such as an electron is called a fermion, named in Fermi's honor. At the tender age of twenty-six Fermi was elected to a new chair in theoretical physics at the University of Rome and thereafter led a vi- brant group of students, including several subsequent Nobel laureates, as they explored atomic and then nuclear physics. In 1933, Fermi was motivated by another proposal of Pauli's, that for the new particle produced in the decay of neutrons, which Fermi labeled a neutrino. But naming the new particle was just an aside. Fermi had much bigger fish to fry, and he produced a theory for neutron decay that revealed the possible existence of a new fundamental force in na- ture, the first new force known to science beyond electromagnetism and gravity—which was in its own way inspired by thinking about light. Al- though it wasn't obvious at the time, this was to be the first of two new 2P_GlealerASIonEverTold_AC.indd 127 12/16116 3:06 PIA EFTA00286049 128 THE GREATEST STORY EVER TOLD-SO FAR forces associated with atomic nuclei, which together with electromag- netism and gravity, comprise all the forces known to operate in nature, from the smallest subatomic scales to the motion of galaxies. When Fermi submitted his proposal to the journal Nature, the edi- tor turned it down because it was "too remote from physical reality to be of interest to readers." For many of us who have since had papers rejected by equally high-handed editors at that journal, it is comfort- ing to know that Fermi's paper, one of the most important proposals in twentieth-century physics, also didn't make the cut. This inappropriate rejection was undoubtedly frustrating to Fermi, but it did have a useful side effect. Fermi decided instead to return to experimental physics, and in short order he began to experiment with the neutrons discovered by Chadwick two years earlier. Within several months Fermi had developed a powerful radioactive source of neutrons and found that he was able to induce radioactive decays in otherwise stable atoms by bombarding them with neutrons. Bombarding ura- nium and thorium with neutrons, he also witnessed nuclear decays and thought he had created new elements. In fact, he had actually caused the nuclei to split, or fission, into lighter nuclei, which were later found to also emit more neutrons than they absorbed in the process—as other scientists discovered in 1939. Fermi's segue into experiment turned out to be good for him. Four years later, in 1938, at the age of thirty-seven, he was awarded the Nobel Prize for introducing artificial radioactivity, creating new radioactive elements by neutron bombardment. Yet by 1938 the Nazis had begun to establish their racial laws in Germany, and Italy had followed suit, so Fermi's Jewish wife, Laura, was endangered. So, after receiving the prize in Stockholm, Fermi and his family didn't return to Italy but moved to New York City, where he accepted a position at Columbia. When Fermi learned the news about nuclear fission in 1939 in New York, following a lecture by Niels Bohr at Princeton, Fermi amended his earlier Nobel acceptance speech to clarify his earlier error and in short order re- 2P_Glealer-StoryEverTold_Atindd 128 122/18/16 3:06 PIA EFTA00286050 From Here to infinity: Shedding Light on the Sun 129 produced the German results. Before long, he and his collaborators realized that this produced the possibility of a chain reaction. Neutrons could bom- bard uranium, causing it to fission and release energy, and to release more neutrons that could bombard more uranium atoms and so on. Soon after, Fermi gave a lecture to the US Navy warning of the po- tential significance of this result, but few took him seriously. Later that year, Einstein's famous letter made its way to President Roosevelt and changed the course of history. Fermi had recognized the potential dangers inherent in releasing the energy of the atomic nucleus even earlier. A year after getting his doctor- ate, in 1923, he wrote the appendix for a book on relativity and talked of the potential of E = me, writing at the time, "It does not seem possible, at least in the near future, to find a way to release these dreadful amounts of energy—which is all to the good because the first effect of an explosion of such a dreadful amount of energy would be to smash into smithereens the physicist who had the misfortune to find a way to do it." That idea must have been on his mind in 1941 when, as part of the newly established Manhattan Project, Fermi was assigned the task of creating a controlled chain reaction—namely creating a nuclear reactor. While those in charge were understandably worried about doing this in an urban area, Fermi was confident enough to convince the leader of the project to allow him to build it at the University of Chicago. On Decem- ber z, 1942, the reactor went critical, and Chicago survived. Two and a half years later, Fermi was on hand in New Mexico to observe the first nuclear explosion, the Trinity test. Typical of Fermi, while the others stood in awe and horror, he conducted an impromptu experiment to estimate the bomb's strength by dropping several strips of paper when the blast wave came by, to see how far they were carried. Fermi's constant experimental approach to physics is one of the rea- sons I cherish his memory. He always found a simple, easy way to reach the correct answer. Even though he had great mathematical skill, he dis- liked complication, and he realized that he could get an approximate 2P_GrealestSleryEverTold_AC.indd 129 12/16116 3:06 PIA EFTA00286051 130 THE GREATEST STORY EVER TOLD-SO FAR answer that was "good enough" in a short time, while getting the exact answer might take months or years. He refined his abilities and helped his students do so by inventing what we now call Fermi Problems, which he is also said to have assigned at lunchtime each day to the team working for him. My favorite problem, which I always assign to my introductory- physics students, is `How many piano tuners are there in Chicago? Try it. If you get between one hundred and five hundred, you did well. Fermi won the Nobel Prize for his experimental work, but his theo- retical legacy for physics may be far greater. True to form, the `theory" he proposed in his famously rejected paper on neutron decay was re- markably simple, yet it did the job. It wasn't a full theory at all, and at the time it would have been premature to develop one. Instead he made the simplest possible assumption. He imagined some new kind of inter- action between particles that took place at a single point. The four par- ticles were a neutron, a proton, an electron, and the new particle Pauli and Fermi named the neutrino. The starting point of Fermi's thinking involved light, as did almost all of modern physics, and in this case the modern quantum theory of light inter- acting with matter. Recall that Feynman developed a pictorial framework to think about fundamental processes in space and time, when he argued that antimatter should exist. The space-time picture of an electron emitting a photon is reproduced here, but with the electron replaced by a proton, p: 2P_Glealer-StoryEverrold_Atirdd 130 12/16116 3:06 PIA EFTA00286052 From Here to infinity: Shedding Light on the Sun 131 Fermi imagined the decay of a neutron in a similar fashion, but in- stead of the neutron emitting a photon and remaining the same particle, the neutron, n, would emit a pair of particles—an electron, e, and a neu- trino, v, and would be converted into a proton, p: In electromagnetism the strength of the interaction between charged particles and photons (determining the probability of emitting a photon at the point shown in the first figure on the previous page) is proportional to the charge of the particle. Since the charge is what allows particles to interact, or "couple" to the electromagnetic field, we call the magnitude of the fundamental quantum of charge—the charge on a single electron or proton—the "coupling constant" of electromagnetism. In Fermi's interaction the numerical quantity that appears at the in- teraction point in the figure where a neutron converts into a proton de- termines the probability of such a conversion. The value of this quantity is determined by experiment, and we now call it the Fermi constant. Relative to electromagnetism, the numerical value of this quantity is small because the neutron takes a long time to decay—compared, for example, to the rate at which electromagnetic transitions take place in atoms. As a result, Fermi's interaction, describing a new force in nature, became known as the weak interaction. One of the things that made Fermi's proposal so remarkable was that it was the first time in physics that anyone had proposed that par- 2P_Glealer-StoryEverrold_Atirdd 131 12/16116 3:06 PIA EFTA00286053 192 THE GREATEST STORY EVER TOLD-SO FAR ticks other than photons could be spontaneously created in the quan- tum world. (In this case the electron and the neutrino are created at the same time as the neutron converts into a proton.) This both inspired and became the prototype for much of the subsequent exploration of the quantum character of the fundamental forces in nature. Moreover, it didn't just make postdictions about nature. It made predictions precisely because a single mathematical form for the inter- action that caused neutron decay could also predict a host of other phe- nomena, which were later observed. Even more important, this interaction, with precisely the same strength, governs similar decays of other particles in nature. For example, in 2936 Carl Anderson, the discoverer of the positron, discovered another new particle in cosmic rays—the first of what would be so many that par- ticle physicists would wonder whether the progression would ever end. When informed of this discovery, the atomic physicist and later Nobel laureate I. I. Rabi is said to have exclaimed, "Who ordered that?" We now know that this particle, called the muon and characterized by the Greek letter µ, is essentially an exact copy of the electron, only about two hundred times heavier. Because it is heavier, it can decay, emitting an electron and a neutrino in an interaction that looks identi- cal to neutron decay, except the muon converts into another type of neutrino (called the muon neutrino) instead of a proton. Remarkably, if we use the same Fermi constant for the strength of this interaction, we derive exactly the right lifetime for the muon. Clearly a new fundamental force is at work here, universal in nature, with some similarities to electromagnetism, and some important differ- ences. First, the interaction is much weaker. Second, unlike electromag- netism, the interaction appears to operate over only a small range—in Fermi's model at a single point. Neutrons don't turn into protons in one place and cause electrons to turn into neutrinos somewhere else, whereas the interaction between electrons and photons allows electrons to exchange virtual photons and be repelled by each other even at a 2P_Glealer-StoryEverTold_Atincld 132 12/16116 3:06 PIA EFTA00286054 From Here to infinity: Shedding Light on the Sun 133 great distance. Third, the interaction changes one type of particle into another. Electromagnetism involves the creation and absorption of pho- tons—the quanta of light—but the charged particles that interact with them preserve their identity before and after the interaction. Gravity too is long-range, and when a ball falls toward the Earth, it remains a ball. But the weak interaction causes neutrons to decay into protons, muons into neutrinos, and so on. Clearly something about the weak interaction is different, but you may wonder if it is worth worrying about. Neutron decay is interesting, but hap- pily the properties of nuclei protect us from it so that stable atoms can exist. Thus it seems to have little impact on everyday lives. Unlike gravity and electromagnetism, we don't sense it. If the weak interaction were of little other importance, then its anomalous nature could be easily overlooked. However, the weak interaction, at least as much as gravity and elec- tromagnetism, is directly responsible for our existence. In 1939, Hans Bethe, who would soon help lead the effort to build the atomic bomb, re- alized that the interactions that broke apart heavy nuclei as the source of the explosive power of the bomb could, under different circumstances, be utilized to build larger nuclei from smaller nuclei. This could release even more energy than was released in the A-bomb. Up until that time the energy source of the Sun was a mystery. It was well established that the temperature in the solar core could not exceed a few tens of millions of degrees—which may seem extreme, but the energies available to the colliding nuclei at those temperatures had already been achieved in the lab. Moreover, the Sun could not involve simple burning, like a candle. It had been established as early as the eighteenth century that an object with the mass of the Sun could only burn with its observed brightness for perhaps ten thousand years if it were just something like a burning lump of coal. While that meshed nicely with Bishop Ussher's estimates for the age of the universe as inferred from the Bible's tale of creation, geologists and biologists had already established by the mid- 2P_Glealer-StoryEverTold_AC.indd 133 12/16116 3:06 PIA EFTA00286055 134 THE GREATEST STORY EVER TOLD-SO FAR nineteenth century that Earth itself was far older. With no apparent new energy source, the longevity and brightness of the Sun was inexplicable. Enter Hans Bethe. Another of the incredibly talented and prolific theoretical physicists coming out of Germany in the first half of the twentieth century, Bethe was also another doctoral student of Arnold Sommerfeld's and also went on to win the Nobel Prize. Bethe began his career in chemistry because the introductory physics instruction at his university was poor—a common problem. (I also dropped physics in my first year for the same reason, but happily the physics department at my university let me take a more advanced course the following year.) Bethe switched to physics before moving on to graduate studies and emigrated to the United States to escape the Nazis. A consummate physicist, Bethe could work through detailed calcula- tions to solve a wide variety of problems on the blackboard, beginning at the upper left of the board and ending at the lower right with almost no ensures. Bethe strongly influenced Richard Feynman, who used to marvel at Bethe's patient methodological approach to problems. Feyn- man himself often jumped from the beginning of a problem to the end and worked out the steps in between afterward. Bethe's solid technical prowess and Feynman's brilliant insights combined well when they both worked at Los Alamos on the atomic bomb. They would go down the hallway with Feynman loudly countering the patient but persistent Bethe, and their colleagues labeled them "the Battleship and the Torpedo Boat." Bethe was legendary when I was a young physicist because even into his nineties he was still writing important physics articles. He was also happy to talk to anyone about physics. When I gave a visiting lecture at Cornell—where Bethe spent most of his professional career—I felt im- mensely honored when he walked into my office to ask me questions and then listened intently to me, as if I actually had something to offer him. He was also physically robust. A physicist friend of mine told me of a time he too visited CornelL One weekend he decided to be ambitious and climb one of the many steep hiking trails near the campus. He was proud of himself 2P_Greales4SlenfEverTold_AC.incld 130 12/1196 3:06 PM EFTA00286056 From Here to infinity: Shedding Light on the Sun 135 for huffing and puffing his way almost to the top until he spied Bethe, then in his late eighties, happily making his way down the trail from the summit While I always liked and admired Bethe, in researching material for this book I found two additional happy personal connections that were satis- fying enough for me to relate them here. First, I found out that I am in a sense his intellectual grandson, as my undergraduate physics honors the- sis adviser, M. K. Sundaresan, was one of his doctoral students. Second, I discovered that Bethe, who had little patience for grand claims made of fundamental results that were carried out without any real motivation or evidence, once wrote a hoax paper while a postdoc poking fun at a paper he deemed ridiculous by the famous physicist Sir Arthur Stanley Eddington. Eddington claimed to "derive" a fundamental constant of electromagne- tism using some fundamental principles, but Bethe correctly viewed the claim as nothing other than misguided numerology. Learning this made me feel better about a hoax paper I wrote when I was an assistant profes- sor at Yale, responding to what I thought was an inappropriate paper, pub- lished in a distinguished physics journal, that claimed to discover a new force in nature (which indeed later turned out to be false). At the time that Bethe wrote his paper, the physics world took itself a little more seriously, and Bethe and his colleagues were forced to issue an apology. By the time I wrote mine, the only negative reaction I got was from my department chair, who was worried that the Physical Review might actually publish my article. When he was in his early thirties, Bethe had already established himself as a master physicist with his name attached to a host of re- sults, from the Bethe formula, describing the passage of charged par- ticles through matter, to the Bethe ansatz, a method to obtain exact solutions for certain quantum problems in many-body physics. A series of reviews he cowrote on the state of the nascent field of nuclear phys- ics in 1936 remained authoritative for some time and became known as Bethe's Bible. (Unlike the conventional Bible, it made testable predic- tions, and it was eventually replaced as scientific progress was made.) In 1938, Bethe was induced to attend a conference on "stellar energy 2P_Glealer-StoryEverTold_Atirdd 135 12/16116 3:06 PIA EFTA00286057 136 THE GREATEST STORY EVER TOLD-SO FAR generation: though at that time astrophysics was not his chief interest By the end of the meeting, he had worked out the nuclear processes by which four individual protons (the nuclei of hydrogen atoms) eventually "fuse"—as a result of Fermi's weak interaction—to form the nucleus of helium, con- taining two protons and two neutrons. This fusion releases about a million times more energy per atom than is released when coal burns. This allows the Sun to last a million times longer than previous estimates would have permitted, or about io billion years instead of ten thousand years. Bethe later showed that other nuclear reactions help power the Sun, including a set that converts carbon to nitrogen and oxygen—the so-called CNO cycle. The secret of the Sun—the ultimate birth of light in our solar system— had been unveiled. Bethe won the Nobel Prize in 1967, and almost forty years after that, experiments on neutrinos coming from the Sun confirmed Bethe's predictions. Neutrinos were the key experimental observable that allowed such confirmation. This is because the whole chain begins with a reaction in which two protons collide, and via the weak interaction one of them converts into a neutron, allowing the two to fuse into the nucleus of heavy hydrogen, called deuterium, and release a neutrino and a positron. The positron later interacts in the Sun, but neutrinos, which interact only via the weak interaction, travel right out of the Sun, to Earth and beyond. Every second of every day, more than 400,000 billion of these neutri- nos are passing through your body. Their interaction strength is so weak that they could traverse on average through ten thousand light-years of solid lead before interacting, so most of them travel right through you, and Earth, without anyone's noticing. But if not for the weak interaction, they would not be produced, the Sun wouldn't shine, and none of us would be here to care. So the weak interaction, although extremely weak, nevertheless is largely responsible for our existence. Which is one of the reasons why, when the Fermi interaction, developed to characterize it, and the neu- trinos first predicted by it, turned out to both defy common sense, phys- icists had to stand up and take notice. And they were driven to change our notions of reality itself. 2P_Glealer-StoryEverTold_Atirdd Ice 12/16116 3:06 PM EFTA00286058 Part Two EXODUS 2P_GrealesISIoryEverrolcl,C.indcl 137 121IVI 3. PM EFTA00286059 2P_GreatestSlowEverrold_AC.incld 138 12/18/18 3:08 PM EFTA00286060 Chapter 11 DESPERATE TIMES AND DESPERATE MEASURES To every thing there is a season, and a time for every purpose. -ECCLESIASTES 3:1 The rapid succession of events during the 1930s, from the discovery of the neutron to probing the nature of neutron decay, as well as the discovery of the neutrino and the consequent discovery of a new and universal short-range weak force in nature, left physicists more con- fused than inspired. The brilliant march that had led to the unification of electricity and magnetism, and the unification of quantum mechanics and relativity, had been built on exploring the nature of light. Yet it wasn't clear how the elegant theoretical edifice of quantum electrody- namics could guide considerations of a new force. The weak interaction is far removed from direct human experience and involves new and ex- otic elementary particles and nuclear transmutations reminiscent of al- chemy but, unlike alchemy, testable and reproducible. The fundamental confusion lay with the nature of the atomic nu- cleus itself and the question of what held it together. The discovery of the neutron helped resolve the paradox that had earlier seemed to re- 139 2P_Glealer-StoryEverrold_AC.indd 139 12/16116 3:06 PIA EFTA00286061 140 THE GREATEST STORY EVER TOLD-SO FAR quire electrons to be confined in the nucleus to counter the charge of additional protons necessary to produce correct nuclear masses, but the observation of beta decay—which resulted in electrons emerging from nuclei—didn't help matters. The realization that in beta decay neutrons became protons in the nucleus clarified matters, but then another question naturally arose: Could this transformation somehow explain the strong binding that held protons and neutrons together inside nuclei? In spite of the obvious differences between the weak forces and quan- tum theory of electromagnetism, QED, the remarkable success of QED in describing the behavior of atoms and the interactions of electrons with light colored physicists' thinking about the new weak force as well. The mathematical symmetries associated with QED worked beautifully to ensure that otherwise worrisome infinities in the calculations arising from the exchange of virtual particles vanished when making predic- tions of physical quantities. Would something similar work to under- stand the force binding protons and neutrons in nuclei? Specifically, if the electromagnetic force was due to the exchange of par- ticles, then it was reasonable to think that the force that held together the nucleus might also be due to the exchange of particles. Werner Heisenberg proposed this idea in 1932 around the time the neutron was discovered. If neutrons and protons could convert into each other, with the proton ab- sorbing an electron to become a neutron, then maybe the exchange of elec- trons between them might somehow produce a binding force? A number of well-known problems marred this picture, however. First was the problem of "spin." If one assumed, as Heisenberg did, that the neutron was essentially made up of a proton and an electron bound together, and since both were spin 1/2 particles, then adding them to- gether in the neutron, it couldn't have spin 1/2 as well, since 1/2 + 1/2 can't equal 1/2. Heisenberg argued, in desperation, because those were des- perate times when it seemed all the conventional rules were breaking down, that the "electron" that was transferred between neutrons and 2P_Glealer-StoryEverTold_Atirdd 140 12/10/16 3:06 PIA EFTA00286062 Desperate Times and Desperate Measures 141 protons, and which bound them together in the nucleus, was somehow different from a free electron and had no spin at all. In retrospect, this picture has another problem. Heisenberg was mo- tivated to consider electrons binding together neutrons and protons because he was thinking about hydrogen molecules. In hydrogen, two protons are bound together by sharing electrons that orbit them. The problem with using a similar explanation for nuclear binding is one of scale. How could neutrons and protons exchange electrons and be bound together so tightly that their average distance apart is more than one hundred thousand times smaller than the size of hydrogen molecules? Here is another way of thinking about this problem that will be use- ful to return to later. Recall that electromagnetism is a long-range force. 'IWo electrons on opposite sides of the galaxy experience a repulsion— albeit extremely small—due to the exchange of virtual photons. The quantum theory of electromagnetism makes this possible. Photons are massless, and virtual photons can travel arbitrarily far, carrying arbitrarily small amounts of energy, before they are absorbed again— without violating the Heisenberg uncertainty principle. If the photons were massive, then this would not be possible. Now if a force between neutrons and protons in nuclei arose due to the absorption and emission of virtual electrons, say, then the force would be short-range because the electrons are massive. How short- range? Well, it works out to be about one hundred times the size of typical nuclei. So, exchanging electrons doesn't work to produce nuclear- scale forces. As I say, those were desperate times. Heisenberg's desperate idea about a strange spinless version of the electron was not lost on a young Japanese physicist, the shy twenty- eight-year-old Hideki Yukawa. Working in 1935 when Japan was just beginning to emerge from centuries of isolation, and just before its im- perial designs ignited the war in the Pacific, Yukawa published the first original work in physics to be published by a physicist educated entirely in Japan. No one took notice of the paper for at least two years, yet four- 2P_Glealer-StoryEverTold_Atincld 141 12/16016 3:06 PIA EFTA00286063 142 THE GREATEST STORY EVER TOLD-SO FAR teen years later he won the Nobel Prize for this work, which had by then become noticed, but for the wrong reasons. Einstein's visit to Japan in 1922 had cemented Yukawa's growing in- terest in physics. When Yukawa was still in high school and searching for material to help him pass examinations in a second foreign language, he found Max Planck's Introduction to Theoretical Physics in German. He rejoiced in reading both the German and the physics and was aided by his classmate Sin-Itiro Tomonaga, a talented physicist who was his colleague both in high school and later at Kyoto University. Tomonaga was so talented that he would later share the 1965 Nobel Prize with Richard Feynman and Julian Schwinger for demonstrating the math- ematical consistency of quantum electrodynamics. That Yukawa, who had been a student in Japan at a time when many of his instructors did not yet fully understand the emerging field of quantum mechanics, came upon a possible solution to the nuclear-force problem that had been overlooked by Heisenberg, Pauli, and even Fermi was remarkable. I suspect that part of the problem was a phenomenon that has occurred several times in the twentieth century and perhaps before, and perhaps after. When the paradoxes and complexities asso- ciated with some physical process begin to seem overwhelming, it is tempting to assume that some new revolution, similar to relativity or quantum mechanics, will require such a dramatic shift in thinking that it doesn't make sense to push forward with existing techniques. Fermi, unlike Heisenberg or Pauli, was not looking for a wholesale revolution. He was willing to propose, as he called it, a "tentative theory" of neutron decay that got rid of electrons in the nucleus by allowing them to be spontaneously created during beta decay. He proposed a model that worked, which he knew was just a model and not a complete theory, but it did allow one to do calculations and make predictions. That was the essence of Fermi's practical style. Yukawa had followed these developments, translated Heisenberg's paper on nuclei along with an introduction, and published it in Japan, so 2P_Glealer-StoryEverrold_Atirdd 142 12/16116 3:06 PIA EFTA00286064 Desperate Times and Desperate Measures 143 the problems of Heisenberg's proposal were already clear to him. Then in 1934 Yukawa read Fermi's theory of neutron decay, which catalyzed a new idea in Yukawa's mind. Perhaps the nuclear force binding protons and neutrons was due not to the exchange of virtual electrons between them, but to the exchange of both the electron and the neutrino that were created when neutrons changed to protons. Another problem immediately arose, however. Neutron decay is a result of what would become known as the weak interaction, and the force responsible for it is weak. Plugging in values for the possible force that might result between protons and neutrons by the exchange of an electron-neutrino pair made it clear that this force would be far too weak to bind them. Yukawa then allowed himself to do what none of the others had done. He questioned why the nuclear force, if it, like QED, results from the exchange of virtual particles, had to be due to the exchange of one or more of the particles already known or assumed to exist. Remembering how loath physicists such as Dirac and Pauli had been to propose new particles, even when they were correct, you can perhaps appreciate how radical Yukawa's idea was. As Yukawa later described it: At this period the atomic nucleus was inconsistency itself, quite inexplicable. And why?—because our concept of elementary particle was too narrow. There was no such word in Japanese and we used the English word—it meant proton and electron. From somewhere had come a divine message forbidding us to think about any other particle. To think outside of these limits (except for the photon) was to be arrogant, not to fear the wrath of the gods. It was because the concept that matter continues forever had been a tradition since the times of Democritus and Epicurus. To think about creation of particles other than photons was suspect, and there was a strong inhibition of such thoughts that was almost unconscious. 2P_Glealer-StoryEverrold_Atirdd 143 12/16116 3:06 PIA EFTA00286065 144 THE GREATEST STORY EVER TOLD-SO FAR One of my good physics friends has said that the only time he was able to do complicated calculations was after the birth of each of his children, when he couldn't sleep anyway, so he stayed up and worked. Thus in October of 1934, just after the birth of his second child and unable to sleep, Yukawa realized that if the range of the strong nuclear force was to be restricted to the size of a nucleus, then any exchanged particle must be far more massive than the electron. The next morning he estimated the mass to be two hundred times the electron mass. It would have to carry an electric charge if it was to be exchanged between neutrons and protons, and it could have no spin, so as not to change the proton's or neutron's spin when it was absorbed or emitted. What has all this concern over strong nuclear forces to do with neu- tron decay, the subject that started this chapter and ended the last? you may ask. In the 1930s, just as it went against the grain to imagine new particles, so too inventing new forces seemed unnecessary at best and heretical at worst. Physicists were convinced that all the processes that occurred in the nucleus, strong or weak, must be connected. Yukawa envisaged a clever way to do this, connecting ideas of both Fermi and Heisenberg, and also generalizing ideas from the successful quantum theory of electromagnetism. If instead of emitting a photon, neutrons in the nucleus emitted a new, heavy, spinless charged particle, which Yukawa originally called a mesotron—until Heisenberg corrected Yukawa's Greek and the name was shortened to meson—then that par- ticle could be absorbed by protons in the nucleus, producing a force of attraction whose magnitude Yukawa was able to calculate using equa- tions that were extrapolated from, you guessed it, electromagnetism. The analogy with electromagnetism could not be exact, however, be- cause the meson is massive and the photon is massless. Yukawa took the attitude that Fermi might have, if he had thought of it. Yes, the theory wasn't complete, but Yukawa was willing to ignore the other aspects of electromagnetism that this theory couldn't reproduce. Damn the torpe- does, full speed ahead. 2P_Glealer-StoryEverTold_Atirdd U4 12/16116 3:06 PIA EFTA00286066 Desperate Times and Desperate Measures 145 Yukawa ingeniously—and ultimately incorrectly—connected this strong force to observed neutron decay by suggesting that mesons might not always simply be exchanged between neutrons and protons in the nucleus. A small fraction of the mesons emitted by neutrons might decay en route into an electron and neutrino before they could be re- absorbed, causing neutron decay. In this case, the neutron decay would not be described by something like the figure below and on the left, where the decay and the emission of the other particles all occur at a single point. It would appear like the figure on the right, where the decay gets spread out and a new particle, shown by the dashed line (which rep- resents Yukawa's meson), travels a short distance after emission before decaying into the electron and neutrino. With the new intermediate particle, the weak interaction mediating neutron decay begins to look more like the electromagnetic interaction between charged particles: A Yukawa had proposed a new intermediate particle, a heavy meson, which made neutron decay look similar to the earlier picture of photon exchange in electromagnetism—which had motivated his thinking in the first place—but with significant differences. In this case the inter- mediate particle was both massive and electrically charged, and also unlike the photon it had no spin angular momentum. Nevertheless, Yukawa was able to show that for a heavy meson his theory would be indistinguishable from Fermi's point interaction de- scribing neutron decay—at least for predicting the details of neutron 2P_Glealer-StoryEverTold_Atincld US 12/16116 3:06 PIA EFTA00286067 146 THE GREATEST STORY EVER TOLD-SO FAR decay. In addition, Yukawa's theory offered the possibility of reducing all of the strange properties of the nucleus—from beta decay of neutrons inside the nucleus to the strength of the interaction binding together protons and neutrons—to merely understanding the properties of a single new interaction, due to the exchange of a new particle, his meson. However, if this new heavy meson existed, where was it? Why hadn't it yet been seen in cosmic rays? Because of this, and also because Yukawa was an unknown entity working in a location far from all the action, no real attention was paid to his proposal to explain both the strong interaction between nucleons and the weaker one that appeared to be responsible for neutron decay. Nevertheless, his proposal, unlike those of Heisenberg and others (including Fermi), was simpler and made more sense. All of this changed in 2936, less than two years after Yukawa's predic- tion, when Carl Anderson, the discoverer of the positron, together with collaborator Seth Neddermeyer, discovered what appeared to be a new set of particles in cosmic rays. The characteristics of the tracks of these new particles in cloud chambers implied that they produced too little radiation in traversing matter to be protons or electrons. They were also more massive than electrons and appeared to be sometimes negative and sometimes positive. Before long the new particles were determined to have a mass in the range that Yukawa had predicted—about two hun- dred times the mass of the electron. It is remarkable how quickly the rest of the world caught on. Yukawa published a short note to point out that his theory predicted just such particles. Within weeks the major physicists in Europe began exploring his model and incorporating his ideas in their work. In 1938, in the last major conference before the Second World War interrupted essentially all international collaborations in science, of the eight main speakers, three dealt with Yukawa's theory—citing a name they would have been unfamiliar with a year or two before. While much of the rest of the physics world celebrated the apparent 2P_Glealer-StoryEverTold_Atirdd US 12/16116 306 PIA EFTA00286068 Desperate Times and Desperate Measures 147 discovery of Yukawa's meson, this discovery was not without its own problems. In 1940 the decay of a meson to an electron, predicted by Yu- kawa, was observed in cosmic-ray tracks. However, over the years 1943 to 1947 it became clear that the particles Anderson and Neddermeyer had discovered interacted much more weakly with nuclei than Yukawa's particle should have. Something was wrong. Three of Yukawa's Japanese colleagues suggested that mesons were of two different sorts, and that a Yukawa-type meson might decay into yet another, different and more weakly interacting meson. But their articles were in Japanese and didn't appear in English until after the war, by which time a similar proposal had been made by the US physicist Robert Marshak. This delay proved fortuitous. New techniques were being developed to observe the tracks of cosmic rays in photographic emulsions, and a series of brave researchers dragged their equipment up to high eleva- tions to search for possible new signals. Many cosmic rays interact and disappear before reaching sea level, so this group and others interested in exploring this wondrous new source of particles coming from the heavens had no choice but to seek higher elevations. Here cosmic rays would have traversed less distance in the atmosphere and might be more easily detected. The former Italian mountain guide turned physicist Giuseppe Oc- chialini had been invited from Brazil to join a British team working on the A-bomb during the war. As a foreign national, he couldn't work on the project, so instead he joined the cosmic-ray physics group at Bris- tol. Occhialini's mountain training proved useful as he dragged photo- graphic emulsions up to the Pic du Midi at twenty-eight hundred meters in France. Today you can travel to the observatory on top of this peak by cable car, and it is a terrifyingly exciting ride. But in 1946 Occhialini had to climb to the top, risking his health in the effort to discover signals of exotic new physics. And he and his team did discover exotic new physics. As Cecil Pow- 2P_Glealer-StorgverTold_Atincld 141 12/16116 3:06 PIA EFTA00286069 148 THE GREATEST STORY EVER TOLD-SO FAR ell, Occhialini's collaborator at Bristol (and future Nobel laureate, while Occhialini, who had done the climbing, did without), put it, they saw "a whole new world. It was as if, suddenly, we had broken into a walled orchard, where protected trees flourished and all kinds of exotic fruits had ripened in great profusion! Less poetically, perhaps, what they discovered were two examples in which an initial meson stopped in the emulsion and gave rise to a second meson, just as had been suggested by the theorists. Many more events were observed with emulsions taken to an elevation almost twice as high as Pic du Midi. In October of 1947, in the journal Nature, Pow- ell, Occhialini, and Powell's student Cesare Lattes published a paper in which they named the initial meson the pion—which seemed to inter- act with the nuclear strength appropriate to Yukawa's meson—and the subsequent meson the muon. It seemed at long last that Yukawa's meson had been discovered. As for its "partner" the muon, which had been confused with Yukawa's meson, it was nothing of the sort. Not spinless, it instead had the same spin as the electron and the proton. And its interactions with matter were nowhere near strong enough to play a role in nuclear binding. The muon turned out to be simply a heavy, if unstable, copy of the electron, which is what motivated Rabi's question "Who ordered that?" So, the particle that made Yukawa famous wasn't the particle he predicted after all. His idea became famous because the original ex- perimental result had been misinterpreted. Fortunately, the Nobel committee waited until the 1947 discovery of the pion before awarding Yukawa their prize in 1949. But, given the track record of errors and mislabeling, it is natural to wonder if the pion was in fact the particle Yukawa had predicted. The answer is both yes and no. Exchange of charged pions between protons and neutrons is indeed one accurate way of trying to estimate the strong nuclear force holding nuclei together. But in addition to charged pions- 2P_Glealer-StoryEverTold_Atirdd las 12/16116 3:06 PIA EFTA00286070 Desperate Times and Desperate Measures 149 the mesons that Yukawa had predicted—there are neutral pions as well. Who ordered those? Moreover, the theory that Yukawa wrote down to describe the strong force, like Fermi's theory to describe neutron decay, was not fully math- ematically consistent, as Yukawa had conceded when he proposed it. There was, at the time, no correct relativistic theory involving the ex- change of massive particles. Something was still amiss, and a series of surprising experimental discoveries, combined with prescient theoreti- cal ideas that were unfortunately applied to the wrong theories, helped lead to more than a decade of confusion before the fog lifted and light appeared at the end of the tunnel. Or perhaps at the mouth of the cave. 2P_Gtealer-StoryEverTold_Atirdd 149 12/16116 3:06 PIA EFTA00286071 2P_GreatestSlowEverrold_AC.indd 150 12/16/16 3:06 PM EFTA00286072 Chapter 12 MARCH OF THE TITANS The wolf also shall dwell with the lamb, and the leopard shall lie down with the kid. -ISAIAH 11:6 The relationship between theoretical insight and experi- mental discovery is one of the most interesting aspects of the progress of science. Physics is at its heart, like all of science, an empirical disci- pline. Yet at times brief bursts of theoretical insight change everything. Certainly Einstein's insights into space and time in the first two decades of the twentieth century are good examples, and the remarkable theo- retical progress associated with the development of quantum mechan- ics by Schrodinger, Heisenberg, Pauli, Dirac, and others in the 1920s is another. Less heralded is another period, from 19s4 to 1974, which, while not as revolutionary, will, when sufficient time has passed, be regarded as one of the most fruitful and productive theoretical physics eras in the twentieth century. These two decades took us, not without turmoil, from chaos to order, from confusion to confidence, and from ugliness to beauty. It's a wild ride, with a few detours that might seem to come from left field, but bear with me. If you find it a tad uncomfortable, then 151 2P_Glealer-StoryEverTold_Atirdd 151 12/16116 3:06 PIA EFTA00286073 152 THE GREATEST STORY EVER TOLD-SO FAR recall what I said in the introduction about science and comfort. By put- ting yourself in the frame of mind of those involved in the quest, whose frustration eventually led to insights, the significance of the insights can be truly appreciated. This tumultuous period followed one in which experimental bomb- shells had produced widespread confusion, making nature "curiouser and curiouser," as Lewis Carroll might have put it. The discoveries of the positron and quickly thereafter the neutron were just the begin- ning. Neutron decay, nuclear reactions, muons, pions, and a host of new elementary particles that followed made it appear as if fundamental physics was hopelessly complicated. The simple picture of a universe in which electromagnetism and gravity alone governed the interactions of matter made from protons and electrons disappeared into the dustbin of history. Some physicists at the time, like some on the political right today, yearned for the (often misremembered) simplicity of the good old days. This newfound complexity drove some, by the 1960s, to imagine that nothing was fundamental. In a Zen-like picture, they imagined that all elementary particles were made from all other elementary particles, and that even the notion of fundamental forces might be an illusion. Nevertheless, percolating in the background were theoretical ideas that would draw back the dark curtains of ignorance and confusion, revealing an underlying structure to nature that is as remarkable as it is strangely simple, and one in which light would once again play a key role. It all began with two theoretical developments, one profound and unheralded and another relatively straightforward but brilliant and im- mediately feted. Remarkably, the same man was involved in both. Born in 1922 to a mathematician father, Chen-Ning Yang was edu- cated in China, moving in 1938 from Beijing to Kunming to avoid the Japanese invasion of China. He graduated four years later from National Southwestern Associated University and remained there for another 2P_Glealer-StorgverTold_Atirdd 152 12/16116 3:06 PIA EFTA00286074 March of the Titans 153 two years. There he met another student who had been forced to re- locate to Kunming, Tsung-Dao Lee. While they only had a marginal acquaintance with the United States, in 1946 both of them received scholarships set up by the US government, with funds received from China to allow talented Chinese students to pursue graduate study in America. Yang had a master's degree and therefore had greater freedom to pursue a PhD, and went with Fermi from Columbia to the University of Chicago. Lee had less choice, as he did not have a master's degree, but the only US university where he could work directly toward a PhD was also the University of Chicago. Yang did his PhD under the supervision of Edward Teller and worked directly with Fermi as his assistant for only a year after graduation, while Lee did his PhD with Fermi directly. During the 1940s, the University of Chicago was one of the greatest centers of theoretical and experimental physics in the country, and its graduate students benefited from their exposure to a remarkable set of scientists—not only Fermi and Teller, but others including the brilliant but unassuming astrophysicist Subrahmanyan Chandrasekhar. When he was nineteen, Chandra, as he was often called by colleagues, had proved that stars greater than 1.4 times the mass of the Sun must col- lapse catastrophically at the end of their nuclear-burning lifetime, either through what is now known to be a supernova explosion, or directly in what is now known as a black hole. While his theory was ridiculed at the time, he was awarded the Nobel Prize for that work fifty-three years later. Chandra was not just a brilliant scientist but, like Fermi, a dedicated teacher. Even though he was pursuing research at the Yerkes Observa- tory in Wisconsin, he drove one hundred miles round-trip each week to teach a class to just two registered students, Lee and Yang. Ultimately, the entire class, professor included, became Nobel laureates, which is probably unique in the history of science. Yang moved to the venerable Institute for Advanced Study in Prince- ton in 1949, where he nurtured his budding collaboration with Lee on 2P_Glealer-Storgverrold_Atinid 15a 12/16116 3:06 PIA EFTA00286075 154 THE GREATEST STORY EVER TOLD-SO FAR a variety of topics. In 1952 Yang was made a permanent member of the institute, while Lee moved in 19s3 to nearby Columbia in New York City, where he remained for the rest of his career. Each of these men made major contributions to physics in a variety of areas, but the collaboration that made them famous began with a strange experimental result, again coming from cosmic-ray observa- tions. In the same year that Yang moved from Chicago to the IAS, Cecil Powell, the discoverer of the pion, discovered a new particle in cosmic rays, which he called the tau meson. This particle was observed to decay into three pions. Another new particle was discovered shortly thereaf- ter, called the theta meson, which decayed into two pions. Surprisingly, this new particle turned out to have precisely the same mass and life- time as that tau meson. This might not seem that strange. Might they be the same particle, simply observed to decay in two different ways? Remember that in quan- tum mechanics, anything that is not forbidden can happen, and as long as the new particle was heavy enough to decay into either two or three pions—and the weak force allowed such decays—both should occur. But, if it were sensible, the weak force shouldn't have allowed both decays. Think for a moment about your hands. Your left hand differs from your right hand. No simple physical process, short of entering through the looking glass, can convert one into the other. No series of move- ments, up or down, turning around, or jumping up and down, can turn one into the other. The forces that govern our experience, electromagnetism and gravity, are blind to the distinction between left and right. No process moder- ated by either force can turn something such as your right hand into its mirror image. I cannot turn your right hand into your left hand merely by shining light on it, for example. Put another way, if I shine a light on your right hand and look at it 2P_GrealetaleryEverTold_AC.indd 160 12/16116 3:06 PIA EFTA00286076 March of the Titans 155 from a distance, the intensity of reflected light will be the same as it would be if I did the same thing to your left hand. The light doesn't care about left or right when it is reflecting off something. Our definition of left and right is imposed by human convention. Tomorrow we could decide that left is right and vice versa, and nothing would change except our labels. As I write this on an airplane, flying economy class, the person to my right may be quite different from the person to my left, but again that is just an accident of my circumstances. I don't expect that the laws governing the flight of this plane are differ- ent for the right wing than for the left wing. Think about this in the subatomic world. Recall that Enrico Fermi found that, given the rules of quantum mechanics, the mathematical behavior of groups or pairs of elementary particles depends on whether they have spin 54, i.e., are fermions. The behavior of groups of fermions is quite different from the behavior of particles such as photons, which have a spin value of 1 (or any integer value of spin angular momentum, i.e., o, i, 2, 3, etc.). The mathematical "wave function" that describes a pair of fermions, for example, is santisymmetric," while one describing a pair of photons is "symmetric." This means that if one interchanges one particle with another, the wave function describing fermions changes sign. But for particles such as photons, the wave function re- mains the same under such an interchange. Interchanging two particles is the same as reflecting them in the mirror. The one on the left now becomes the one on the right. Thus an intimate connection exists between such exchanges and what physicists call parity, which is the overall property of a system under reflection (i.e., interchanging left and right). If an elementary particle decays into two other particles, the wave function describing the "parity" of the final state (i.e., whether the wave function changes sign or not under left-right interchange of the par- ticles) allows us then to assign a quantity we can call parity to the initial particle. In quantum mechanics if the force that governs the decay is 2P_GlealerASIonEverTold_Atirdd 155 12/16116 3:06 PIA EFTA00286077 156 THE GREATEST STORY EVER TOLD-SO FAR blind to left and right, then the decay will not change the parity of the quantum state of the system. If the wave function of the system is antisymmetric under inter- change of the particles after the decay, then the system has "negative" parity. In this case the wave function describing the initial quantum state of the decaying particle must also have negative parity (i.e., it would change sign if left and right were interchanged). Now, pions, the particles discovered by Powell and hypothesized by Yukawa, have negative parity, so that the wave function that describes the quantum state of their mirror image would change sign compared to the original wave function. The distinction between positive and negative parity is kind of like considering first a nice spherical ball, which looks identical when reflected in the mirror, and hence has positive parity: O 0 Versus, say, your hand, which changes character (from left to right) when reflected in a mirror and could therefore be said to have negative parity: 2P_G,mmstSloryEverTOd_AC.indd 166 12116116 3:06 PM EFTA00286078 March of the Titans 157 These somewhat abstract considerations made the observed data on the decays of the new particles that Powell discovered perplexing. Be- cause a pion has negative parity, two pions would have positive parity, since (-0.= 1. A system of three pions, however, would, by the same consideration, have negative parity, since (-03 = —1. Therefore if parity doesn't change when a particle decays, a single original particle cannot decay into two different final states of different parity. If the force responsible for the decay behaved like all the other known forces at the time, such as electromagnetism or gravity, it would be blind to parity (it would not distinguish between right and left), so it shouldn't change the original parity of the system after the decay, just as shining a light on your right hand will not cause it to look like your left hand. Since it seemed impossible for a single type of particle to decay some- times into two, and sometimes into three, pions, the solution seemed simple. There must be two different new elementary particles, with op- posite parity properties. Powell dubbed these the tau particle and theta particle—one of which could decay into two pions, and one into three pions. Observations suggested that the two particles had precisely the same masses and lifetimes, which was a bit strange, but Lee and Yang pro- posed that this might be a general property for various elementary par- ticles, which they suggested might come in pairs with opposite parity. They called this idea "parity doubling." Such was the situation in the spring of 190 when the International Conference on High Energy Physics, held every year at the University of Rochester, took place. In 1956, the entire community of physicists inter- ested in particle and nuclear physics could fit in a single university lec- ture hall, and these physicists, including all the major players, tended to gather at this annual meeting. Richard Feynman was sharing a room at the meeting with Marty Block. Being an experimentalist, Block was not as burdened by the possible heresy inherent in the suggestion that some 2P_GrealestSloiyerterTald_AC.indd 157 12/16116 3:06 PIA EFTA00286079 158 THE GREATEST STORY EVER TOLD-SO FAR force in nature was not blind to the distinction between left and right, and he asked Feynman if possibly the weak interaction governing the decays Powell observed might distinguish left from right. This would allow a single particle to decay to states of differing parity—meaning the tau and theta could both be the same particle. Block didn't have the temerity to raise this question in the public session, but Feynman did, even though he privately thought this was extremely unlikely. Yang replied that he and Lee had thought about this, but so far nothing had come of the idea. Eugene Wigner, who would later win a Nobel Prize for elucidating the importance of such things as parity in atomic and nuclear physics, was also present, and he too raised the same question about the weak interaction. But to the victor go the spoils, and speculating about the possible violation of parity by a new force in nature that might distinguish left from right was different from demonstrating it. A month later Lee and Yang were at a café in New York, and they decided to examine all known experiments involving the weak interaction to see if any of them could dispel the possibility of parity violation. To their great surprise, they realized that not a single one definitively resolved the issue. As Yang later said, The fact that parity conservation in the weak interaction was believed for so long without experimental support was very startling. But what was more startling was the prospect that a space-time symme- try law which the physicists have learned so well may be violated. This prospect did not appeal to us." To their credit, Lee and Yang proposed a variety of experiments that could test the possibility that the weak interaction distinguished right from left. They suggested considering the beta decay of a neutron in the nucleus of cobalt-6o. Because this radioactive nucleus has nonzero spin angular momentum—i.e., it behaves as if it is spinning—it also acts like a little magnet. In an external magnetic field the nuclei will line up in the direction of the field. If the electron emitted when a neutron in the nucleus decays preferentially ends up in one hemisphere instead of an- 2P_Glealer-StoryEverTold_Atindd 158 12/16116 3:06 PIA EFTA00286080 March of the Titans 159 other, this would be a sign of parity violation, because in the mirror the electrons would end up in the opposite hemisphere. If this was true, then at a fundamental level, nature would be able to distinguish right from left. The human-created distinctions between them (i.e., sinister versus good) would not then be totally artificial. Thus the world in a mirror could be distinguished from the real world, or, as Richard Feynman poetically put it later, we could use this experiment to send a message to tell a Martian what direction is "left"—say, the hemisphere where more electrons were observed to emerge—without drawing a picture. At the time, this was viewed as such a long shot that many in the physics community were amused, but no one ran out to perform the experiment. No one, that is, except Lee's colleague at Columbia the ex- perimentalist Chien-Shiung Wu, known as Madame Wu. Even as we bemoan today the paucity of female physicists trained at American institutions, the situation was much worse in 1956. After all, women weren't even admitted as undergraduates at Ivy League institu- tions until the late 1960s. Almost thirty years after Wu arrived from China to study at Berkeley in 1936, she noted in a Newsweek article about her, "It is shameful that there are so few women in science.... In China there are many, many women in physics. There is a misconception in America that women scientists are all dowdy spinsters. This is the fault of men. In Chinese society, a woman is valued for what she is, and men encourage her to accomplishments—yet she remains eternally femi- nine." Be that as it may, Wu was an expert in neutron decay and became in- trigued by the tantalizing possibility of searching for parity violation in the weak interaction after learning of it from her friends Lee and Yang. She canceled a European vacation with her husband and embarked on an experiment in June, one month after Lee and Yang had first thought of the problem, and by October of that year—the same month Lee and Yang's paper appeared in print—she and several colleagues had as- 2P_Glealer-StoryEverrold_Atincld 159 12/16116 3:06 PIA EFTA00286081 180 THE GREATEST STORY EVER TOLD-SO FAR sembled the apparatus necessary to do the experiment. TWo days after Christmas of that year they had a result. In modern times particle physics experiments might take decades from design to completion, but that was not the case in the 195os. It was also a time when physicists apparently didn't bother to take holi- days. Despite its being the yuletide, the Friday "Chinese Lunches" orga- nized by Lee continued, and the first Friday after New Year's Day Lee announced that Wu's group had discovered that not only was parity violated, but it was violated by the maximum amount possible in the ex- periment. The result was so surprising that Wu's group continued their work to ensure they weren't being fooled by an experimental glitch. Meanwhile, Leon Lederman and colleagues Dick Garwin and Mar- cel Weinrich, also at Columbia, realized that they could check the result in their experiments on pion and muon decays at Columbia's cyclotron. Within a week, both groups, as well as Jerry Friedman and Val Telegdi in Chicago, independently confirmed the result with high confidence, and by mid-January 1957 they submitted their papers to the Physical Review. They changed our picture of the world forever. Columbia University called what was probably the first press confer- ence ever announcing a scientific result. Feynman lost a 55o bet, but Wolfgang Pauli was luckier. He had written a letter from Zurich on Jan- uary is to Victor Weisskopf at MIT betting that Wu's experiment would not show parity violation, not knowing that the experiment already had. Pauli exclaimed in the letter, "I refuse to believe that God is a weak left- hander," demonstrating an interesting appreciation for baseball as well. Weisskopf, who by then knew of the actual result, was too kind to take the bet. Upon hearing the news, Pauli later wrote, "Now that the first shock is over, I begin to collect myself." It really was a shock. The idea that one of the fundamental forces in nature distinguished between right and left flew in the face of common sense, as well as of much of the basis of modern physics as it was understood then. 2P_Glealer-StoryEverTold_Atind6 160 12/16116 3:06 PIA EFTA00286082 March of the Titans 161 The shock was so great that, for one of the few times in the history of the Nobel Prizes, Nobel's will was actually carried out properly. His will stipulates that the prize should go to the person or persons in each field whose work that year was the most important. In October of 19s7, almost exactly a year from the publication of Lee and Yang's paper, and only ten months after Wu and Lederman confirmed the notion, the thirty-year-old Lee and the baby-faced thirty-four-year-old Yang shared the Nobel Prize for their proposal. Sadly, Madame Wu, known as the Chinese "Madame Curie," had to be content with winning the inaugural Wolf Prize in Physics twenty years later. Suddenly the weak interaction became more interesting, and also more confusing. Fermi's theory, which had sufficed up to that point, was roughly modeled after electromagnetism. We can think of the elec- tromagnetism interaction as a force between two different electric cur- rents, each corresponding to the two separate moving electrons that interact with each other. The weak interaction could be thought of in a somewhat similar way, if in one current a neutron, during the inter- action, converts into a proton, and in the other current is an outgoing electron and neutrino. There are two crucial differences, however. In Fermi's weak interac- tion the two different currents interact at a single point rather than at a distance, and the currents in the weak interaction allow particles to change from one type to another as they extend through space. While electromagnetic interactions are the same in the mirror as they are in the real world, if parity is violated in the weak interaction, the "currents" involved would have to have a "handedness," as Pauli al- luded, as for example a corkscrew or pair of scissors has, so that their mirror images will not be the same. Parity violation in weak interactions would then be like the social rule that we always shake hands with our right hand. In a mirror world, people would always shake with their left hand. Thus, the real world dif- fers from its mirror image. If the currents in the weak interaction had a 2P_Glealer-StoryEverTold_Atindd 181 12/16116 3:06 PIA EFTA00286083 162 THE GREATEST STORY EVER TOLD-SO FAR handedness, then the weak interaction could distinguish right from left and in a mirror world would be different from the force in the world in which we live. A great deal of work and confusion resulted as physicists tried to figure out precisely what types of new possible interaction could replace Fermi's simple current-to-current interaction, in which no apparent handedness could be attributed to the particles involved. Relativity al- lowed a variety of possible generalizations of Fermi's interaction, but the results of different experiments led to different, mutually exclusive mathematical forms for the interaction, so it appeared impossible that one universal weak interaction could explain all of them. Around the time when the first experimental results on neutron and muon decay had come out suggesting that parity violation was as large as it could be, a young graduate student at the University of Rochester, George Sudarshan, began exploring the confused situation and came up with what eventually was the correct form of a universal interaction that could replace Fermi's form—something that also required that at least some of the experimental results at the time were wrong. The rest of the story is a bit tragic. At the Rochester conference three months after the parity-violation discovery, and a year after Lee and Yang had presented their first thoughts on parity doubling, Sudarshan asked to present his results. But because he was a graduate student, he wasn't allowed. His supervisor, Robert Marshak, who had suggested the research problem to Sudarshan, was by then preoccupied with another problem in nuclear physics and chose to present a talk on that subject at the meeting. Another faculty member, who was asked to mention Sudarshan's work, also forgot. So all of the discussion at the meeting on the possible form of the weak interaction ended up leading nowhere. Earlier, in '947, Marshak had been the first to suggest that two dif- ferent mesons were discovered in Cecil Powell's experiments—with one being the particle proposed by Yukawa, and the other being the particle now called a muon. Marshak was also the originator of the Rochester 2P_Glealer-StoryEverTold_Atind6 162 12/16116 3:06 PIA EFTA00286084 March of the Titans 163 conferences and probably felt it would show favoritism to allow his own student to speak. In addition, since Sudarshan's idea required at least some of the experimental data to be wrong, Marshak may have decided it was premature to present it at the meeting. That summer Marshak was working at the RAND Corporation in Los Angeles and invited Sudarshan and another student to join him. The two most renowned particle theorists in the world then, Feynman and Murray Gell-Mann, were at Caltech, and each had become obsessed with unraveling the form of the weak interaction. Feynman had missed out on the discovery of parity violation by not following his own line of questioning, but had since realized that his work on quantum electrodynamics could shed light on the weak in- teraction. He desperately wanted to do this because he felt his work on QED was simply a bit of technical wizardry and far less noble than unearthing the form of the law governing another of the fundamental interactions in nature. But Feynman's proposal for the form of the weak interaction also appeared to disagree with experiments at the time. Over the igsos, Gell-Mann would produce many of the most impor- tant and lasting ideas in particle physics from that time. He was one of two physicists to propose that protons and neutrons were made of more fundamental particles, which he called quarks. He had his own reasons for thinking about parity and the weak interaction. Much of his success was based on focusing on new mathematical symmetries in nature, and he had used these ideas to come up with a new possible form for the weak interaction as well, but again his idea conflicted with experiment. While they were in LA, Marshak arranged for Sudarshan to have lunch with Gell-Mann to talk about their ideas. They also met with an eminent experimentalist, Felix Boehm, whose experiments, he said, were now consistent with their ideas. Sudarshan and Marshak learned from Gell-Mann that his ideas were consistent with Sudarshan's pro- posal, but that at best Gell-Mann was planning to include the notion in one paragraph of a long general paper on the weak interaction. 2P_Glealer-StoryEverTold_Atind6 163 12/16116 3:06 PIA EFTA00286085 184 THE GREATEST STORY EVER TOLD-SO FAR Meanwhile, Marshak and Sudarshan prepared a paper on their idea, and Marshak decided to save it for a presentation at an international conference in Italy in the fall. Learning of the new experimental data from Boehm, Feynman decided—rather excitedly—that his ideas were correct and began to write a paper on the subject. Gell-Mann, who was competitive in the extreme, decided he too should write up a paper since Feynman was writing one. Eventually their department chairman convinced them they needed to write their paper together, which they did, and it became famous. Although the paper had an acknowledgment to Sudarshan and Marshak for discussions, their paper appeared later in the conference proceedings and could not compete for the attention of the community. Later, in 1963, Feynman, who tried to be generous with ideas, publicly stated, "The ... theory that was discovered by Sudarshan and Marshak, publicized by Feynman and Gell-Mann ..." But it was too little, too late. It would have been hard in the best of times to compete in the limelight with Feynman and Gell-Mann, and Sudarshan had to live for years with the knowledge that the universal form of the weak interaction, which two of the world's physics heroes had discovered, was first proposed— and with more confidence—by him. Sudarshan's theory, as elucidated beautifully in Feynman and Gell- Mann's paper, became known as the V-A theory of the weak interaction. The reason for the name is technical and will make more sense in com- ing chapters, but the fundamental idea is simple, though it sounds both ridiculous and meaningless: the currents in the Fermi theory must be "left-handed." To understand this terminology, recall that in quantum mechanics elementary particles such as electrons, protons, and neutrinos have spin angular momentum—they behave as if they are spinning even though classically a point particle without extension can't be pictured as spin- ning. Now, consider the direction of their motion and pretend for a mo- ment the particle is like a top spinning around that axis. Put your right 2P_Glealer-StoryEverTold_Atirdd 184 12/18/18 3:06 PIA EFTA00286086 March of the Titans 166 hand out and let your thumb point in the direction of the particle's mo- tion. Then curl your other fingers around. If they are curling in the same (counterclockwise) direction that the particle/top is spinning about the direction of motion, the particle is said to be right-handed. If you put your left hand out and do the same thing, a left-handed particle would be spinning clockwise to match the direction of your left-curled hand: right-handed left-handed Just as viewing your left hand in a mirror will make it look like a right hand, if you see a spinning arrow in the mirror, its direction of motion will be flipped, so that if the arrow is moving away from you in the real world, it will be moving toward you in the mirror, but the spin will not be flipped. Thus, in the mirror a left-handed particle will turn into a right-handed particle. (And so, if the poor souls in Plato's cave had had mirrors, they might have felt less strange about the shadows of arrows flipping direction.) This working picture of left-handed particles is not exact, because if you think about it, you can also turn a left-handed particle into a right- handed particle by simply moving faster than the particle. In a frame in which a person at rest observes the particle zipping by, it may be moving to the left. But if you hop in a rocket and head off to the left and pass by that particle, then relative to you, it is moving to the right. As a result, only for particles that are massless—and are therefore moving at the speed of light—is the above description exact. For, if a particle is moving at the speed of light, nothing can move fast enough to pass the particle. Mathematically, the definition of left-handed has to take this effect into account, but this complication need not concern us any more here. 2P_Glealer-StoryEverTold_Atincld 165 12/16116 3:06 PIA EFTA00286087 IBS THE GREATEST STORY EVER TOLD-SO FAR Electrons can spin in either direction, but what the V-A interaction implies mathematically is that only those moving electrons whose cur- rents are left-handed can "feel" the weak force and participate in neu- tron decay. Right-handed currents don't feel the force. What is more amazing is that neutrinos only feel the weak force, and no other force. As far as we can tell, neutrinos are only left-handed. It is not just that only one sort of neutrino current engages in the weak interaction. In all the experimental observations so far, there are no right-handed neutrinos—perhaps the most explicit demonstration of the violation of parity in nature. The seeming silliness of this nomenclature was underscored to me years ago when I was watching a Star Thek Deep Space Nine episode, during which a science officer on the space station discovers something wrong with the laws of probability in a gaming casino. She sends a neu- trino beam through the facility, and the neutrinos are observed to be coming out only left-handed. Clearly something was wrong. Except that is the way it really is. What is wrong with nature? How come, for at least one of the fun- damental forces, left is different from right? And why should neutrinos be so special? The simple answer to these questions is that we don't yet know, even though our very existence, which derives from the nature of the known forces, ultimately depends on it. That is one reason we are trying to find out. The elucidation of a new force led to a new puzzle, and like most puzzles in science, it ultimately provided the key that would lead physicists down a new path of discovery. Learning that nature lacked the left-right symmetry that everyone had assumed was funda- mental led physicists to reexamine how symmetries are manifested in the world, and more important, how they are not. 2P_Glealer-StoryEverTold_Atirdd 1611 12/16116 3:06 PIA EFTA00286088 Chapter 13 ENDLESS FORMS MOST BEAUTIFUL: SYMMETRY STRIKES BACK Now faith is the substance of things hoped for, the evidence of things not seen. -HEBREWS 11:1 Borrowing from Pauli, we can say Mother Nature is a weak left-hander. With the shocking realization that nature distinguishes left from right, physics itself took a strange left turn down a road with no familiar guideposts. The beautiful order of the periodic table governing phenomena on atomic scales gave way to the mystery of the nucleus and the inscrutable nature of the forces that governed it. Gone were the seemingly simple days of light, motion, electromag- netism, gravity, and quantum mechanics. The spectacularly successful theory of quantum electrodynamics, which had previously occupied the forefront of physics, seemed to be replaced by a confusing world of ex- otic phenomena associated with the other two newly discovered weak and strong nuclear forces that governed the heart of matter. Their ef- fects and properties could not easily be isolated, despite that one force 167 2P_Glealer-StoryEverTaid_AC.incld 187 12/16116 3:06 PIA EFTA00286089 168 THE GREATEST STORY EVER TOLD-SO FAR was thousands of times stronger than the other. The world of funda- mental particles appeared to be ever more complicated, and the situa- tion was getting more confusing with each passing year. If the discovery of parity violation created shadows of confusion by demonstrating that nature had completely unexpected preferences, the first rays of light arose from the realization that other nuclear quantities, which on the surface seemed quite different, might, when viewed from a fundamental perspective, be not so different at all. Perhaps the most important discovery in nuclear physics was that pro- tons and neutrons could convert into each other, as Yukawa had specu- lated years earlier. This was the basis of the emerging understanding of the weak interaction. But most physicists felt that it was also the key to understanding the strong force that appeared to hold nuclei together. Two years before his revolutionary work with T.-D. Lee, exposing the demise of the sacred left-right symmetry of nature, C.-N. Yang had concentrated his efforts on trying to understand how a different type of symmetry, borrowed from quantum electrodynamics, might reveal an otherwise hidden beauty inside the nucleus. Perhaps, as Galileo discov- ered regarding the basis of motion, the most obvious things we observe about nature are also the things that most effectively mask its funda- mental properties. What had slowly become clear, not only from the progress in under- standing neutron decay and other weak effects in nuclei, but also from looking at strong nuclear collisions, was that the obvious distinction be- tween protons and neutrons—the proton is charged and the neutron is neutral—might, as far as the underlying physics governing the nucleus is concerned, be irrelevant. Or at least as irrelevant as the apparent dis- tinction between a falling feather and a falling rock is to our under- standing of the underlying physics of gravity and falling objects. First off, the weak force could convert protons into neutrons. More 2P_Glealer-StoryEverTold_Atind6 168 12/16/16 3:06 PIA EFTA00286090 Endless Forms Most Beautiful: Symmetry Strikes Back 169 important, when one examined the rates of other, stronger nuclear re- actions involving proton or neutron collisions, replacing neutrons by protons and vice versa didn't significantly change the results. In 1932, the year the neutron was discovered, Heisenberg had sug- gested that the neutron and proton might be just two states of the same particle, and he invented a parameter he called isotopic spin to distinguish them. After all, their masses are almost the same, and light-stable nuclei contain equal numbers of them. Following this, and after the recognition by the distinguished nuclear physicists Benedict Cassen, Edward Con- don, Gregory Breit, and Eugene Feenberg that nuclear reactions seemed to be largely blind to distinguishing protons and neutrons, the brilliant mathematical physicist Eugene Wigner suggested that isotopic spin was "conserved" in nuclear reactions—implying an underlying symmetry governing the nuclear forces between protons and neutrons. (Wigner had earlier developed rules demonstrating how symmetries in atomic systems ultimately allowed a complete classification of atomic states and the transitions between them, for which he later won the Nobel Prize.) Earlier, when discussing electromagnetism, I noted that the net electric charge doesn't change during electromagnetic interactions— i.e., electric charge is conserved—because of an underlying symmetry between positive and negative charges. The underlying connection be- tween conservation laws and symmetries is far broader and far deeper than this one example. The deep and unexpected relationship between conservation laws and symmetries of nature has been the single most important guiding principle in physics in the past century. In spite of its importance, the precise mathematical relationship be- tween conservation laws and symmetries was only made explicit in 1915 by the remarkable German mathematician Emmy Noether. Sadly, al- though she was one of the most important mathematicians in the early twentieth century, Noether worked without an official position or pay for much of her career. Noether had two strikes against her. First, she was a woman, which 2P_Glealer-StoryEverrold_Atindd 169 12/16116 3:06 PIA EFTA00286091 170 THE GREATEST STORY EVER TOLD-SO FAR made obtaining education and employment during her early career dif- ficult, and second, she was Jewish, which ultimately ended her academic career in Germany and resulted in her exile to the United States shortly before she died. She managed to attend the University of Erlangen as one of 2 female students out of 986, but even then she was only allowed to audit classes after receiving special permission from individual profes- sors. Nevertheless, she passed the graduation exam and later studied at the famed University of Gottingen for a short period before returning to Erlangen to complete her PhD thesis. After working for seven years at Erlangen as an instructor without pay, she was invited in 1915 to return to Gottingen by the famed mathematician David Hilbert. Historians and philosophers among the faculty, however, blocked her appointment. As one member protested, "What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman?" In a retort that eternally reinforced my admiration for Hilbert, beyond that for his remarkable talent as a mathematician, he replied, 1 do not see that the sex of the candidate is an argument against her ad- mission as a Privatdozent. After all, we are a university, not a bathhouse." Hilbert was overruled, however, and while Noether spent the next seventeen years teaching at Gottingen, she was not paid until 1923, and in spite of her remarkable contributions to many areas of mathemat- ics—so many and so deep that she is often considered one of the great mathematicians of the twentieth century—she was never promoted to the position of professor. Nevertheless, in 1915, shortly after arriving at Gottingen, she proved a theorem that is now known as Noether's theorem, which all graduate students in physics learn, or should learn, if they are to call themselves physicists. Returning once again to electromagnetism, the relationship between the arbitrary distinction between positive and negative (had Benjamin Frank- 2P_Glealer-StoryEverTold_Atincld 170 12/16116 3:06 PM EFTA00286092 Endless Forms Most Beautiful: Symmetry Strikes Sack 171 lin had a better understanding of nature when he defined positive charge, electrons would today probably be labeled as having positive, not negative, charge) and the conservation of electric charge—namely, that the total charge in a system before and after any physical reaction doesn't change— is not at all obvious. It is in fact a consequence of Noether's theorem, which states that for every fundamental symmetry of nature—namely for every transformation under which the laws of nature appear unchanged—some associated physical quantity is conserved. In other words, some physical quantity doesn't change over time as physical systems evolve. Thus: • The conservation of electric charge reflects that the laws of nature don't change if the sign of all electric charges is changed. • The conservation of energy reflects that the laws of nature don't change with time. • The conservation of momentum reflects that the laws of nature don't change from place to place. • The conservation of angular momentum reflects that the laws of na- ture don't depend on which direction a system is rotated. Hence, the claimed conservation of isotopic spin in nuclear reactions is a reflection of the experimentally verified claim that nuclear interac- tions remain roughly the same if all protons are changed into neutrons and vice versa. It is reflected as well in the world of our experience, in that for light elements, at least, the number of protons and neutrons in the nucleus is roughly the same. In 1954, Yang, and his collaborator at the time, Robert Mills, went one important step further, once again thinking about light. Electromagne- tism and quantum electrodynamics do not just have the simple symme- try that tells us that there is no fundamental difference between negative charge and positive charge, and that the label is arbitrary. As I described at length earlier, a much more subtle symmetry is at work as well, one that ultimately determines the complete form of electrodynamics. 2P_Glealer-StoryEverTold_AC.incld 171 12/16116 3:06 PIA EFTA00286093 172 THE GREATEST STORY EVER TOLD-SO FAR Gauge symmetry in electromagnetism tells us that we can change the definition of positive and negative charge locally without changing the physics, as long as there is a field, in this case the electromagnetic field, that can account for any such local alterations to ensure that the long-range forces between charges are independent of this relabeling. The consequence of this in quantum electrodynamics is the existence of a massless particle, the photon, which is the quantum of the electro- magnetic field, and which conveys the force between distant particles. In this sense, that gauge invariance is a symmetry of nature ensures that electromagnetism has precisely the form it has. The interactions between charged particles and light are prescribed by this symmetry. Yang and Mills then asked what would happen if one extended the symmetry that implies that we could interchange neutrons and protons everywhere without changing the physics, into a symmetry that allows us to change what we label as "neutron" and "proton" differently from place to place. Clearly by analogy with quantum electrodynamics, some new field would be required to account for and neutralize the effect of these arbitrarily varying labels from place to place. If this field is a quan- tum field, then could the particles associated with this field somehow play a role in, or even completely determine, the nature of the nuclear forces between protons and neutrons? These were fascinating questions, and to their credit Yang and Mills didn't merely ask them, they tried to determine the answers by explor- ing specifically what the mathematical implications of such a new type of gauge symmetry associated with isotopic spin conservation would be. It became clear immediately that things would get much more com- plicated. In quantum electrodynamics, merely switching the sign of charges between electrons and positrons does not change the magnitude of the net charge on each particle. However, relabeling the particles in the nucleus replaces a neutral neutron with a positively charged proton. Therefore whatever new field must be introduced in order to cancel out the effect of such a local transformation so that the underlying physics is 2P_GrealestSloiyEverTald_AC.indd 172 12/16116 3:06 PIA EFTA00286094 Endless Forms Most Beautiful: Symmetry Strikes Back 173 unchanged must itself be charged. But if the field is itself charged, then, unlike photons—which, being neutral, don't themselves interact directly with other photons—this new field would also have to interact with itself. Introducing the need for a new charged generalization of the elec- tromagnetic field makes the mathematics governing the theory much more complex. In the first place, to account for all such isotopic spin transformations one would need not just one such field but three fields, one positively charged, one negatively charged, and one neutral. This means that a single field at each point in space, like the electromagnetic field in QED, which points in a certain direction in space with a certain magnitude (and is called a vector field in physics for this reason), is not sufficient. The electric field must be replaced by a field described by a mathematical object called a matrix—not to be confused with anything having to do with Keanu Reeves. Yang and Mills explored the mathematics behind this new and more complex type of gauge symmetry, which today we call either a non- abelian gauge symmetry—arising from a particular mathematical prop- erty of matrices that makes multiplying them different from multiplying numbers—or, in deference to Yang and Mills, a Yang-Mills symmetry. Yang and Mills's article appears at first glance to be an abstract—or purely speculative—mathematical exploration of the implications of a guess about the possible form of a new interaction, motivated by the ob- servation of gauge symmetry in electromagnetism. Nevertheless, it was not an exercise in pure mathematics. The paper tried to explore possible observable consequences of the hypothesis to see if it might relate to the real world. Unfortunately the mathematics was sufficiently complicated such that the possible observable signatures were not so obvious. One thing was clear, however. If the new "gauge fields" were to ac- count for and thus cancel out the effects of separate isotopic spin transformations made in distant locations, the fields would have to be massless. This is equivalent to saying that only because photons are massless can the force they transmit between particles be arbitrarily 2P_Glealer-StoryEverrold_Aairdd 173 12/16116 3:06 PIA EFTA00286095 174 THE GREATEST STORY EVER TOLD-SO FAR long-range. To return to my chessboard analogy, you need a single rule- book to tell you how to properly move over the entire board if I have pre- viously changed the colors of the board randomly from place to place. But having massive gauge fields, which cannot be exchanged over arbi- trarily long distances, is equivalent to having a rulebook that tells you how to compensate for changing colors only on nearby squares around your starting point. But this would not allow you to move pieces across the board to distant locations. In short, a gauge symmetry such as that in electromagnetism, or in the more esoteric Yang-Mills proposal, only works if the new fields re- quired by the symmetry are massless. Amid all the mathematical com- plexity, this one fact is inviolate. But we have observed in nature no long-range forces involving the exchange of massless particles other than electromagnetism and grav- ity. Nuclear interactions are short-range—they only apply over the size of the nucleus. This obvious problem was not lost on Yang and Mills, who recog- nized it and, frankly, punted. They proposed that somehow their new particles could become massive when they interacted with the nucleus. When they tried to estimate masses from first principles, they found the theory was too mathematically complicated to allow them to make reasonable estimates. All they knew was that empirically the mass of the new gauge particles would have to be greater than that of pions in order to have avoided detection in then-existing experiments. Such a willingness to throw their hands in the air might have seemed either lazy or unprofessional, but Yang and Mills knew, as Yukawa had known before them, that no one had been able to write down a sensible quantum field theory of a particle like the photon, but one that, unlike the photon, had a mass. So it didn't seem worthwhile at the time to try to solve all the problems of quantum field theory at once. Instead, with less irreverence than Jonathan Swift, they merely presented their paper as a modest proposal, to spur the imagination of their colleagues. 2P_Glealer-StoryEverTold_Atirdd 174 12/16116 3:06 PIA EFTA00286096 Endless Forms Most Beautiful: Symmetry Strikes Sack 175 Wolfgang Pauli, however, would have none of it. While he had thought of some related ideas a year earlier, he had discarded them. Moreover, he felt that all this talk about quantum uncertainties in estimating masses was a red herring. If there was to be a new gauge symmetry in nature as- sociated with isotopic spin and governing nuclear forces, the new Yang- Mills particles, like the photon, would have to be massless. For these reasons, among others, the Yang-Mills paper made far less of a stir at the time than the later Yang and Lee opus. To most physicists it was an interesting curiosity at best, and the discovery of parity viola- tion seemed much more exciting. But not to Julian Schwinger, who was no ordinary physicist. A child prodigy who had graduated from university by the age of eighteen, he received his PhD by the age of twenty-one. Perhaps no two physicists could have been as different as he and Richard Feynman, who shared the Nobel Prize in 196s for their separate but equivalent work devel- oping the theory of quantum electrodynamics. Schwinger was refined, formal, and brilliant. Feynman was brilliant, casual, and certainly not refined. Feynman relied often on intuition and guesswork, building on prodigious mathematical skill and experience. Schwinger's mathemati- cal skill was every bit Feynman's equal, but Schwinger worked in an orderly fashion, manipulating complicated mathematical expressions with an ease not possible for ordinary mortals. He joked about Feynman diagrams, which Feynman had developed to make what had previously been perilously laborious calculations in quantum field theory manage- able, saying, "Like the silicon chips of more recent years, the Feynman diagram was bringing computation to the masses." Both of them shared one characteristic, however. They marched to the beat of a different drummer... in opposite directions. Schwinger took the Yang-Mills idea seriously. The mathematical beauty must have appealed to him. In 3.9s7, the same year that parity violation was discovered, Schwinger made a bold and seemingly highly unlikely suggestion that the weak interaction responsible for the decay 2P_GrealestSloryEverTald_AC.indd 175 12/16116 3:06 PIA EFTA00286097 176 THE GREATEST STORY EVER TOLD-SO FAR of neutrons into protons, electrons, and neutrinos might benefit from the possibility of Yang-Mills fields, but in a new and remarkable way. He proposed that the observed gauge symmetry of electromagnetism might simply be one part of a larger gauge symmetry in which new gauge particles might mediate the weak interaction that caused neu- trons to decay. An obvious objection to this kind of unification is that the weak interaction is far weaker than electromagnetism. Schwinger had an answer for this. If somehow the new gauge particles were very heavy, almost one hundred times heavier than protons and neutrons, then the interaction they might mediate would be of much shorter range than even the size of a nucleus, or even a single proton or neutron. In this case, one could work out that the probability that this interaction would cause a neutron to decay would be small. Thus, if the range of the weak interaction was small, these new fields, the strength of whose intrinsic coupling to electrons and protons on small scales could be comparable to the strength of electromagnetism, could nevertheless, on the scale of nuclei and larger, appear to be much, much weaker. Put more bluntly, Schwinger proposed the outrageous idea that electromagnetism and the weak interaction were part of a single Yang- Mills theory, in spite of the remarkable and obvious differences between them. He thought that perhaps the photon could be the neutral member of a Yang-Mills-type set of three gauge particles required by treating isotopic spin as a gauge symmetry, with the charged versions convey- ing the weak interaction and being responsible for mediating the decay of neutrons. Why the charged particles would have a huge mass while the photon was massless, he had no idea. But, as I have often said, lack of understanding is neither evidence for God, nor evidence that one is necessarily wrong. It just is evidence of lack of understanding. Schwinger was not only a brilliant physicist but a brilliant teacher and mentor. While Feynman had few successful students, probably be- cause none of them could keep up with him, Schwinger seemed to have 2P_GrealestStrayC-verTaleLAC.indd lit 122/16/16 3:06 PIA EFTA00286098 Endless Forms Most Beautiful: Symmetry Strikes Sack 177 a knack for guiding brilliant PhD students. In his life he supervised more than seventy PhDs, and four of his students later won the Nobel Prize. Schwinger was sufficiently interested in relating the weak interac- tion to electromagnetism that he encouraged one of his dozen graduate students at Harvard at the time to explore the issue. Sheldon Glashow graduated in 1958 with a thesis on the subject and continued to explore the issue for the next few years as a National Science Foundation post- doctoral researcher in Copenhagen. In his Nobel lecture twenty years later, Glashow indicated that he and Schwinger had planned to write a manuscript on the subject after Glashow graduated, but one of them lost the first draft of the manuscript, and they never got back to it. Glashow was no clone of Schwinger's. Refined and brilliant, yes, but also brash, playful, and boisterous, Glashow did research that was not characterized by mathematical acrobatics, but rather by a keen focus on physical puzzles and exploring new possible symmetries of nature that might resolve them. When I was a young graduate student in physics at MIT, I was ini- tially drawn to deep mathematical questions in physics and had written my admissions essay for my PhD application on just this subject. Within a few years I found myself depressed by the nature of the mathematical investigations I was pursuing. I met Glashow at a summer school for PhD students in Scotland and became friends with both him and his family—a friendship that continued to blossom when we later became colleagues at Harvard. The year after we met, he spent a sabbatical year at MIT. During this important time for me, when I was considering alternatives, he said to me, "There's physics, and there's formalism, and you have to know the difference." Implicit in this advice was the sugges- tion that I should pursue physics. When I saw the fun he was having, it became easier to consider joining in. I soon realized that for me to make progress in physics I needed to work on questions driven primarily by physical issues, not ones driven primarily by mathematical issue. The only way I could do that would 2P_Glealer-StoryEverTold_Atirdd 177 12/16116 3:06 PIA EFTA00286099 178 THE GREATEST STORY EVER TOLD-SO FAR be to keep in touch with ongoing experiments—and new experimental results. By watching Shelly and how he did physics, I realized that he had an uncanny ability to know which experiments were interesting, and which results might be significant or might point toward some- thing new. Part of this was undoubtedly innate, but part was based on a lifetime of keeping in touch with what was happening on the ground. Physics is an empirical science, and we lose touch with that at our peril. In Copenhagen, Glashow realized that if he wanted to properly im- plement Schwinger's proposal to connect the weak interaction with the electromagnetic interaction, then simply making the photon be the neu- tral member of a triplet of gauge particles, with the charged members becoming massive by some as yet unknown miracle, wouldn't fly. This couldn't explain the proper nature of the weak interaction, in particular the strange fact that the weak interaction seemed to apply only to left- handed electrons (and neutrinos), whereas electromagnetic interactions don't depend on whether the electrons are left- or right-handed. The only solution to this problem would be if another neutral gauge particle existed—in addition to the photon—which itself coupled to only left-handed particles. But clearly the new neutral particle would also have to be heavy since the interactions it mediated would have to be weak as well. Glashow's ideas were reported to the physics community by Murray Gell-Mann at the 1960 Rochester meeting, as Gell-Mann had by then recruited Glashow to Caltech to work in Gell-Mann's group. Glashow's paper on the subject, submitted in 1960, appeared in 1961 in print. Yet, no sudden stampede occurred in response. After all, two fundamental problems remained with Glashow's pro- posal. The first was the long-familiar problem of how one could have the different masses of the particles needed to convey the different forces, when gauge symmetries required all the gauge particles to be massless. Glashow simply stated in the introduction of his paper, following in a long line of such hubris, "It is a stumbling block we must overlook." 2P_GrealesiSleryEverTold_AC.indd 178 12/16116 3:06 P1.1 EFTA00286100 Endless Forms Most Beautiful: Symmetry Strikes Back 179 The second problem was more subtle, but from an experimental per- spective equally severe. Neutron decay, pion decay, and muon decay, if they were indeed mediated by some new particles conveying the weak force, all appeared to require only the exchange of new charged par- ticles. No weak interaction had been observed that would require the exchange of a new neutral particle. If such a new neutral particle did exist, calculations at the time suggested it would allow the other known heavier mesons that decayed into two or three pions (and were respon- sible for the original confusion that led to the discovery of parity viola- tion) to decay much more rapidly than they were observed to decay. For these reasons, Glashow's proposal drifted into the background as physicists became entranced with the new particle zoo that was emerging out of accelerators, and the concomitant opportunity for new discoveries. Yet several of the key theoretical ingredients needed to complete a revolution in fundamental physics were in place, but it was far from obvious at the time. That within slightly more than a decade after Glashow's paper was published all of the known forces in nature save gravity would be unveiled and understood would have seemed like pure fantasy at the time. And symmetry would be the key. 2P_GrealesiSleryEverTold_AC.indd 179 12/16116 3:06 PIA EFTA00286101 2P_Gtealer-StoryEverTold_AC.irdd ISO 12/16116 3:06 PM EFTA00286102 Chapter 14 COLD, STARK REALITY: BREAKING BAD OR BEAUTIFUL? From whose womb has come the ice? And the frost of heaven, who has given it birth? -JOB 38:29 It is easy to pity the poor protagonists in Plato's cave, who may understand everything there is to know about the shadows on the wall, except that they are shadows. But appearances can be deceiving. What if the world around us is just a similar shadow of reality? Imagine, for example, that you wake up one cold winter morning and look out your window, and the view is completely obscured by beautiful ice crystals, forming strange patterns on the glass. It might look like this: blidOgf aril by Hokin AM:v.2 181 2P_Gtealer-StoryEverrold_Atindd 181 12/16116 3:06 PM EFTA00286103 182 THE GREATEST STORY EVER TOLD-SO FAR The beauty of the image is striking at least in part because of the re- markable order on small scales lurking within the obvious randomness on large scales. Ice crystals have grown gorgeous treelike patterns, start- ing in random directions and bumping into each other at odd angles. The dichotomy between small-scale order and large-scale randomness suggests that the universe would look very different to tiny physicists or mathematicians confined to live on the spine of one of the ice crystals in the image. One direction in space, corresponding to the direction along the spine of the ice crystal, would be special. The natural world would ap- pear to be oriented around that axis. Moreover, given the crystal lattice structure, electric forces along the spine would appear to be quite dif- ferent from the forces perpendicular to it: the forces would behave as if they were different forces. If the physicist or mathematician living on the crystal was clever, or, like the mathematician in Plato's cave, lucky enough to leave the crystal, it would soon become clear that the special direction that governed the physics of the world they were used to was an illusion. They would find, or surmise, that other crystals could point in many other directions. Ultimately if they could observe the window from the outside on large enough scales, the underlying symmetry of nature under rotations in all directions, reflected in the growth of the crystals in all directions, would become manifest. The notion that the world of our experience is a similar accident of our particular circumstances rather than a direct reflection of underly- ing realities has become central to modern physics. We even give it a fancy name: spontaneous symmetry breaking. I mentioned one sort of spontaneous symmetry breaking earlier when discussing parity, or left-right symmetry. Our left hands look dif- ferent from our right hands even though electromagnetism—the force that governs the building of large biological structures such as our bod- ies—doesn't distinguish between left and right. 2P_GrealetaleryEverTold_AC.indd 182 12/18/18 308 PIA EFTA00286104 Cold. Stark Reality: Breaking Bad or Beautiful? 183 Two other examples I know of, both presented by distinguished physicists, also help illuminate spontaneous symmetry breaking in dif- ferent ways that might be useful. Abdus Salam, who won a Nobel Prize in 1979 for work that depended crucially on this phenomenon, described a situation that is familiar to all of us: sitting down with a group of people at a round dining table set for, say, eight people. When you sit down, it may not be obvious which wineglass is yours and which is your neighbor's—the one on the right or the one on the left. But regardless of the laws of etiquette, which dictate it should be on your right, once the first person picks up her glass, everyone else at the table has only one option if everyone is to get a drink. Even though the underlying symme- try of the table is manifest, the symmetry gets broken when a direction is chosen for the wineglasses. Yoichiro Nambu, another Nobelist who was the first physicist to de- scribe spontaneous symmetry breaking in particle physics, gave another example that I will adapt here. Take a rod, or even a drinking straw, hold it up with one end on a table, and press down on the top end of the rod. Ultimately the rod will bend. It could bend in any direction, and if you try the experiment several times, you may find it bending in different directions each time. Before you press down, the rod has complete cy- lindrical symmetry. Afterward, one direction among many possibilities has been chosen, not determined by the underlying physics of the rod but by the accident of the particular way you press on the rod each time. The symmetry has been broken spontaneously. If we now return to the world of the frozen window, the character- istics of materials can change as we cool systems down. Water freezes, gases liquefy, and so on. In physics, such a change is called a phase tran- sition, and as the window example demonstrates, whenever a system undergoes a phase transition, it is not unusual to find that symmetries associated with one phase will disappear in the other phase. Before the ice froze into the crystals on the window, the water droplets wouldn't have been so ordered, for example. 2P_GrealetaleryEverTold_AC.indd 183 12/18/18 308 PIA EFTA00286105 184 THE GREATEST STORY EVER TOLD-SO FAR One of the most astonishing phase transitions ever witnessed in sci- ence was first observed by the Dutch physicist Kamerlingh Onnes on April 8, 1911. Onnes had—remarkably—been able to cool materials to temperatures never before achieved, and he was the first person to liq- uefy helium, at just four degrees above absolute zero. For this experi- mental prowess he was later awarded a Nobel Prize. On April 8, when cooling a mercury wire down to 4.2 degrees above absolute zero in a liquid helium bath and measuring its electrical resistance, to his aston- ishment he discovered that the resistance suddenly dropped to zero. Currents could flow in the wire indefinitely once they began, even after any battery that started the flow was removed. Demonstrating that his talent for public relations was as astute as his experimental talents, he coined the term superconductivity to describe this remarkable and com- pletely unexpected result. Superconductivity was so unexpected and strange that it would take almost fifty years after the discovery of quantum mechanics, on which it depends, before a fascinating physics explanation was developed by the team of John Bardeen, Leon Cooper, and Robert Schrieffer, in 1957. (That was same year that parity violation was observed, and that Schwinger proposed a model to try to unify the weak and electromagnetic interac- tion.) Their work was a tour de force, built on a succession of insights made over several decades of work. Ultimately the explanation relies on an unexpected phenomenon that can only occur in certain materials. In empty space, electrons repel other electrons because like charges repel each other. However, in certain materials, as they are cooled, elec- trons can actually bind to other electrons. This happens in the mate- rial because a free electron tends to attract around it positively charged ions. If the temperature is extremely low, then another electron can be attracted to the positively charged field around the first electron. Pairs of electrons can bind together, with the glue, if you wish, being the posi- tively charged field caused by the attraction of the first electron on the lattice of positive charges associated with the atoms in the material. 2P_Glealer-StoryEverTold_Atirdd 184 12/18/18 3:08 PM EFTA00286106 Cold. Stark Reality: Breaking Sad or Beautiful? 185 Since the nuclei of atoms are heavy and pinned in place by relatively strong atomic forces, the first electron slightly distorts the lattice of nearby atoms, moving some of the atoms slightly closer to the electron than they would otherwise be. Distortions of the lattice in general cause vibrations, or sound waves, in the material. In the quantum world these vibrations are quantized and are called phonons. Leon Cooper discov- ered that these phonons can bind pairs of electrons, as I have described above, so these are called Cooper pairs. The true magic of quantum mechanics occurs next. When mer- cury (or any of several other materials) is cooled below a certain point, a phase transition occurs and all the Cooper pairs suddenly coalesce into a single quantum state. This phenomenon, called Bose-Einstein condensation, occurs because unlike fermions, particles with integral quantum mechanical spin, such as photons, or even particles with zero spin, instead prefer to all be in the same state. This was proposed first by the Indian physicist Satyendra Nath Bose and later elaborated upon by Einstein. Once again light played a crucial role, as Bose's analysis involved the statistics of photons, and Bose-Einstein condensation is intimately related to the physics governing lasers, in which many indi- vidual photons all behave coherently in the same state. For this reason particles with integral spin such as photons are called bosons, to distin- guish them from fermions. In a gas or a solid at room temperature, normally so many collisions occur between particles that their individual states are changing rapidly and any collective behavior is impossible. However, a gas of bosons can coalesce at a low enough temperature into a Bose-Einstein condensate, in which the individual particles identities disappear. The whole system behaves like a single, sometimes macroscopic, object, but in this case acting via the rules of quantum mechanics, rather than classical me- chanics. As a result, a Bose-Einstein condensate can have exotic properties, the way laser light can behave very differently from normal light coming 2P_Glealer-StoryEverTold_Atirdd 185 12/16116 3:06 PIA EFTA00286107 186 THE GREATEST STORY EVER TOLD-SO FAR from flashlights. Since a Bose-Einstein condensate is a huge amalga- mation of what would otherwise be individual noninteracting particles, now tied together into a single quantum state, creating such a conden- sate required exotic and special atomic physics experiments. The first direct observation of such a condensation from a gas of particles did not take place until 1995, by the US physicists Carl Wieman and Eric Cor- nell, another feat that was deemed worthy of a Nobel Prize. What makes the possibility of such a condensation inside bulk ma- terials such as mercury so strange is that the fundamental particles initially involved are electrons—which not only normally repel other electrons, but in addition have spin 1/2 and, as fermions, have precisely the opposite behavior of bosons, as I described above. But when the Cooper pairs form, the two electrons each act in con- cert, and since both of them have spin 1/2, the combined object has integral (2 x 54) spin. Voile, a new kind of boson is created. The lowest- energy state of the system, to which it relaxes at low temperature, is a condensate of Cooper pairs—all condensed into a single state. When that happens, the properties of the material change completely. Before the condensate forms, when a voltage is applied to a wire, individual electrons begin to move to form an electric current. As they bump into atoms along the way, they dissipate energy, producing an electrical resistance that we are all familiar with, and heating up the wire. Once the condensate forms, however, the individual electrons and even each Cooper pair no longer have any individual identity. Like the Borg in Star Trek, they have assimilated into a collective. When a cur- rent is applied, the whole condensate moves as one entity. Now, if the condensate were to bounce off an individual atom, the trajectory of the whole condensate would change. But this would take a lot of energy, much more than would have been required to redirect the flow of an individual electron. Classically we can think of the result as follows: at low temperatures, not enough heat energy is available in the random jittering of atoms to cause a change of motion of the bulk 2P_Glealer-StoryEverTold_Atirdd 188 12/16116 3:06 PIA EFTA00286108 Cold. Stark Reality: Breaking Bad or Beautiful? 187 condensate of particles. It would again be like trying to move a truck by throwing popcorn at it. Quantum mechanically the result is similar. In this case we would say that to change the configuration of the conden- sate would require the whole condensate of particles to shift by a large fixed amount to a new quantum state that differs in energy from the state it is in. But no such energy is available from the thermal bath at low temperature. Alternatively, we might wonder if the collision could break apart two electrons from a Cooper pair in the condensate—sort of like knocking off the rearview mirror when a truck collides with a post. But at low temperatures everything is moving too slowly for that to happen. So the current flows unimpeded. The Borg would say, resistance is futile. But in this case resistance is simply nonexistent. A current, once initi- ated, will flow forever, even if the battery initially attached to the wire is removed. This was the Bardeen-Cooper-Schrieffer (BCS) theory of supercon- ductivity, a remarkable piece of work, which ultimately explained all of the experimental properties of superconductors such as mercury. These new properties signal that the ground state of the system has changed from what it had been before it became a superconductor, and like ice crystals on a window, these new properties reflect spontaneous sym- metry breaking. In superconductors the breaking of symmetry is not as visually obvious as it is in the ice crystals on a windowpane, but it is there, under the surface. Mathematically, the signature of this symmetry breaking is that sud- denly, once the condensate of Cooper pairs forms, a large minimum en- ergy is now required to change the configuration of the whole material. The condensate acts like a macroscopic object with some large mass. The generation of such a "mass gap" (as it is called—expressed as the minimum energy it takes to break the system out of its superconducting state) is a hallmark of the symmetry-breaking transition that produces a superconductor. You might be wondering what all of this, as interesting as it might be, 2P_Glealer-StoryEverTold_Atindd 187 12/16116 3:06 PIA EFTA00286109 188 THE GREATEST STORY EVER TOLD-SO FAR has to do with the story we have been focusing on, namely understand- ing the fundamental forces of nature. With the benefit of hindsight, the connection will be clear. However, in the tangled and confused world of particle physics in the 19505 and '6os the road to enlightenment was not so direct. In 1956, Yoichiro Nambu, who had recently moved to the Univer- sity of Chicago, heard a seminar by Robert Schrieffer on what would become the BCS theory of superconductivity, and it left a deep impres- sion on him. He, like most others interested in particle physics at the time, had been wrestling with how the familiar particles that make up atomic nuclei—protons and neutrons—fit within the particle zoo and the jungle of interactions associated with their production and decay. Nambu, like others, was struck by the almost identical masses of the proton and the neutron. It seemed to him, as it had to Yang and Mills, that some underlying principle in nature must produce such a result. Nambu, however, speculated that the example of superconductivity might provide a vital clue—in particular the appearance of a new char- acteristic energy scale associated with the excitation energy required to break apart the Cooper-pair condensate. For three years Nambu explored how to adapt this idea to symmetry breaking in particle physics. He proposed a model by which a similar condensate of some fields that might exist in nature and the minimum energy to create excitations out of this condensate state could be charac- teristic of the large mass/energy associated with protons and neutrons. Independently, he and the physicist Jeffrey Goldstone discovered that a hallmark of such symmetry breaking would be the existence of other massless particles, now called Nambu-Goldstone (NG) bosons, whose interactions with other matter would also reflect the nature of the sym- metry breaking. An analogy of sorts can be made here to a more familiar system such as an ice crystal. Such a system spontaneously breaks the symmetry under spatial translation because moving in one direction things look very different from when moving in another direction. But 2P_Glealer-StoryEverTold_Atincld 188 12/16116 3:06 PIA EFTA00286110 Cold. Stark Reality: Breaking Sad or Beautiful? 189 in such a crystal, tiny vibrations of individual atoms in the crystal about their resting positions are possible. These vibrational modes—called phonons, as I have mentioned—can store arbitrarily small amounts of energy. In the quantum world of particle physics, these modes would be reflected as Nambu-Goldstone massless particles, because where the equivalence between energy and mass is manifest, excitations that carry little or no energy correspond to massless particles. And, lo and behold, the pions discovered by Powell closely fit the bill. They are not exactly massless, but they are much lighter than all other strongly interacting particles. Their interactions with other particles have the characteristics one would expect of NG bosons, which might exist if some symmetry-breaking phenomenon existed in nature with a scale of excitation energy that might correspond to the mass/energy scale of protons and neutrons. But, in spite of the importance of Nambu's work, he and almost all of his colleagues in the field overlooked a related but much deeper conse- quence of the spontaneous symmetry breaking in the theory of super- conductivity that later provided the key to unlock the true mystery of the strong and weak nuclear forces. Nambu's focus on symmetry break- ing was inspired, but the analogies that he and others drew to supercon- ductivity were incomplete. It seems that we are much closer to the physicists on that ice crystal on the windowpane than we ever imagined. But just as one might imag- ine would be the case for those physicists, this myopia was not immedi- ately obvious to the physics community. 2P_Glealer-StorgverTold_Atindd 189 12/16116 3:06 PIA EFTA00286111 2P_GreatestSlowEverrold_AC.indd 190 12/16/16 3:06 PM EFTA00286112 Chapter 15 LIVING INSIDE A SUPERCONDUCTOR Everyone lies to their neighbor; they flatter with their lips but harbor deception in their hearts. -PSALMS 12:2 The mistakes of the past may seem obvious with the ben- efit of hindsight, but remember that objects viewed in the rearview mir- ror are often closer than they appear. It is easy to castigate our predecessors for what they missed, but what is confusing to us today may be obvious to our descendants. When working on the edge, we travel a path often shrouded in fog. The analogy to superconductivity first exploited by Nambu is use- ful, but largely for reasons very different from what Nambu and others imagined at the time. In hindsight the answer may seem almost obvi- ous, just as the little clues that reveal the murderer in Agatha Christie stories are clear after the solution. But, as in her mysteries, we also find lots of red herrings, and these blind alleys make the eventual resolution even more surprising. We can empathize with the confusion in particle physics at the time. New accelerators were coming online, and every time a new collision- 181 2P_Glealer-Storgverrold_Aairdd 191 12/16116 3:06 PIA EFTA00286113 192 THE GREATEST STORY EVER TOLD-SO FAR energy threshold was reached, new strongly interacting cousins of neu- trons and protons were produced. The process seemed as if it would be endless. This embarrassment of riches meant that both theorists and experimentalists were driven to focus on the mystery of the strong nu- clear force, which seemed to be where the biggest challenge to existing theory lay. A potentially infinite number of elementary particles with ever- higher masses seemed to characterize the microscopic world. But this was incompatible with all the ideas of quantum field theory—the suc- cessful framework that had so beautifully provided an understanding of the relativistic quantum behavior of electrons and photons. Berkeley physicist Geoffrey Chew led the development of a popu- lar, influential program to address this problem. Chew gave up the idea that any truly fundamental particles exist and also gave up on any microscopic quantum theory that involved pointlike particles and the quantum fields associated with them. Instead, he assumed that all of the observed strongly interacting particles were not pointlike, but com- plicated, bound states of other particles. In this sense, there could be no reduction to primary fundamental objects. In this Zen-like picture, appropriate to Berkeley in the 196os, all particles were thought to be made up of other particles—the so-called bootstrap model, in which no elementary particles were primary or special. So this approach was also called nuclear democracy. While this approach captivated many physicists who had given up on quantum field theory as a tool to describe any interactions other than the simple ones between electrons and photons, a few scientists were sufficiently impressed by the success of quantum electrodynam- ics to try to mimic it in a theory of the strong nuclear force—or strong interaction, as it has become known—along the lines earlier advocated by Yang and Mills. One of these physicists, J. J. Sakurai, published a paper in 1960 rather ambitiously titled "Theory of Strong Interactions." Sakurai took the 2P_GrealestSleryEverTold_AC.indd 192 12/16116 3:06 PIA EFTA00286114 Living inside a Superconductor 193 Yang-Mills suggestion seriously and tried to explore precisely which photonlike particles might convey a strong force between protons and neutrons and the other newly observed particles. Because the strong interaction was short-range—spanning just the size of the nucleus at best—it seemed the particles required to convey the force would be massive, which was incompatible with any exact gauge symmetry. But otherwise, they would have many properties similar to the photon's, having spin i, or a so-called vector spin. The new predicted particles were thus dubbed massive vector mesons. They would couple to vari- ous currents of strongly interacting particles similar to the way photons couple to currents of electrically charged particles. Particles with the general properties of the vector mesons predicted by Sakurai were discovered experimentally over the next two years, and the idea that they might somehow yield the secret of the strong interac- tion was exploited to try to make sense of the otherwise complex inter- actions between nucleons and other particles. In response to this notion that some kind of Yang-Mills symmetry might be behind the strong interaction, Murray Gell-Mann developed an elegant symmetry scheme he labeled in a Zen-like fashion the Eight- fold Way. It not only allowed a classification of eight different vector me- sons, but also predicted the existence of thus-far-unobserved strongly interacting particles. The idea that these newly proposed symmetries of nature might help bring order to what otherwise seemed a hopeless menagerie of elementary particles was so exciting that, when his pre- dicted particle was subsequently discovered, it led to a Nobel Prize for Gell-Mann. But Gell-Mann is remembered most often for a more fundamen- tal idea. He, and independently George Zweig, introduced what Gell- Mann called quarks—a word borrowed from James Joyce's Finnegans Wake—which would physically help explain the symmetry properties of his Eightfold Way. If quarks, which Gell-Mann viewed simply as a nice mathematical accounting tool (just as Faraday had earlier viewed 2P_Glealer-StoryEverTold_Atindd 193 12/16116 3:06 PIA EFTA00286115 194 THE GREATEST STORY EVER TOLD-SO FAR his proposal of electric and magnetic fields), were imagined to comprise all strongly interacting particles such as protons and neutrons, the sym- metry and properties of the known particles could be predicted. Once again, the smell of a grand synthesis that would unify diverse particles and forces into a coherent whole appeared to be in the air. I cannot stress how significant the quark hypothesis was. While Gell-Mann did not advocate that his quarks were real physical parti- cles inside protons and neutrons, his categorization scheme meant that symmetry considerations might ultimately determine the nature not only of the strong interaction, but of all fundamental particles in nature. However, while one sort of symmetry might govern the structure of matter, the possibility that this symmetry might be extended to some kind of Yang-Mills gauge symmetry that would govern the forces be- tween particles seemed no closer. The nagging problem of the observed masses of the vector mesons meant that they could not truly reflect any underlying gauge symmetry of the strong interaction in a way that could unambiguously determine its form and potentially ensure that it made quantum-mechanical sense. Any Yang-Mills extension of quantum elec- trodynamics required the new photonlike particles to be massless. Period. Faced with this apparent impasse, an unexpected wake-up call from superconductivity provided another, more subtle, and ultimately more profound, possibility. The first person to stir the embers was a theorist who worked di- rectly in the field of condensed matter physics associated with super- conductivity in materials. Philip Anderson, at Princeton, later a Nobel laureate for other work, suggested that one of the most fundamental, ubiquitous phenomena in superconductors might be worth exploring in the context of particle physics. One of the most dramatic demonstrations one can perform with su- perconductors, especially the new high-temperature superconductors that allow superconductivity to become manifest at liquid-nitrogen tempera- tures, is to levitate a magnet above the superconductor as shown below: 2P_GrealesiSleryEverTold_AC.indd 194 12/16016 3:06 PIA EFTA00286116 Living inside a Superconductor 195 Pnotopapn biPm This is possible for a reason discovered in an experiment in 1933 by Walther Meissner and colleagues, explained by theorists Fritz and Heinz London two years later, which goes by the name the Meissner effect. As Faraday and Maxwell discovered sixty years earlier, electric charges respond in different ways to magnetic and electric fields. In par- ticular, Faraday discovered that a changing magnetic field can cause a current to flow in a distant wire. Equally important, but which I didn't emphasize earlier, is that the resulting current will flow in a way that produces a new magnetic field in a direction that counters the changing external magnetic field. Thus, if the external field is decreasing, the cur- rent generated will produce a magnetic field that counters that decrease. If it is increasing, the current generated will be in an opposite direction, producing a magnetic field that works to counter that increase. You may have noticed that when you are talking on your cell phone and get in certain elevators, particularly ones in which the outer part of the elevator cage is encased in metal, when the door closes your call gets dropped. This is an example of something called a Faraday cage. Since the phone signal is being received as an electromagnetic wave, the metal shields you from the outside signal because currents flow in the metal in a way that counters the changing electric and magnetic fields in the signal, diminishing its strength inside the elevator. If you had a perfect conductor, with no resistance, the charges in the metal could essentially cancel any effects of the outside changing elec- 2P_Glealer-StoryEverTold_Atirdd 195 12/16116 3:06 PIA EFTA00286117 196 THE GREATEST STORY EVER TOLD-SO FAR tromagnetic field. No signal of these changing fields—i.e., no telephone signal—would remain to be detected inside the elevator. Moreover, a perfect conductor will also shield out the effects of any constant exter- nal electric field, since the charges can realign in the superconductor in response to any field and completely cancel it out. But the Meissner effect goes beyond this. In a superconductor, all magnetic fields—even constant magnetic fields such as those due to the magnet above—cannot penetrate into the superconductor. This is be- cause, when you slowly bring a magnet in closer from a large distance, the superconductor generates a current to counter the changing mag- netic field that increases as the magnet approaches. But since the mate- rial is superconducting, the current continues to flow and does not stop if you stop moving the magnet. Then as you bring the magnet in closer, a larger current flows to counter the new increase. And so on. Thus, because electric currents can flow without dissipation in a supercon- ductor, not only are electric fields shielded, but so are magnetic fields. This is why magnets levitate above superconductors. The currents in the superconductor expel the magnetic field due to the external magnet, and this repels the magnet just as if another magnet were at the surface of the superconductor with north pole facing north pole or south pole facing south pole. The London brothers, who first attempted to explain the Meissner effect, derived an equation describing this phenomenon inside a su- perconductor. The result was suggestive. Each different type of super- conductor would create a unique characteristic length scale below the surface of the superconductor—determined by the microscopic nature of the supercurrents that are created to compensate any external field— and any external magnetic field would be canceled on this length scale. This is called the London penetration depth. The depth is different for different superconductors and depends on their detailed microphysics in a way the brothers couldn't determine since they didn't have a micro- scopic theory of superconductivity at the time. 2P_Glealer-StoryEverrold_Atirdd 198 12/16116 3:06 PIA EFTA00286118 Living inside a Superconductor 197 Nevertheless, the presence of a penetration depth is striking because it implies that the electromagnetic field behaves differently inside a su- perconductor—it is no longer long-range. But if electromagnetic fields become short-range inside the surface, then the carrier of electromag- netic forces must behave differently. The net effect? The photon behaves as if it has mass inside the superconductor. In superconductors, virtual photons—and the electric and magnetic fields they mediate—can only propagate below the surface through a distance comparable to the London penetration depth, just as would be the case if electromagnetism inside the superconductor resulted from the exchange of massive—not massless—photons. Now imagine what it would be like to live inside a superconductor. To you, electromagnetism would be a short-range force, photons would be massive, and all the familiar physics that we associate with electro- magnetism as a long-range force would disappear. I want to emphasize how remarkable this is. No experiment you could perform within the superconductor, as long as it remained su- perconducting, would reveal that photons are massless in the outside world. If you were Plato's philosopher inside such a superconductor, you would have to intuit an incredible amount about the outside world be- fore you could infer that a mysterious and invisible phenomenon was the cause of an illusion. It might take several thousand years of thinking and experiment before you or your descendants could guess the nature of the reality underlying the shadow world in which you live, or be- fore you could build a device with enough energy to break apart Cooper pairs and melt the superconducting state, restoring electromagnetism to its normal form, and revealing the photon to be massless. In retrospect, we physicists might have expected, just on the grounds of symmetry, and without considering the Meissner effect directly, that photons should behave as massive particles inside a superconductor. The Cooper-pair condensate, being made of electron pairs, has a net electric charge. This breaks the gauge symmetry of electromagnetism because 2P_GlealerASIonEverTold_Atindd 197 12/16116 3:06 PIA EFTA00286119 198 THE GREATEST STORY EVER TOLD-SO FAR in this background any positive charges one adds to the material will behave differently from negative charges added to the material. So now there is a real distinction between positive and negative. But recall that the masslessness of photons is a sign that the electromagnetic field is long-range, and the long-range nature of the electromagnetic field re- flects that it allows local variations in the definition of electric charge in one place to not affect the physics globally throughout the material. But if gauge invariance is gone, then local variations in the definition of electric charge will have a real physical effect, so there can be no such long-range field that cancels out such variations. One way to get rid of a long-range field is to make the photon massive. Now the $64,000 question: Could something like this happen in the world in which we find ourselves living? Could the masses of heavy pho- tonlike particles arise because we are actually living in something akin to a cosmic superconductor? This was the fascinating question that An- derson raised, at least by analogy with regular superconductors. Before we can answer this question, we need to understand a techni- cal bit of wizardry that allows the generation of mass for a photon in a superconductor. Recall that in an electromagnetic wave the electric (E) and magnetic (B) fields oscillate back and forth in directions that are perpendicular to the direction of the wave, as shown: Since there are two perpendicular directions, one could draw an electromagnetic wave in two ways. The wave could look like that shown 2P_Glealer-StoryEverTold_Atindd 198 12/18/16 3:06 PIA EFTA00286120 Living inside a Superconductor 199 above, or one could interchange the E and B fields. This reflects that electromagnetic waves have two degrees of freedom, which are called two different polarizations. This arises from the gauge invariance of electromagnetism, or equiv- alently from the masslessness of photons. If, however, photons had a mass, then not only would gauge invariance be broken, but a third pos- sibility can arise. The electric and magnetic fields could oscillate along the direction of motion, instead of just oscillating perpendicular to this direction. (Since the photons will no longer be traveling at the speed of light, oscillations along the direction of motion of the particles become possible.) But this means that the corresponding massive photons would have three degrees of freedom, not just two. How can photons pick up this extra degree of freedom in superconductors? Anderson explored this issue in superconductors, and its resolution is intimately related to a fact that I described earlier. In the absence of electromagnetic interactions in a superconductor, it's possible to pro- duce slight spatial variations in the Cooper-pair condensate that would have arbitrarily small energy cost because Cooper pairs would not in- teract with each other. However, when electromagnetism is taken into account, those low-energy modes (which would destroy superconduc- tivity) disappear precisely because of the interactions of the charges in the condensate with the electromagnetic field. That interaction causes photons in the superconductor to behave as if they are massive. The new polarization mode of the massive photons in the superconductor comes about as the condensate oscillates in response to the passing electro- magnetic wave. In particle physics language, the massless Nambu-Goldstone modes that correspond to the particle version of the otherwise vanishingly small energy oscillations in the condensate get "eaten" by the electro- magnetic field, giving photons a mass, and a new degree of freedom, making the electromagnetic force short-range in the superconductor. 2P_GrealestSleryEverTold_AC.indd 199 12/16116 3:06 PIA EFTA00286121 200 THE GREATEST STORY EVER TOLD-SO FAR Anderson suggested that this phenomenon—whereby the other- wise massless photon disappears in superconductors and the otherwise massless Nambu-Goldstone mode also disappears, and the two combine to produce a massive photon—might be relevant for the long-standing problem of creating massive Yang-Mills photonlike particles that might be associated with strong nuclear forces. Anderson stopped short at this point and left hanging the suggestion that this mechanism, motivated by analogy to superconductors, might be applicable in particle theory. Just as when Nambu had stopped short by considering spontaneous symmetry breaking in particle physics using the analogy of superconductivity but did not exploit the phenomenon associated with superconductivity that Anderson later focused on—the Meissner effect that gives mass to photons in superconductors—the ex- plicit application of all these ideas to particle physics was yet to occur. As a result, the possible profound implications of superconductiv- ity for understanding fundamental particle physics were not immedi- ately recognized by the physics community and remained hidden in the shadows. Still, the notion that we might live in some kind of cosmic supercon- ductor stretches credulity. After all, humans are capable of generating wild stories to explain what is otherwise not understood, inventing fan- tastical and hidden causes, such as gods and demons. Was the claimed existence of some hidden condensate of fields throughout space to ex- plain the nature of what were otherwise inexplicable strong nuclear forces any more plausible? 2P_GrealestSlentEverTold_AC.indd 200 12/16116 806 PIA EFTA00286122 Chapter 16 THE BEARABLE HEAVINESS OF BEING: SYMMETRY BROKEN, PHYSICS FIXED Gather up the fragments that remain, that nothing be lost. -JOHN 6:12 There is remarkable poetry in nature, as there often is in human dramas. And in my favorite epic poems from ancient Greece, written even as Plato was writing about his cave, there emerges a com- mon theme: the discovery of a beautiful treasure previously hidden from view, unearthed by a small and fortunate band of unlikely travelers, who, after its discovery, are changed forever. Oh, to be so lucky. That possibility drove me to study physics, be- cause the romance of possibly discovering some new and beautiful hid- den corner of nature for the first time had an irresistible allure. This story is all about those moments when the poetry of nature merges with the poetry of human existence. Much poetry exists in almost every aspect of the episodes I am about to describe, but to see it clearly requires the proper perspective. Today, 201 2P_GreatestSteryEverrold_AC.indd 201 12/16/16 3:06 PM EFTA00286123 202 THE GREATEST STORY EVER TOLD-SO FAR in the second decade of the twenty-first century, we might easily agree about which of the great theories of the twentieth century are most beautiful. But to appreciate the real drama of the progress of science, one has to understand that, at the time they are proposed, beautiful theories often aren't as seductive as they are years later—like a fine wine, or a distant love. So it was that the ideas of Yang and Mills, and Schwinger and the rest, based on the mathematical poetry of gauge symmetry, failed at the time to inspire or compete with the idea that quantum field theory, with quantum electrodynamics as its most beautiful poster child, wasn't a productive approach to describe the other forces in nature—the weak and strong nuclear forces. For forces such as these, operating on short ranges appropriate to the scale of atomic nuclei, many felt that new rules must apply, and that the old techniques were misplaced. So too the subsequent attempts by Nambu and Anderson to apply ideas from the physics of materials—called many-body physics, or con- densed matter physics—to the subatomic realm were dismissed by many particle physicists, who deeply distrusted whether this emerg- ing field could provide any new insights for "fundamental" physics. The skepticism in the community was expressed by the delightful theorist Victor Weisskopf, who was reported to have said at a seminar at Cornell, "Particle physicists are so desperate these days that they have to bor- row from the new things coming up in many-body physics.... Perhaps something will come of it." There was some basis for the skepticism. Nambu had, after all, ar- gued that spontaneous symmetry breaking might explain the large and similar masses of protons and neutrons, and he hoped it might do so while explaining why the pion was so much lighter. But the ideas he bor- rowed had at their foundation the understanding that the hallmark of spontaneous symmetry breaking was the existence of exactly massless, not very light, particles. Anderson's work was also interesting, to be sure. But because it 2P_Glealer-StoryEverrold_Atirdd 202 12/16116 3:06 PIA EFTA00286124 The Bearable Heaviness of Being: Symmetry Broken, Physics Fixed 203 was written down in the context of a nonrelativistic condensed matter setting—combined with its violating Goldstone's theorem from particle physics, which implied that symmetry breaking and massless particles were inseparable—meant that his claim that massless states disap- peared in his example—in electromagnetism in superconductors—was largely also ignored by particle physicists. Julian Schwinger, however, had not given up the idea that a Yang- Mills gauge theory might explain nuclear forces, and he had continued to argue that the Yang-Mills versions of photons could be massive, albeit without demonstrating how this could come to pass. Schwinger's work caught the attention of a mild-mannered young British theorist, Peter Higgs, who was then a lecturer in mathemati- cal physics at the University of Edinburgh. A gentle soul, no one would imagine him to be a revolutionary. But reluctant revolutionary he was, although, due to some shortsighted journal editors, he almost didn't get the chance. In 1960 Higgs had just taken up his post and had been asked to serve on the committee that coordinated the first Scottish Universities Summer School in Physics. This became a venerable school, devoted to different areas of physics. Every four years or so, during three weeks, ad- vanced graduate students and young postdocs would attend lectures on particle physics by senior scientists amid meals lubricated by fine wine and, afterward, hearty whiskey. Among the students that year were the future Nobelists Sheldon Glashow and Martinus Veltman, and Nicola Cabibbo, who in my opinion should also have won the prize. Apparently Higgs, who had been made the wine steward, noticed that these three students never made the morning lectures. They apparently spent the evenings debating physics while drinking wine that they sneaked out of the dining room during meals. Higgs didn't have the opportunity to join the discussions then and therefore didn't learn from Glashow about his novel proposal for unifying the electromagnetic and weak forces, which he had already submitted for publication. 2P_Glealer-StoryEverTold_Atincld 203 12/1146 3:06 PIA EFTA00286125 204 THE GREATEST STORY EVER TOLD-SO FAR The Scottish summer schools have a poetry of their own. They rotate around the country and periodically return to the beautiful coastal city of St. Andrews, right next to the famous Old Course, the birthplace of golf. In 1980 at St. Andrews, Glashow, fresh from having won a Nobel Prize, and Gerardus 't Hooft, a famous former student of Veltman's, lec- tured at the school, and I was privileged to attend as a graduate student. I arrived late and got the smallest room, up in an attic overlooking the Old Course, and enjoyed not only the physics, but also the alcohol, as well as being fleeced for free drinks by one of the lecturers, Oxford physicist Graham Ross, at a miniature-golf putting range next door nicknamed the Himalayas, for good reason. Besides being a physicist of almost otherworldly ability, 't Hooft is also a remarkable artist. He won the 1980 summer school's annual T-shirt design contest, and I still have my autographed 't Hooft T-shirt. Can't bear to part with it, even as eBay beckons. (Twenty years after that program, in z000, I returned to the summer school, but this time as a lecturer. Unlike Glashow, 't Hooft, Veltman, and Higgs, I didn't return with a Nobel Prize, but I finally got to wear a kilt. Another bucket-list item ticked.) Following Higgs's stint at the summer school in 1960, he began to study the literature on symmetry and symmetry breaking, examin- ing the work of Nambu, Goldstone, Salam, Weinberg, and Anderson. Higgs became depressed by the seemingly hopeless task of reconciling Goldstone's theorem with the possibility of massive Yang-Mills vector particles that might mediate the strong force. Then in 1964, the magical year when Gell-Mann introduced quarks, Higgs read two papers that gave him hope. First was a paper by Abraham Klein and Ben Lee—who, before he died in a car crash while driving to a physics meeting, was one of the brightest upcoming particle physicists in the world. They suggested a way to avoid Goldstone's theorem and get rid of otherwise unobserved massless particles in quantum field theories. Next, Walter Gilbert, a young physicist at Harvard who would soon 2P_Glealer-StoryEverTold_Atind0 204 12/16116 3:06 PIA EFTA00286126 The Bearable Heaviness of Being: Symmetry Broken, Physics Fixed 206 decide to leave the confusion dominating particle physics for the greener pastures of molecular biology—where he too would win a Nobel Prize, in this case for helping to develop DNA-sequencing techniques—wrote a paper showing that the proposed solution of Klein and Lee's appeared to introduce a conflict with relativity and therefore was suspect. As we've seen, gauge theories have the interesting property that you can arbitrarily change the definition of positive versus negative charges at each point in space without changing any of the observable physical properties of the system, as long as you allow the electromagnetic field to have the interactions it has and to also change in a way that prop- erly accounts for this new local variation. As a result, you can perform mathematical calculations in any gauge—that is, using any specific local definitions of charges and fields consistent with the symmetry. A sym- metry transformation will take you from one gauge to another. Even though the theory might look quite different in these differ- ent gauges, the symmetry of the theory ensures that calculations of any physically measurable quantity are independent of the gauge choice— namely that the apparent differences are illusions that do not reflect the underlying physics that determines the measured values of all physically observable quantities. Thus one could choose whichever gauge made the calculation easier to do and expect to arrive at the same predictions for physically observable quantities by calculating in any other gauge. As Higgs read Schwinger's papers, Higgs realized that some gauge choices could appear to have the same conflict with relativity that Gil- bert had pointed out as plaguing Klein and Lee's proposal. But this ap- parent conflict was simply an artifact of that choice of gauge. In other gauges it disappeared. Therefore it didn't reflect any real conflict with relativity when it came to making physical predictions that could be tested. Maybe in a gauge theory Klein and Lee's proposal for getting rid of massless particles associated with spontaneous symmetry breaking might be workable after all. Higgs concluded that spontaneous symmetry breaking in a quantum 2P_Glealer-StoryEverrold_Atincld 205 12/16116 3:06 PIA EFTA00286127 206 THE GREATEST STORY EVER TOLD-SO FAR field theory setting involving a gauge symmetry might obviate Goldstone's theorem and produce a mass for vector bosons that might mediate the strong nuclear force without any leftover massless particles. This would correlate with Anderson's finding of electromagnetism in superconduc- tors in the nonrelativistic case. In other words, the strong force could be a short-range force because of spontaneous symmetry breaking. Higgs worked for a weekend or two to write down a model adding electromagnetism to the model Goldstone had used to explore sponta- neous symmetry breaking. Higgs found just what he had expected: the otherwise massless mode that would have been predicted by Goldstone's theorem became instead the additional polarization degree of freedom of a now massive photon. In other words, Anderson's nonrelativistic ar- gument in superconductors did carry over to relativistic quantum fields. The universe could behave like a superconductor after all. When Higgs wrote up his result and submitted it to the European journal Physics Letters, the paper was promptly rejected. The referee sim- ply didn't think it was relevant to particle physics. So, Higgs added some passages commenting on possible observable consequences of his idea and submitted it to the US journal Physical Review Letters. In particular, he added, "It is worth noting that an essential feature of this type of theory is the prediction of incomplete multiplets of scalar and vector bosons." In English this means that Higgs demonstrated that while one could remove the massless scalar particle (aka Goldstone boson) in favor of a massive vector particle (massive photon) in his model, there would also exist a leftover massive scalar (i.e., spinless) boson particle associated with the field whose condensate broke the symmetry in the first place. The Higgs boson was born. Physical Review Letters promptly accepted the paper, but the referee asked Higgs to comment on the relation of his paper to a paper by Fran- cois Englert and Robert Brout that had been received by the journal a month or so earlier. Much to Higgs's surprise, they had independently ar- rived at essentially the same conclusions. Indeed, the similarity between 2P_Glealer-StoryEverTold_Atirdd 208 12/16116 3:06 PIA EFTA00286128 The Bearable Heaviness of Being: Symmetry Broken, Physics Fixed 207 the papers is made clear by their titles. Higgs's paper was called "Broken Symmetries and the Masses of Gauge Bosons." The Englert and Brout paper was entitled "Broken Symmetry and the Mass of Gauge Vector Me- sons." It is hard to imagine a closer match without coordinating names. As if to add to the remarkable serendipity, twenty years later Higgs met Nambu at a conference and learned that Nambu had refereed both papers. How much more fitting could it be that the man who first brought the ideas of symmetry breaking and superconductivity to particle phys- ics should referee the papers of the people who would demonstrate just how prescient this idea was. And like Nambu, all of these authors were fixated on the strong interaction, and on the possibility of figuring out how protons, neutrons, and mesons could have large masses. Illustrating that the time was ripe for this discovery, within a month or so another team, Gerald Guralnik, C. R. Hagen, and Tom Kibble, also published a paper including many of the same ideas. You may wonder why we call it the Higgs boson and not the Higgs- Brout-Englert-Guralnik-Hagen-Kibble boson. Besides the obvious answer that this label doesn't trip lightly off the tongue, of all the papers the only one to explicitly predict an accompanying massive scalar boson in mas- sive gauge theories with spontaneous symmetry breaking was Higgs's paper. And, interestingly, Higgs only included the extra remark because the original version of his paper without that remark had been rejected. One last bit of poetry. A couple of years after the original paper was published, Higgs completed a longer paper and was invited (in 1966) to speak at several locations in the USA, where he was spending a sabbati- cal year. After Higgs's talk at Harvard, where Sheldon Glashow was now a professor, Glashow apparently complimented him on having invented a "nice model" and moved on. Such was the fixation on the strong in- teraction that Glashow didn't realize then that this might be the key to resolving the issues in the weak interaction theory he had published five years earlier. 2P_Glealer-StoryEverrold_Atirdd 207 12/16116 3:06 PIA EFTA00286129 2P_Gtealer-SfonEverTold_AC.0.00 208 12/16116 3:06 PM EFTA00286130 Part Three REVELATION EFTA00286131 2P_GreatestSlowEverrold_AC.indd 210 12/16/16 3:06 PM EFTA00286132 Chapter 17 THE WRONG PLACE AT THE RIGHT TIME Be not deceived: evil communications corrupt good manners. -I COR:11THiANS 15:33 Al of the six authors of the papers that describe what is most commonly called the Higgs mechanism (though after the recent Nobel Prize that Higgs shared with Englert, some are now calling it the BEH mechanism, for Brout, Englert, and Higgs) suspected and hoped that their work would help in understanding the strong force in nuclei. In their papers, any discussions of possible experimental probes of their ideas referenced the strong interaction—and in particular Sakurai's pro- posal of heavy vector mesons mediating this force. They hoped that a theory of the strong interaction that explained nuclear masses and short-range strong nuclear forces was around the corner. Besides the general fascination with the strong nuclear force in nu- clear physics, I suspect physicists tried to apply their new ideas to this theory for another reason. Given the range and strength of this force, the masses of new Yang-Mills-like particles that would be necessary to mediate the strong interaction would be comparable to the masses of 211 2P_Glealer-StoryEverrold_Atirdd 211 12/16116 3:06 PIA EFTA00286133 212 THE GREATEST STORY EVER TOLD-SO FAR protons and neutrons themselves and also of the other new particles being discovered in accelerators. Since experimental confirmation is the highest honor that theorists can achieve, it was natural to focus on un- derstanding physics at these accessible energy scales, where new ideas, and new particles, could be quickly tested and explored in existing ma- chines—with fame, if not fortune, around the corner. By contrast, as Schwinger had shown, any theory involving new particles associated with the weak force would require them to have masses several orders of magnitude larger than those available at accelerators at the time. This was clearly a problem to be considered at a later time, or so most physi- cists thought. One of the many people who were fascinated by the physics of the strong interaction was the young theorist Steven Weinberg. There is po- etry here as well. Weinberg grew up in New York City and attended the Bronx High School of Science, from which he graduated in 195o. One of his high school classmates was Sheldon Glashow, and the two of them moved together to study at Cornell University, living together in a temporary dorm there in their first semester before going their sepa- rate ways. While Glashow went to Harvard for graduate school, Wein- berg moved on to Copenhagen—where Glashow would spend time as a postdoc—before arriving at Princeton to complete his PhD. Both of them were on the faculty at Berkeley in the early 196os, leaving in the same year, 1966, for Harvard, where Glashow took up a professorship and Weinberg took a visiting position while on leave from Berkeley. Weinberg then moved to MIT in 1967, only to return to Harvard in 1973 to take the same chair and office that had been vacated by Julian Schwinger, Glashow's former supervisor. (When Weinberg moved into the office, he found in the closet a pair of shoes that Schwinger had left, clearly as a challenge to the younger scientist to try to fill them. He did.) When Weinberg left Harvard in 1982, Glashow then moved to occupy the same chair and office, but no shoes were left in the closet. The lives of these two scientists were intertwined perhaps as closely 29_Glealer-SlowEverTold_Aairdd 212 12/16116 3:06 PIA EFTA00286134 The Wrong Place al the Eight Time 213 as those of any other scientists in recent times, yet they form an inter- esting contrast. Glashow's brilliance is combined with an almost child- like enthusiasm for science. His strength lies in his creativity and his understanding of the experimental landscape and not so much in his detailed calculational abilities. By contrast, Weinberg is perhaps the most scholarly and serious (about physics) physicist I have ever known. While he has a wonderful ironic sense of humor, he never undertakes any physics project lightly, without the intent of mastering the relevant field. His physics textbooks are masterpieces, and his popular writing is lucid and full of wisdom. An avid reader of ancient history Weinberg fully communicates the historical perspective not only on what he is doing, but on the whole physics enterprise. Weinberg's approach to physics is like that of a steamroller. When I was at Harvard, we postdocs used to call Weinberg "Big Steve." When he was working on a problem, the best thing you could do was get out of the way, or you would be rolled over by the immense power of his intellect and energy.Earlier, before I moved to Harvard and was still at MIT, a friend of mine at the time, Lawrence Hall, was a graduate student at Harvard. Lawrence was ahead of me in his work, graduating before me. He told me that he was only able to complete the work that became his thesis with Weinberg because Weinberg had just won the Nobel Prize in 1979, and the ensuing hubbub forced him to slow down enough so that Lawrence could complete his calculations before Weinberg beat him to the punch. One of the great fortunes of my life was to have the opportunity to work closely with both Glashow and Weinberg during the early and for- mative years of my own career. After Glashow helped rescue me from the black hole of mathematical physics, he became my collaborator at Harvard and for years later. Weinberg taught me much of what I know about particle theory. At MIT one doesn't have to take courses, just pass exams, so I only took one or two physics courses at MIT while working toward my PhD. But one of the perks of being at MIT was that I could take classes at Harvard. I took or sat in on every graduate class that 29_Glealer-StoryEverrold_Atirdd 213 12/1006 3:06 PM EFTA00286135 214 THE GREATEST STORY EVER TOLD-SO FAR Weinberg taught during my graduate career, from quantum field theory onward. Glashow and Weinberg formed complementary role models for my own career. At my best I've tried to emulate aspects I learned from each of them, while recognizing that most often my "best" wasn't much in comparison. Weinberg had, and has, a broad and abiding interest in the details of quantum field theory, and like many others during the early 1960s, he tried to focus on how one might understand the nature of the strong interaction using ideas of symmetry that, in large part due to the work of Gell-Mann, so dominated the field at the time. Weinberg too was thinking about the possible application of ideas of symmetry breaking to understanding nuclear masses, based on Nambu's work, and like Higgs, Weinberg was quite disappointed by Goldstone's result that massless particles would always accompany such physics. So Weinberg decided, as he almost always did when he was interested in some physics idea, that he needed to prove it to himself. Thus his sub- sequent paper with Goldstone and Salam provided several independent proofs of the theorem in the context of strongly interacting particles and fields. Weinberg was so despondent about possible explanations of the strong interaction using spontaneous symmetry breaking that he added an epigraph to the draft of the paper that echoed Lear's response to Corde- lia: "Nothing will come of nothing: speak again? (My book A Universe from Nothing makes plain why I am not a big fan of this quote. Quantum mechanics blurs the distinction between something and nothing.) Weinberg subsequently learned about Higgs's (and others') result that one could get rid of unwanted massless Goldstone bosons that occur through symmetry breaking if the symmetry being broken was a gauge symmetry—where in this case the massless Goldstone bosons would disappear and otherwise massless gauge bosons would become massive—but Weinberg wasn't particularly impressed, viewing it as many other physicists did, as an interesting technicality. Moreover, in the early 196os the idea that the pion resembled in many 2P_Glealer-StoryEverrold_Atirdd 214 121161I6 3:06 PM EFTA00286136 The Wrong Place at the Eight Time 215 ways a Goldstone boson was useful in deriving some approximate for- mulas for certain strong interaction reaction rates. Thus, the notion of getting rid of Goldstone bosons in the strong interaction became less attractive. Weinberg spent several years during this period exploring these ideas. He worked out a theory whereby some symmetries that were thought to be associated with the strong interaction might become bro- ken spontaneously, and various strongly interacting vector gauge par- ticles that convey the strong interaction might get masses via the Higgs mechanism. The problem was he couldn't get agreement with observa- tions without spoiling the initial gauge symmetry that would protect the theory. The only way he could avoid this and preserve the initial gauge symmetry he needed was if some vector particles became massive, and others remained massless. But this disagreed with experiment. Then one day in 2967 while driving in to MIT, he saw the light, liter- ally and metaphorically. (I have driven with Steve in Boston, and while I have lived to talk about it, I have seen how when he is thinking about physics, all awareness of large masses such as other cars disappears.) Weinberg suddenly realized that maybe he, and everyone else, was ap- plying the right ideas of spontaneous symmetry breaking, but to the wrong problem! Another example in nature could involve two different vector bosons, one type massless and one type massive. The massless vector boson could be the photon, and the massive one (or ones) could be the massive mediator(s) of the weak interaction that had been specu- lated by Schwinger a decade earlier. If this was true, then the weak and electromagnetic interactions could be described by a unified set of gauge theories—one correspond- ing to the electromagnetic interaction (remaining unbroken) and one corresponding to the weak interaction, with a broken-gauge symmetry resulting in several massive mediators for that interaction. In this case the world we live in would be precisely like a superconductor. The weak interaction would be weak because of the simple accident that the ground state of fields in our current universe breaks the gauge 2P_GrealestSlontEverTald_AC.indd 215 12/15/16 3:06 PIA EFTA00286137 216 THE GREATEST STORY EVER TOLD-SO FAR symmetry that would otherwise govern the weak interaction symmetry. The photonlike gauge particles would get large masses, and as Schwinger had expected, the weak interaction would become so short-range that it would almost die off even on the length scale of protons and neutrons. This would also explain why neutron decay would happen so slowly. The massive particles mediating the weak interaction would appear to us just as photons would appear to hypothetical physicists living in- side a superconductor. So too the distinction between electromagnetism and the weak interaction would be just as illusory as the distinction that physicists on the ice crystals on that windowpane would make between forces along the direction of their icicle versus those perpendicular to that direction. It would be a simple accident that one gauge symmetry gets broken in the world of our experience, and the other doesn't. Weinberg wanted to avoid thinking about strongly interacting par- ticles since the situation there was still confused. So he decided to think about particles that interact only via the weak or electromagnetic in- teraction, namely electrons and neutrinos. Since the weak interaction turns electrons into neutrinos, he had to imagine a set of charged vector photonlike particles that would produce such a transformation. These are nothing other than the charged vector bosons that Schwinger envis- aged, conventionally called W plus and W minus bosons. Since only left-handed electrons and neutrinos get mixed together by the weak interaction, one type of gauge symmetry would have to govern just the interactions of left-handed particles with the W par- ticles. But since both left-handed electrons and right-handed electrons interact with photons, the gauge symmetry of electromagnetism would somehow have to be incorporated in this unified model in such a way that left-handed electrons could interact with both photons and the new charged W bosons—while right-handed electrons would interact only with photons and not the W particles. Mathematically, the only way to do this—as Sheldon Glashow had discovered when he was thinking about electroweak unification six 2P_Glealer-StoryEverTold_Atindd 218 12/16116 3:06 PIA EFTA00286138 The Wrong Place al the Eight Time 217 years earlier—was if there was one additional neutral weak boson that right- and left-handed electrons could interact with in addition to in- teracting with photons. This new boson Weinberg dubbed the Z, zero. A new field would have to exist in nature that would form a conden- sate in empty space to spontaneously break the symmetries governing the weak interaction. The elementary particle associated with this field would be the massive Higgs, while the remaining would-be Goldstone bosons would now be eaten by the W and Z bosons to make them mas- sive, by the mechanism that Higgs first proposed. This would leave only the photon left over as a massless gauge boson. But there's more. By virtue of the gauge symmetry he introduced, Weinberg's new Higgs particle would also interact with electrons, and when the condensate formed, the effect would be to give electrons a mass as well as the W and Z particles. Thus, not only would this model explain the masses of the gauge particles that mediate the weak force— and therefore determine the strength of that force—but the same Higgs field would also give electrons mass. All the ingredients necessary for the unification of the weak and electromagnetic interaction were present in this model. Moreover, by starting with a Yang-Mills gauge theory with massless gauge bosons before symmetry breaking, there was hope that the same remarkable symmetry properties of gauge theories first exploited in quantum elec- trodynamics might also allow this theory to produce finite sensible re- sults. While a fundamental theory with massive photonlike particles clearly had pathologies, the hope was that if the masses only resulted after symmetry breaking, these pathologies might not appear. But it was just a hope at the time. Clearly in a realistic model the Higgs particle would couple to other particles engaged in the weak interaction, beyond the electron. In the absence of a Higgs condensate all these particles, protons, or the par- ticles that made them up, and muons, etc., all of them would be exactly massless. Every facet that is responsible for our existence, indeed the very 2P_GrealestSlosyC-verTaleLAC.indd 217 12/16116 3:06 PIA EFTA00286139 218 THE GREATEST STORY EVER TOLD-SO FAR existence of the massive particles from which we are made, would thus arise as an accident of nature—the formation of a specific Higgs conden- sate in our universe. The particular features that make our world what it is—the galaxies, stars, planets, people, and the interactions among all of these—would be quite different if the condensate had never formed. Or if it had formed differently. Just as the world experienced by imaginary physicists on the ice crystal on that windowpane on a cold winter morning would have been com- pletely different if the crystal had lined up in a different direction, so too the features of our world that allow our existence depend crucially on the nature of the Higgs condensate. What might seem so special about the features of the particles and fields that make up the world we live in would thus be no more special, planned, or significant than would be the acci- dental orientation of the spine of that ice crystal, even if it might appear to have special significance to beings living on the crystal. And one last bit of poetry. The unique Yang-Mills model that Wein- berg was driven to in 2967, which Abdus Salam would also stumble upon a year later, was precisely the model proposed six years earlier by his old high school friend Sheldon Glashow when he responded to Schwinger's challenge to find a symmetry that might unify the weak and electromagnetic interactions. No other choice could mathemati- cally reproduce what we see in the world today. Glashow's model had been largely ignored in the interim because no mechanism was then known to give the weak bosons masses. But now such a mechanism existed, the Higgs mechanism. Weinberg and Glashow, whose lives had crisscrossed since they were children, would later share the Nobel Prize, along with Salam, for com- pletely independent discoveries of the greatest unification in physical theory since Maxwell had unified electricity and magnetism and Ein- stein had unified space and time. 29_Glealer-StoryEverTold_Atindd 218 12/18116 3:06 PIA EFTA00286140 Chapter 18 THE FOG LIFTS Their voice goes out through all the earth, and their words to the end of the world. -PSALM 19:4 You might expect that physicists around the world would have thrown parties with fireworks when Weinberg's paper came out. But for the next three years following publication of Weinberg's theory, not a single physicist, not even Weinberg himself, would find cause to reference the paper—now one of the most highly cited papers in all of particle physics. If a great discovery about nature had been made, no one had yet noticed. After all, Maxwell's unification made the beautiful prediction that light was an electromagnetic wave whose speed could be calculated from first principles, and lo and behold, the prediction was equal to the mea- sured speed of light. Einstein's unification of space and time predicted that clocks would slow for moving observers, and lo and behold, they do, and in just the way he predicted. In 2967 the Glashow-Weinberg-Salam unification of the weak and electromagnetic interactions predicted three new vector bosons that were almost one hundred times heavier than any particle that had been yet detected. It also predicted new in- 219 29_Glealer-StoryEverTold_Atincld 219 12/16116 3:06 PM EFTA00286141 220 THE GREATEST STORY EVER TOLD-SO FAR teractions between electrons and neutrinos and matter due to the newly predicted Z particle that had not only not been seen, but a number of experiments suggested did not exist. It also required the existence of a new and as yet unobserved massive fundamental scalar boson, the Higgs particle, when no fundamental scalar particles were yet known to exist in nature. And finally, as a quantum theory, no one knew if it made sense. Is it any wonder that the idea did not immediately catch fire? Never- theless, within a decade everything would change, resulting in the most theoretically productive period for elementary particle physics since the discovery of quantum mechanics. While a gauge theory of the weak interaction started the ball rolling, what resulted was far greater. The first crack in the dike holding back the waters of progress came, fit- tingly, with the work of Dutch graduate student Gerardus Hooft, in 1971. I always remember how to spell his name because a particularly brilliant and witty former Harvard colleague, the late Sidney Coleman, used to say that if Gerard had monogrammed cuff links, they would need an apostro- phe on them. Before 1971 many of the greatest theorists in the world had tried to figure out whether the infinities that plague most quantum field theories would disappear for spontaneously broken gauge theories as they do for their unbroken cousins. But the answer eluded them. Remarkably this young graduate student, working under the supervision of a seasoned pro—Martinus Veltman—found a proof that others had missed. Often when presented with a new result, we physicists can work through the details and imagine how we might have discovered it ourselves. But many of 't Hooft's insights, and there were many—almost all the new ideas in the inos derived in one way or another from his theoretical inventions— seemed to come from some hidden reservoir of intuition. The other remarkable thing about Gerard is how gentle, shy, and un- assuming he is. For someone who became famous in the field when he 2P_GrealesiSleryEverTold_AC.indd 12/16116 3:06 PIA EFTA00286142 The Fog Lifts 221 was a student, one might have expected some sense of privilege. But from the first time I met him—again when I was a lowly graduate stu- dent—Gerard treated me as an interesting friend, and I am pleased to say that relationship has continued. I always try to remember this atti- tude when I meet young students who may seem shy or intimidated, and I try to emulate Gerard's open generosity of spirit. His supervisor Tini Veltman, as he is often called, couldn't appear more different. Not that Tini isn't fun to talk to. He is. But he always made explicitly clear to me the moment we started a discussion that whatever I might say, I didn't understand things well enough. I always enjoyed the challenge. It is important to note that 't Hooft would never have approached the problem if Veltman had not been obsessed with it, even as most others gave up. The notion that one might ultimately extend the techniques that Feynman and others had developed to tame quantum electrody- namics to try to understand more complex theories such as spontane- ously broken Yang-Mills theory was simply viewed as naïve by many in the field. But Veltman stayed with the project, and he wisely found a graduate student who was also a genius to help him. It took a while for 't liooft's and Veltman's ideas to sink in and the new techniques 't Hooft had developed to become universally adopted, but within a year or so physicists agreed that the theory that Weinberg, and later Salam, had proposed, made sense. Citations of Weinberg's paper suddenly began to grow exponentially. But making sense and being right are two different things. Did nature actually use the specific theory that Glashow, Weinberg, and Salam had suggested? That remained the key open question, and for a while it looked as if the answer was no. The existence of the new neutral particle, the Z, required by the the- ory, was a significant addition, beyond the charged particles suggested years earlier by Schwinger and others that were required to change neutrons into protons and electrons into neutrinos. It meant that there 2P_Glealer-StoryEverTold_Atirdd 221 12/16116 3:06 PIA EFTA00286143 222 THE GREATEST STORY EVER TOLD-SO FAR would be a new kind of weak interaction, not just for electrons and neu- trinos but also for protons and neutrons, mediated by a new neutral- particle exchange. In this case, as for electromagnetism, the identity of the particles interacting would not change. Such interactions became known as neutral current interactions, and the obvious way to test the theory was to look for them. The best place to look for them was in the interactions of the only particles in nature that just feel the weak inter- action, namely neutrinos. You may recall that the prediction of such neutral currents was one of the reasons that Glashow's 1961 suggestion never caught on. But Glashow's model wasn't a full theory. Particle masses were simply put into the equations by hand, and as a result quantum corrections couldn't be controlled. However, when Weinberg and Salam proposed their model for electroweak unification, all elements that allowed for de- tailed predictions were there. The mass of the Z particle was predicted, and as 't Hooft had shown, one could calculate all quantum corrections in a reliable way, just as one did for quantum electrodynamics. This was a good thing, and a bad thing because no wiggle room was left to argue away any possible disagreements with observation. And in 1967 there appeared to be such disagreements. No such neutral currents had been observed in high-energy collisions of neutrinos with protons, with an upper limit being set of about lo percent of the rate observed for more familiar charge-changing weak interactions of neutrinos and protons, such as neutron decay. Things looked bad, and most physicists assumed weak neutral currents didn't exist. Weinberg had a vested interest in this quest, and in 1971 he reason- ably argued that there was still wiggle room. But this view was not gernerally held by others in the community. In the early 297os, new experiments at the European Organization for Nuclear Research (CERN) in Geneva were performed using the pro- ton accelerator there, which smashed high-energy protons into a long target. Most particles produced in the collision would be absorbed in 2P_Glealer-StoryEverTold_Atirdd 222 12/16116 3:06 PIA EFTA00286144 The Fog Lifts 223 the target, but neutrinos would emerge from the other end—as their in- teractions are so weak that they could traverse the target without being absorbed. The resulting high-energy neutrino beam would then strike a detector placed in its path that could record the few events in which neutrinos might interact with the detector material. A huge new detector was built, named Gargamelle after the giant- ess mother of Gargantua, from the work of the French writer Rabelais. This five-meter-by-two-meter "bubble chamber" vessel was filled with a superheated liquid in which trails of bubbles would form when an ener- getic charged particle traversed it, sort of like seeing the vapor trail high in the sky of a plane that is itself not visible. Interestingly, when the experimentalists who built Gargamelle met in 1968 to discuss their plans for neutrino experiments, the idea of search- ing for neutral currents wasn't even mentioned—an indication of how many physicists thought the issue was then settled. Of far more interest to them was the possibility of following up on recent exciting experi- ments at the Stanford Linear Accelerator (SLAC), where high-energy electrons had been used as probes to explore the structure of protons. Using neutrinos as probes of protons might give cleaner measurements because the neutrinos are not charged. After the results of 't Hooft and Veltman, however, in 1972., experi- mentalists began to take the gauge theory description of the weak in- teraction, and in particular the Glashow-Weinberg-Salam proposal, seriously. That meant looking for neutral currents. The Gargamelle collaboration had the capability to do this, in principle, even though it hadn't been designed for the task. Most of the high-energy neutrinos in the beam would interact with protons in the target by turning into muons, the heavier partners of electrons. The muons would exit the target, producing a long charged- particle track all the way to the edge of the detector. The protons would be converted into neutrons, which would themselves not produce a track but would collide with nuclei, producing a short shower of charged 2P_GrealestStecyC-verTald_AC.indd 223 12/16116 3:06 PIA EFTA00286145 224 THE GREATEST STORY EVER TOLD-SO FAR particles that would leave tracks. Thus, the experiment was designed to detect muon tracks, as well as accompanying charged-particle showers, both arising as separate signals of a single weak interaction. However, sometimes a neutrino would interact with material out- side the detector, producing a neutron that might recoil back into the detector and then interact there. Such events would consist of a single strongly interacting shower of particles due to the colliding neutron, with no accompanying muon track. When Gargamelle began to search for neutral current events, such isolated charged-particle showers without an accompanying muon be- came just the signal the scientists needed to focus on. In neutral current events a neutrino that interacts with a neutron or proton in the detec- tor doesn't convert into a charged muon, but simply bounces off and escapes the detector unobserved. All that would be observable would be the recoiling nuclear shower—the same signature produced by the more standard neutrino interactions outside the detector that produce neu- trons that recoil back into the detector and produce a nuclear shower. The challenge, then, if the experiment was to definitively detect neu- tral current events, was to distinguish neutrino-induced events from such neutron-induced events. (This same problem has provided the chief challenge to experimentalists looking for any weakly interacting particles, including the presumed dark matter particles that are being searched for in underground detectors around the world today.) The observation of a single recoil electron, with no other charged- particle tracks in the detector, was observed in early 1973. This could have arisen from the less frequent predicted neutral current collisions of neutrinos with electrons instead of protons or neutrons. But generally a single event is not enough to definitively claim a new discovery in par- ticle physics. However, it did give hope, and by March of 1973 a careful analysis of neutron backgrounds and observed isolated particle show- ers appeared to provide evidence that weak neutral current interactions actually exist. Nevertheless, not until July of 1973 did the researchers at 2P_Glealer-StoryEverTold_Atirdd 224 12/16116 3:06 PIA EFTA00286146 The Fog Lifts 225 CERN complete a sufficient number of checks to be confident enough to claim a detection of neutral currents, which they did at a conference in Bonn in August. The story might have ended there, but unfortunately, shortly after this, another collaboration searching for neutral currents rechecked their apparatus and found that a previous signal for neutral currents had disappeared. This produced significant confusion and skepticism in the physics community, where once again neutral currents seemed suspect. Ultimately the Gargamelle collaboration returned to the draw- ing board, tested the detector using a proton beam directly, and took a great deal more data. At a conference almost a year later, in June 2974, the Gargamelle collaboration presented overwhelming confirmation of the signal. Meanwhile the competing collaboration had found the cause of its error and confirmed the Gargamelle result. Glashow, Weinberg, and Salam were vindicated. Neutral currents had arrived, and a remarkable unification of the weak and the electromagnetic interactions appeared to be at hand. But two loose ends still remained to be cleared out. The existence of neutral currents in neutrino scattering validated the notion that the Z particle existed, but this didn't guarantee that the weak interaction was identical to that proposed by Glashow, Weinberg, and Salam, where the weak and the electromagnetic interactions were unified. To explore this required an experiment using a particle that participated in both the weak and the electromagnetic interaction. The electron was ideal for this purpose because these are the only two inter- actions it experiences. When electrons interact with other charges by their electromag- netic attraction, left-handed electrons and right-handed electrons behave identically. However, the Weinberg-Glashow-Salam theory re- quired that weak interactions occur differently for left-handed versus right-handed particles. This implied that careful measurements of the scattering of polarized electrons—electrons prepared initially in left- or 2P_GrealesiSleryfverTold_AC.indd 225 12/16116 3:06 PIA EFTA00286147 226 THE GREATEST STORY EVER TOLD-SO FAR right-handed states using magnetic fields—off various targets should re- veal a violation of left-right symmetry, but not as extreme an asymmetry as that observed in neutrino scattering—because the neutrino is purely left-handed. The degree of violation in electron scattering, if it existed, would then reflect the extent to which the weak interaction and electro- magnetism were mixed together in a unified theory. The idea of testing for such interference using electron scattering had actually been suggested as early as 19S8 by the remarkable Soviet physi- cist Yakov B. Zel'dovich. But it would take twenty years for sufficiently sensitive experiments to actually take place. And as for the neutral cur- rent discovery, the road to success was full of potholes and wrong turns along the way. One of the reasons it took so long to test this idea is that the weak interaction is weak. Because the dominant interaction of electrons with matter is electromagnetic, the left-right asymmetry predicted due to a possible exchange of a Z particle was small, smaller than one part in ten thousand. To test for such a small asymmetry required both an intense beam and one whose initial polarization was well determined. The best place to perform these experiments was at the Stanford Linear Accelerator, a two-mile-long electron linear accelerator built in 1962 that was the longest and straightest structure that had ever been built. In 1970 polarized beams were introduced, but not until 1978 was an experiment designed and run with the sensitivity required to look for weak-electromagnetic interference in electron scattering. While the successful observation of neutral currents in 1974 meant that the Weinberg-Glashow-Salam theory began to have wide accep- tance among theorists, what made the 1978 SLAC experiment so im- portant was that in 1977 two atomic physics experiments had reported results that, if correct, convincingly ruled out the theory. In our story thus far, light has played a crucial role, illuminating (if you will forgive the pun) our understanding not only of electricity and magnetism, but space, time, and ultimately the nature of the quantum 2P_Glealer-StoryEverrold_Atirdd 228 12/16116 3:06 PIA EFTA00286148 The Fog Lifts 227 world. So too it was realized that light could help probe for a possible electroweak unification. The first great success of quantum electrodynamics was the correct prediction of the spectrum of hydrogen, and eventually other atoms. But if electrons also feel the weak force, then this will provide a small addi- tional force between electrons and nuclei that should alter—if slightly— the characteristics of their atomic orbits. For the most part these are unobservable because electromagnetic effects swamp weak effects. But weak interactions violate parity, so the same weak-electromagnetic neutral current interference that was being explored using polarized electron beams can produce novel effects in atoms that would vanish if electromagnetism was the only force involved. In particular, for heavy atoms, the Weinberg-Salam theory predicted that if polarized light was transmitted through a gas of atoms, then the direction of the polarization of the light would be rotated by about a millionth of a degree, due to parity-violating neutral current effects in the atoms through which the light passed. In 1977 the results of two independent atomic physics experiments, in Seattle and Oxford, were published in back-to-back articles in Physi- cal Review Letters. The results were dismaying. No such optical rotation was seen at a level ten times smaller than that predicted by the elec- troweak theory. Had only one experiment reported the result, it would have been more equivocal. But the same result from two independent experiments using independent techniques made it appear definitive. The theory appeared to be ruled out. Nevertheless, the SLAC experiment, which had begun three years earlier, was well under way, and since all of the experimental prepara- tion had begun, the experiment was approved to begin to take data in early 1978. Because of the earlier null results from the atomic physics ex- periments, the Stanford collaboration added several bells and whistles to the experiment so that if they saw no effect, they could guarantee that they could have seen such an effect were it there. 2P_GrealestStecyC-verTald_AC.indd 227 12/16116 3:06 PIA EFTA00286149 228 THE GREATEST STORY EVER TOLD-SO FAR Within two months the experiment began to show clear signs of par- ity violation, and by June 1978 the scientists announced a nonzero re- sult, in agreement with the predictions of the Glashow-Weinberg-Salam model, based on measured neutrino neutral current scattering, which measured the strength of the Z interaction. Still, questions remained, especially given the apparent disagree- ment with the Seattle/Oxford results. At a talk at Caltech on the subject, Richard Feynman, characteristically, homed in on a key outstanding ex- perimental question and asked whether the SLAC experimentalists had checked that the detector responded equally well to both left-handed and right-handed electrons. They hadn't, but for theoretical reasons they had had no reason to expect the detectors to behave differently for the different polarizations. (Feynman would famously get to the heart of another complex problem eight years later after the tragic Challenger explosion, when he simply demonstrated the failure of an O-ring seal to the investigating commission and to the public watching the televised proceedings.) Over the fall the SLAC experiment refined their efforts to rule out both this concern and others that had been raised, and by the fall they reported a definitive result in agreement with the Glashow-Weinberg- Salam prediction, with an uncertainty of less than io percent. Elec- troweak unification was vindicated! To date, I don't know if anyone has a good explanation of why the original atomic physics results were wrong (later experiments agreed with the Glashow-Weinberg-Salam theory) except that the experiments, and the theoretical interpretation of the experiments, are hard. But a mere year later, in October 1979, Sheldon Glashow, Abdus Salam, and Steven Weinberg were awarded the Nobel Prize for their electroweak theory, now validated by experiment, that unified two of the four forces of nature based on a single fundamental symmetry, gauge invariance. If the gauge symmetry hadn't been broken, hidden from view, the weak and electromagnetic interactions would look iden- 2P_Glealer-StoryEverTold_Atincld 228 122/18/16 3:06 PIA EFTA00286150 The Fog Lifts 229 tical. But then all of the particles that make us up wouldn't have mass, and we wouldn't be here to notice.... This is not the end of our story, however. Two out of four is still only two out of four. The strong interaction, which had motivated much of the work that led to electroweak unification, had continued to stub- bornly resist all attempts at explanation even as the electroweak theory took shape. No explanation of the strong nuclear force via spontane- ously broken gauge symmetries met the test of experiment. Thus, even as scientist-philosophers of the twentieth century had stumbled—often by a convoluted and dimly lit path—outside our cave of shadows to glimpse the otherwise hidden reality beneath the surface, one more force relevant to understanding the fundamental structure of matter was conspicuously missing from the beautiful emerging tapestry of nature. 2P_Glealer-StoryEverrold_Atirdd 229 12/16116 3:06 PIA EFTA00286151 2P_Gtealer3SIonEverTold_Atird0 230 12/16116 3:06 PM EFTA00286152 Chapter 19 FREE AT LAST Let my people go. -EXODUS 9:1 The long road that led to electroweak unification was a tour de force of intellectual perseverance and ingenuity. But it was also a detour de force. Almost all of the major ideas introduced by Yang, Mills, Yukawa, Higgs, and others that led to this theory were developed in the apparently unsuccessful struggle to understand the strongest force in nature, the strong nuclear force. Recall that this force, and the strongly interacting particles that manifested it, had so bedeviled physi- cists that in the 196os many of them had given up hope of ever explain- ing it via the techniques of quantum field theory that had so successfully now described both electromagnetism and the weak interaction. There had been one success, centered on Gell-Mann and Zweig's proposal that all the strongly interacting particles that had been ob- served, including the proton and the neutron, could be understood as being made up of more fundamental objects, which, as I have described, Gell-Mann called quarks. All the known strongly interacting particles, and at the time undiscovered particles, could be classified assuming they were made of quarks. Moreover, the symmetry arguments that led 231 2P_GrealestStoiyEverTald_AC.indd 23I 12/16116 3:06 PIA EFTA00286153 232 THE GREATEST STORY EVER TOLD-SO FAR Gell-Mann in particular to come up with his model served as the basis for making some sense of the otherwise confusing data associated with the reactions of strongly interacting matter. Nevertheless, Gell-Mann had allowed that his scheme might merely be a mathematical construct, useful for classification, and that quarks might not represent real particles. After all, no free quarks had ever been observed in accelerators or cosmic-ray experiments. He was also probably influenced by the popular idea that quantum field theory, and hence the notion of elementary particles themselves, broke down on nuclear scales. Even as late as 1972 Gell-Mann stated, "Let us end by emphasizing our main point, that it may well be possible to construct an explicit theory of hadrons, based on quarks and some kind of glue.. . . Since the entities we start with are fictitious, there is no need for any conflict with the bootstrap ... point of view." Viewed in this context, the effort to describe the strong interaction by a Yang-Mills gauge quantum field theory, with real gauge particles medi- ating the force, would be misplaced. It also seemed impossible. The strong force appeared to operate only on nuclear scales, so if it was to be de- scribed by a gauge theory, the photonlike particles that would convey the force would have to be heavy. But there was also no evidence of a Higgs mechanism, with massive strongly interacting Higgs-like particles, which experiments could have easily detected. Compounding this, the force was simply so strong that even if it was described by a gauge theory, then all of the quantum field theory techniques developed for deriving predictions— which worked so well for the other forces—would have broken down if applied to the strong force. This is why Gell-Mann in his quote referred to the "bootstrap"—the Zen-like idea that no particles were truly fundamen- tal. The sound of no hands clapping, if you will. Whenever theory faces an impasse like this, it sure helps to have ex- periment as a guide, and that is exactly what happened, in 1968. A series of pivotal experiments, performed by Henry Kendall, Jerry Friedman, and Richard Taylor, using the newly built SLAC accelerator to scatter 2P_Glealer-StoryEverTold_Atirdd 232 12/16116 3:06 PIA EFTA00286154 Free at Last 233 high-energy electrons off protons and neutrons, revealed something re- markable. Protons and neutrons did appear to have some substructure, but it was strange. The collisions had properties no one had expected. Was the signal due to quarks? Theorists were quick to come to the rescue. lames Bjorken demon- strated that the phenomena observed by the experimentalists, called scaling, could be understood if protons and neutrons were composed of virtually noninteracting pointlike particles. Feynman then interpreted these objects as real particles, which he dubbed partons, and suggested they could be identified with Gell-Mann's quarks. This picture had a big problem, however. If all strongly interact- ing particles were composed of quarks, then quarks should surely be strongly interacting themselves. Why should they appear to be almost free inside protons and neutrons and not be interacting strongly with each other? Moreover, in 196s, Nambu, Moo-Young Han, and Oscar Greenberg had convincingly argued that, if strongly interacting particles were composed of quarks and if they were fermions, like electrons, then Gell- Mann's classification of known particles by various combinations of quarks would only be consistent if quarks possessed some new kind of internal charge, a new Yang-Mills gauge charge. This would imply that they interacted strongly via a new set of gauge bosons, which were then called gluons. But where were the gluons, and where were the quarks, and why was there no evidence of quarks interacting strongly inside protons and neutrons if they were really to be identified with Feynman's partons? In yet another problem with quarks, protons and neutrons have weak interactions, and if these particles were made up of quarks, then the quarks would also have to have weak interactions in addition to strong interactions. Gell-Mann had identified three different types of quarks as comprising all known strongly interacting particles at the time. Mesons could be comprised of quark-antiquark pairs. Protons and neutrons 2P_GrealesiSleryEverTold_AC.indd 233 1216116 3:06 PM EFTA00286155 234 THE GREATEST STORY EVER TOLD-SO FAR could be made up of three fractionally charged quarks, which Gell- Mann called up (u) and down (d) quarks. The proton would be made of two up quarks and one down quark, while the neutron would be made of two down quarks and one up quark. In addition to these two types of quarks, one additional type of quark, a heavier version of the down quark, was required to make up exotic new elementary particles. Gell- Mann called this the strange (s) quark, and particles containing s quarks were dubbed to possess "strangeness." When neutral currents were first proposed as part of the weak inter- action, this created a problem. If quarks interacted with the Z particles, then u, d, and s quarks could remain u, d, and s quarks before and after the neutral current interaction, just as electrons remained electrons be- fore and after the interaction. However, because the d and s quarks had precisely the same electric and isotopic spin charges, nothing would pre- vent an s quark from converting into a d quark when it interacted with a Z particle. This would allow particles containing s quarks to decay into particles containing d quarks. But no such "strangeness-changing decays" were observed, with high sensitivity in experiments. Something was wrong. This absence of "strangeness-changing neutral currents" was ex- plained brilliantly, at least in principle, by Sheldon Glashow, along with collaborators John Iliopoulos and Luciano Maiani, in 1970. They took the quark model seriously and suggested that if a fourth quark, dubbed a charm (c) quark, existed, which had the same charge as the u quark, then a remarkable mathematical cancellation could occur in the calcu- lated transformation rate for an s quark into a d quark, and strangeness- changing neutral currents would be suppressed, in agreement with experiments. Moreover, this scheme began to suggest a nice symmetry between quarks and particles such as electrons and muons, all of which could exist in pairs associated with the weak force. The electron would be paired with its own neutrino, as would the muon. The up and down 2P_Glealer-StorgverTold_Atincld 234 12/16116 3:06 PIA EFTA00286156 Free at Last 235 quarks would form one pair, and the charm and the strange quark an- other pair. W particles interacting with one particle in each pair would turn it into the other particle in the pair. None of these arguments addressed the central problems of the strong interaction between quarks, however. Why had no one ever ob- served a quark? And, if the strong interaction was described by a gauge theory with gluons as the gauge particles, how come no one had ever observed a gluon? And if the gluons were massless, how come the strong force was short-range? These problems continued to suggest to some that quantum field theory was the wrong approach for understanding the strong force. Freeman Dyson, who had played such an important role in the develop- ment of the first successful quantum field theory, quantum electrody- namics, asserted, when describing the strong interaction, "The correct theory will not be found in the next hundred years." One of those who were convinced that quantum field theory was doomed was a brilliant young theorist, David Gross. Trained under Geoffrey Chew, the inventor of the bootstrap picture of nuclear democ- racy, in which elementary particles were an illusion masking a structure in which only symmetries and not particles were real, Gross was well primed to try to kill quantum field theory for good. Recall that even as late as 196s, when Richard Feynman received his Nobel Prize, it was still felt that the procedure he and others had developed for getting rid of infinities in quantum field theory was a trick—that something was fundamentally wrong at small scales with the picture that quantum field theory presented. Russian physicist Lev Landau had shown in the 195os that the elec- tric charge on an electron depends on the scale at which you measure it. Virtual particles pop out of empty space, and electrons and all other elementary particles are surrounded by a cloud of virtual particle- antiparticle pairs. These pairs screen the charge, just as a charge in a di- electric material gets screened. Positively charged virtual particles tend 2P_GlealerASIonEverTold_Atirdd 235 122/16/16 3:06 PIA EFTA00286157 236 THE GREATEST STORY EVER TOLD-SO FAR to closely surround the negative charge, and so at a distance the physical effects of the initial negative charge are reduced. This meant, according to Landau, that the closer you get to an elec- tron, the larger its actual charge will appear. If we measure the electron charge to be some specific value at large distances, as we do, that would mean that the "bare" charge on the electron—namely the charge on the fundamental particle considered without all the infinite dressing by particle-antiparticle pairs surrounding it on ever-smaller scales—would have to be infinite. Clearly something was rotten with this picture. Gross was influenced not only by his supervisor, but also by the pre- vailing sentiments of the time, mostly arguments by Gell-Mann, who dominated theoretical particle physics in the late fifties and early sixties. Gell-Mann advocated using algebraic relations that arise from thinking about field theories, then keeping the relations and throwing away the field theory. In a particularly Gell-Mann-esque description, he stated, "We may compare this process to a method sometimes employed in French cuisine: a piece of pheasant meat is cooked between two slices of veal, which are then discarded." Thus one could abstract out properties of quarks that might be useful for predictions, but then ignore the actual possible existence of quarks. However, Gross began to be disenchanted by just using ideas associated with global symmetries and algebras and longed to explore dynamics that might actually describe the physical processes that were occurring inside strongly interacting particles. Gross and his collaborator Cur- tis Callan built upon earlier work by James Bjorken to show that the charged particle apparently located inside protons and neutrons had to have spin 1/2, identical to that of electrons. Later, with other collabora- tors, Gross showed that a similar analysis of neutrino scattering off pro- tons and neutrons as measured at CERN revealed that the components looked just like the quarks that Gell-Mann had proposed. If it quacks like a duck and walks like a duck, it is probably a duck. Thus, for Gross, and others, the reality of quarks was now convincing. 2P_Glealer-StoryEverTold_Atirdd 218 12/16116 3:06 PIA EFTA00286158 Free at Last 237 But as convinced as many such as Gross were by the reality of quarks, they were equally convinced that this implied that field theory could not possibly be the correct way to describe the strong interaction. The re- sults of the experiment required the constituents to be essentially non- interacting, not strongly interacting. In 1969 Gross's colleagues at Princeton Curtis Callan and Kurt Sy- manzik rediscovered a set of equations explored by Landau, and then Gell-Mann and Francis Low, that described how quantities in quantum field theory might evolve with scale. If the partons inferred by the SLAC experiments had any interactions at all—as quarks must have—then measurable departures from the scaling that Bjorken had derived would occur, and the results that Gross and his collaborators had also derived when comparing theory and the SLAC experiments would also have to be modified. Over the next two years, with the results of 't Hooft and Veltman, and the growing success of the predictions of the theory of the weak and electromagnetic interactions, more people began to turn their at- tention once again to quantum field theory. Gross decided to prove in great generality that no sensible quantum field theory could possibly re- produce the experimental results about the nature of protons and neu- trons observed at SLAC. Thus he hoped to kill this whole approach to attempting to understand the strong interaction. First, he would prove that the only way to explain the SLAC results was if somehow, at short distances, the strength of the quantum field interactions would have to go to zero, i.e., the fields would essentially become noninteracting at short distances. Then, after that, he would show that no quantum field theory had this property. Recall that Landau had shown that quantum electrodynamics, the prototypical consistent quantum field theory, has precisely the opposite behavior. The strength of electric charges becomes larger as the scale at which you probe particles (such as electrons) gets smaller due to the cloud of virtual particles and antiparticles surrounding them. 2P_GrealestStecyC-verTaleLAC.indd 23T 12/16116 3:06 PIA EFTA00286159 238 THE GREATEST STORY EVER TOLD-SO FAR Early in 1973 Gross and his collaborator Giorgio Parisi had completed the first part of the proof, namely that scaling as observed at SLAC im- plied the strong interactions of the proton's constituents must go to zero at small-distance scales if the strong nuclear force was to be described by any fundamental quantum field theory. Next, Gross attempted to show that no field theories actually had this behavior—the strength of interactions going to zero at small-distance scales—which he dubbed asymptotic freedom. With help from Har- vard's Sidney Coleman, who was visiting Princeton at the time, Gross was able to complete this proof for all sensible quantum field theories, except for Yang-Mills-type gauge theories. Gross now took on a new graduate student, twenty-one-year-old Frank Wilczek, who had come to Princeton from the University of Chi- cago planning to study mathematics, but who switched to physics after taking Gross's graduate class in field theory. Gross was either lucky or astute because he served as the graduate supervisor of probably the two most remarkable intellects among physi- cists in my generation, Wilczek and Edward Witten, who helped lead the string theory revolution in the 198os and '9os and who is the only physicist ever to win the prestigious Fields Medal, the highest award given to mathematicians. Wilczek is probably one of the few true phys- ics polymaths. Frank and I became frequent collaborators and friends in the early 1980s, and he is not only one of the most creative physicists I have ever worked with, he also has an encyclopedic knowledge of the field. He has read almost every physics text ever written, and he has assimilated the information. In the intervening years, he has made nu- merous fundamental contributions not only to particle physics, but to cosmology and also the physics of materials. Gross assigned Wilczek to explore with him the one remaining loophole in Gross's previous proof—determining how the strength of the interaction in Yang-Mills theories changed as one went to shorter- distance scales—to prove that these theories too could not exhibit 2P_Glealer-StoryEverTold_Atindd 238 12/16116 3:06 PIA EFTA00286160 Free at Last 239 asymptotic freedom. They decided to directly and explicitly calculate the behavior of the interactions in the theories at shorter and shorter- distance scales. This was a formidable task. Since that time tools have been developed for doing the calculation as a homework problem in a graduate course. Moreover, things are always easier to calculate when you know what the answer will be, as we now do. After several hectic months, with numerous false starts and numerical errors, in February of 1973 they completed their calculations and discovered, to Gross's great surprise, that in fact Yang-Mills theories are asymptotically free-the interaction strength in these theories does approach zero as interacting particles get closer together. As Gross later put it, in his Nobel address, "For me the discovery of asymptotic freedom was totally unexpected. Like an atheist who has just received a message from a burning bush, I became an immediate true believer! Sidney Coleman had assigned his own graduate student David Politzer to do a similar calculation, and his independent result agreed with Gross and Wilczek's and was obtained at about the same time. That the results agreed gave both groups greater confidence in them. Not only can Yang-Mills theories be asymptotically free, they are the only field theories that are. This led Gross and Wilczek to suggest, in the opening of their landmark paper, that because of this uniqueness, and because asymptotic freedom seemed to be required for any theory of the strong interaction given the 1968 SLAC experimental results, per- haps a Yang-Mills theory could explain the strong interaction. Which Yang-Mills theory was the right one needed to be deter- mined, and also why the massless gauge particles that are the hallmark of Yang-Mills theories had not been seen. And related to this, perhaps the most important long-standing question remained: Where were the quarks? But before I address these questions, you might be wondering why Yang-Mills theories have such a different behavior from their sim- 2P_Glealer-StoryEverTold_Atincld 239 12/16116 3:06 PIA EFTA00286161 240 THE GREATEST STORY EVER TOLD-SO FAR pier cousin quantum electrodynamics, where Landau had shown the strength of the interaction between electric charges gets larger on small-distance scales. The key is somewhat subtle and lies in the nature of the massless gauge particles in Yang-Mills theory. Unlike photons in QED, which have no electric charge, the gluons that were predicted to mediate the strong interaction possess Yang-Mills charges, and therefore gluons in- teract with each other. But because Yang-Mills theories are more com- plicated than QED, the charges on gluons are also more complicated than the simple electric charges on electrons. Each gluon not only looks like a charged particle, but also like a little charged magnet. If you bring a small magnet near some iron, the iron gets magnetized and you end up with a more powerful magnet. Something similar hap- pens with Yang-Mills theories. If I have some particle with a Yang-Mills charge, say, a quark, then quarks and antiquarks can pop out of the vac- uum around the charge and screen it, as happens in electromagnetism. But gluons can also pop out of the vacuum, and since they act like little magnets, they tend to align themselves along the direction of the field produced by the original quark. This increases the strength of the field, which in turn induces more gluons to pop out of the vacuum, which further increases the field, and so on. As a result, the deeper into the virtual gluon cloud you penetrate— i.e., the closer you get to the quark—the weaker the field will look. Ulti- mately, as you bring two quarks closer together, the interaction will get so weak that they will begin to act as if they are not interacting at all, the characteristic of asymptotic freedom. I used gluons and quarks as labels here, but the discovery of asymp- totic freedom did not point uniquely to any specific Yang-Mills theory. However, Gross and Wilczek recognized the natural candidate was the Yang-Mills theory that Greenberg and others had posited was neces- sary for Gell-Mann's quark hypothesis to explain the observed nature of elementary particles. In this theory each quark carries one of three 2P_Glealer-StoryEverTold_Atirdd 240 12/16116 3:06 PIA EFTA00286162 Free at Last 241 different types of charges, which are labeled, for lack of better names, by colors, say, red, green, or blue. Because of this nomenclature Gell-Mann coined a name for this Yang-Mills theory: quantum chromodynamics (QCD), the quantum theory of colored charges, in analogy to quantum electrodynamics, the quantum theory of electric charges. Gross and Wilczek posited, based on the observational arguments in favor of such a symmetry associated with quarks, that quantum chro- modynamics was the correct gauge theory of the strong interaction of quarks. The remarkable idea of asymptotic freedom got an equally remark- able experimental boost within a year or so of these theoretical develop- ments. Experiments at SLAC and at another accelerator in Brookhaven, Long Island, made the striking and unexpected discovery of a new mas- sive elementary particle that appeared as if it might be made up of a new quark—indeed, the so-called charmed quark that had been predicted by Glashow and friends four years earlier. But this new discovery was peculiar, because the new particle lived far longer than one might imagine based on the measured lifetime of unstable lighter strongly interacting particles. As the experimentalists who discovered this new particle said, observing it was like wandering in the jungle and finding a new species of humans who lived not up to one hundred, but up to ten thousand years. Had the discovery been made even five years earlier, it would have seemed inexplicable. But in this case, fortune favored the prepared mind. Tom Appelquist and David Politzer, both at Harvard at the time, quickly realized that if asymptotic freedom was indeed a property of the strong interaction, then one could show that the interactions governing more massive quarks would be less strong than the interactions govern- ing the lighter, more familiar quarks. Interactions that are less strong would mean particles decay less quickly. What would otherwise have been a mystery was in this case a verification of the new idea of asymp- totic freedom. Everything seemed to be fitting into place. 2P_GlealerASIonEverTold_Atirdd 241 12/16116 3:06 PIA EFTA00286163 242 THE GREATEST STORY EVER TOLD-SO FAR Except for one pretty bt:g. thing. If the theory of quantum chromo- dynamics was a theory of the interactions of quarks and gluons, where were the quarks and gluons? How come none had ever been seen in an experiment? Asymptotic freedom provides a key clue. If the strength of the strong interaction gets weaker the closer one gets to a quark, then conversely it should get stronger and stronger the farther one is away from the quark. Imagine, then, what happens if I have a quark and an antiquark that are bound together by the strong interaction and I try to pull them apart. As I try to pull them apart, I need more and more energy because the strength of the attraction between them grows with distance. Eventually so much energy becomes stored in the fields surrounding the quarks that it becomes energetically favorable instead for a new quark-antiquark pair to pop out of the vacuum and then for each to become bound to one of the original particles. The process is shown schematically below. quark anti-quark a 1 + 00 40-0 40-0 It would be like stretching a rubber band. Eventually the band will snap into two pieces instead of stretching forever. Each piece in this case would then represent a new bound quark-antiquark pair. What would this mean for experiments? Well, if I accelerate a par- ticle such as an electron and it collides with a quark inside a proton, it will kick the quark out of the proton. But as the quark begins to exit the 2P_Glealer-StoryEverTold_Atincld 242 12/16116 3:06 PIA EFTA00286164 Free at Last 243 proton, the interactions of the quark with the remaining quarks will in- crease, and it will eventually be energetically favored for virtual quark- antiquark pairs to pop out of the vacuum and bind to both the ejected quark and the other quarks as well. This means that one will create a shower of strongly interacting particles, such as protons or neutrons or pions or so on, moving along the direction of the original ejected quark, and similarly a shower of strongly interacting particles recoiling in the direction of motion of the original remaining quarks left over from the proton. One will never see the quarks themselves. Similarly, if a particle collides with a quark, in recoiling sometimes the quark will emit a gluon before it binds with an antiquark popping out of the vacuum. Then since gluons interact with each other as well as with quarks, the new gluon might emit more gluons. The gluons in turn will be surrounded by new quarks that pop out of the vacuum, creating new strongly interacting particles moving along the direction of each original gluon. In this case one would expect in some cases to see not a single shower moving in the direction of the original quark, but several showers, corresponding to each new gluon that is emitted along the way. Because quantum chromodynamics is a specific, well-defined the- ory, one can predict the rate at which quarks will emit gluons, and the rate at which one would see a single shower, or jet as it is called, kicked out when an electron collides with a proton or neutron, and the rate at which one would see two showers, and so on. Eventually, when ac- celerators became powerful enough to observe all these processes, the observed rates agreed well with the predictions of the theory. There is every reason to believe that this picture of free quarks and gluons quickly getting bound to new quarks and antiquarks so that one would never observe a free quark or gluon is valid. This is called Con- finement because quarks and gluons are always confined inside strongly interacting particles such as protons and neutrons and can never break free from them without getting confined in newly created strongly in- teracting particles. 2P_Glealer-StoryEverrold_Atirdd 243 12/16116 3:06 PIA EFTA00286165 244 THE GREATEST STORY EVER TOLD-SO FAR Since the actual process by which the quarks get confined occurs as the forces become stronger and stronger when the quark moves farther and farther away from its original companions, the standard calcula- tions of quantum field theory, which are valid when the interactions are not too strong, break down. So this picture, validated by experiment, cannot be fully confirmed by tractable calculations at the moment. Will we ever derive the necessary mathematical tools to analyti- cally demonstrate from first principles that confinement is indeed a mathematical property of quantum chromodynamics? This is the million-dollar question, literally. The Clay Mathematics Institute has announced a million-dollar prize for a rigorous mathematical proof that quantum chromodynamics does not allow free quarks or gluons to be produced. While no claimants to the prize have yet come forward, we nevertheless have strong indirect support of this idea, coming not only from experimental observations, but also from numerical simula- tions that closely approximate the complicated interactions in quantum chromodynamics. This is heartening, if not definitive. We still have to confirm that it is some property of the theory and not of the computer simulation. However, for physicists, if not mathematicians, this seems pretty convincing. One final bit of direct evidence that QCD is correct came from a realm where exact calculations can be done. Because quarks are not completely free at short distances, I earlier mentioned that there should be calculable corrections to exotic scaling phenomena observed in the high-energy collisions of electrons off protons and neutrons, as origi- nally observed at SLAC. Perfect scaling would require completely noninteracting particles. The corrections that one could calculate in quantum chromodynamics would only be observable in experiments that were far more sensitive than those originally performed at SLAC. It took the development of new, higher-energy accelerators to probe them. After thirty years or so, enough evidence was in so that comparison of theoretical predictions and experiment agreed at the i percent level, and 2P_Glealer-SlowEverrold_Atirdd 244 12/16116 3:06 PIA EFTA00286166 Free at Last 245 quantum chromodynamics as the theory of the strong interaction was finally verified in a precise and detailed way. Gross, Wilczek, and Politzer were finally awarded the Nobel Prize in 2004 for their discovery of asymptotic freedom. The experimentalists who had first discovered scaling at SLAC, which was the key observa- tion that set theorists off in the right direction, were awarded the Nobel Prize much earlier, in 1990. And the experimentalists who discovered the charmed quark in 1974 won the Nobel Prize two years later, in 1976. But the biggest prize of all, as Richard Feynman has said, is not the recognition by a medal or a cash award, or even the praise one gets from colleagues or the public, but the prize of actually learning something new about nature. • • • In this sense the 197os were perhaps the richest decade in the twentieth century, if not in the entire history of physics. In 1970 we understood only one force in nature completely as a quantum theory, namely quan- tum electrodynamics. By 1979 we had developed and experimentally verified perhaps the greatest theoretical edifice yet created by human minds, the Standard Model of particle physics, describing precisely three of the four known forces in nature. The effort spanned the entire history of modern science, from Galileo's investigations of the nature of moving bodies, through Newton's discovery of the laws of motion, through the experimental and theoretical investigations of the nature of electromagnetism, through Einstein's unification of space and time, through the discoveries of the nucleus, quantum mechanics, protons, neutrons, and the discovery of the weak and strong forces themselves. But the most remarkable characteristic of all in this long march toward the light is how different the fundamental nature of reality is from the shadows of reality that we experience every day, and in par- ticular how the fundamental quantities that appear to govern our exis- tence are not fundamental at all. 2P_Gtealer-StoryEverTold_Atirdd 245 12118/18 3:08 PIA I EFTA00286167 246 THE GREATEST STORY EVER TOLD-SO FAR Making up the heart of observed matter are particles that had never been directly observed and, if we are correct, will never be directly observable—quarks and gluons. The properties of forces that govern the interactions of these particles—and also the particles that have formed the basis of modern experimental physics for more than a century, electrons— are also, on a fundamental level, completely different from the properties we directly observe and on which we depend for our existence. The strong interaction between protons and neutrons is only a long-distance rem- nant of the underlying force between quarks, whose fundamental proper- ties are masked by the complicated interactions within the nucleus. The weak interaction and the electromagnetic interaction, which could not be more different on the surface—one is short-range, while the other is long- range, and one appears thousands of times weaker than the other—are in fact intimately related and reflect different facets of a single whole. That whole is hidden from us because of the accident of nature we call spontaneous symmetry breaking, which distinguishes the two weak and electromagnetic interactions in the world of our experience and hides their true nature. More than that, the properties of the particles that produce the characteristics of the beautiful world we observe around us are only possible because, after the accident of spontaneous symmetry breaking, just one particle in nature—the photon—remains massless. If symmetry breaking had never occurred so that underlying symme- tries of the forces governing matter were manifest—which in turn would mean that the particles conveying the weak force would also be mass- less, as would most of the particles that make us up—essentially nothing we see in the universe today, from galaxies to stars, to planets, to people, to birds and bees, to scientists and politicians, would ever have formed. Moreover, we have learned that even these particles that make us up are not all that exist in nature. The observed particles combine in simple groupings, or families. The up and down quarks make up protons and neutrons. Along with them one finds the electron, and its partner, the electron neutrino. Then, for reasons we still don't understand, there is 2P_Glealer-StoryEverTold_Atirdd 246 12/16116 3:06 PIA EFTA00286168 Free at Last 247 a heavier family, made up of the charm and strange quark on the one hand, and the muon and its neutrino on the other. And finally, as ex- periments have now confirmed over the past decade or two, there is a third family, made of two new types of quarks, called bottom and top, and an accompanying heavy version of the electron called the tau par- ticle, along with its neutrino. Beyond these particles, as I shall soon describe, we have every reason to expect that other elementary particles exist that have never been ob- served. While these particles, which we think make up the mysterious dark matter that dominates the mass of our galaxy and all observed gal- axies, may be invisible to our telescopes, our observations and theories nevertheless suggest that galaxies and stars could never have formed without the existence of dark matter. And at the heart of all of the forces governing the dynamical behavior of everything we can observe is a beautiful mathematical framework called gauge symmetry. All of the known forces, strong, weak, electromagnetic, and even gravity, possess this mathematical property, and for the three former examples, it is precisely this property that ensures that the theo- ries make mathematical sense and that nasty quantum infinities disappear from all calculations of quantities that can be compared to experiment. With the exception of electromagnetism, these other symmetries re- main completely hidden from view. The gauge symmetry of the strong force is hidden because confinement presumably hides the fundamental particles that manifest this symmetry. The gauge symmetry of the weak force is not manifest in the world in which we live because it is spontane- ously broken so that the W and Z particles become extremely massive. The shadows on the wall of everyday life are truly merely shadows. In this sense, the greatest story every told, so far, has been slowly playing out over the more than two thousand years since Plato first imagined it in his analogy of the cave. 2P_Glealer-StoryEverTold_Atirdd 241 12/16116 3:06 PIA EFTA00286169 248 THE GREATEST STORY EVER TOLD-SO FAR But as remarkable as this story is, two elephants remain in the room. TWo protagonists in our tale could until recently have meant that the key aspects of the story comprised a mere fairy tale invented by theo- rists with overactive imaginations. First, the W and Z particles, postulated in 1960 to explain the weak interaction, almost one hundred times more massive than protons and neutrons, were still mere theoretical postulates, even if the indirect evidence for their existence was overwhelming. More than this, an in- visible field—the Higgs field—was predicted to permeate all of space, masking the true nature of reality and making our existence possible because it spontaneously breaks the symmetry between the weak and the electromagnetic interactions. To celebrate a story that claims to describe how it is that we exist, but that also posits an invisible field permeating all of space, sounds suspiciously like a religious celebration, and not a scientific one. To truly ensure that our beliefs conform to the evidence of reality rather than how we would like reality to be, to keep science worthy of the name, we had to discover the Higgs field. Only then could we truly know if the significance of the features of our world that we hold so dear might be no greater than that of the features of one random ice crystal on a window. Or, more to the point, perhaps, no greater than the significance of the superconducting nature of wire in a laboratory versus the normal resistance of the wires in my computer. The experimental effort to carry out this task was no easier than that in developing the theory itself. In many ways it was more daunting, tak- ing more than fifty years and involving the most difficult fabrication of technology that humans have ever attempted. 2P_Glealer-StoryEverrold_Atirdd 24S 12/16116 3:06 PIA EFTA00286170 Chapter 20 SPANKING THE VACUUM If anyone slaps you on the right cheek, turn to him the other also. -MATTHEW 5:39 As the 197os ended, theorists were on top of the world, triumphant and exultant. With progress leading to the Standard Model so swift, what other new worlds were there to conquer? Dreams of a theory of everything, long dormant, began to rise again and not just in the dim recesses of the collective subconscious of theorists. Still, the W and Z gauge particles had never actually been observed, and the challenge to directly observe them was pretty daunting. Their masses were precisely predicted in the theory at about ninety times the mass of the proton. The challenge to produce these particles comes from a simple bit of physics. Einstein's fundamental equation of relativity, E = me, tells us that we can convert energy into mass by accelerating particles to energies of many times their rest mass. We can then smash them into targets to see what comes out. The problem is that the energy available to produce new particles by smashing other fast-moving particles into stationary targets is given by 249 2P_Glealer-StoryEverTold_Atincld 249 12/16116 3:06 PM EFTA00286171 250 THE GREATEST STORY EVER TOLD-SO FAR what is called the center-of-mass energy. For those undaunted by an- other formula, this turns out to be the square root of twice the product of the energy of the accelerated particle times the rest mass energy of the target particle. Imagine accelerating a particle to one hundred times the rest mass energy of the proton (which is about one gigaelectronvolt— GeV). In a collision with stationary protons in a target, the center-of- mass energy that is available to create new particles is then only about 14 GeV. This is just slightly greater than the center-of-mass energy avail- able in the highest-energy particle accelerator in 1972. To reach the energies required to produce massive particles such as the W or Z bosons, two opposing beams of particles must collide. In this case the total center-of-mass energy is simply twice the energy of each beam. If each colliding beams of particles has an energy of one hundred times the rest mass of a proton, this then yields zoo GeV of energy to be converted into the mass of new particles. Why, then, produce accelerators with stationary targets and not col- liders? The answer is quite simple. If I am shooting a bullet at a barn door, I am more or less guaranteed to hit something. If I shoot a bullet at another incoming bullet, however, have to be a much better shot than probably anyone else alive and have a better gun than any now made to be guaranteed to hit it. This was the challenge facing experimentalists in 1976, by which time they took the electroweak model seriously enough that they thought it worth the time, effort, and money to try to test it. But no one knew how to build a device with the appropriate energy. Accelerating individual beams of particles or antiparticles to high ener- gies had been achieved. By 1976 protons were being accelerated to Soo GeV, and electrons up to so GeV. At lower energies, collisions of elec- trons and their antiparticles had successfully been carried out, and this is how the new particle containing the charmed quark and antiquark had been discovered in 1974 Protons, having greater mass and thus more rest energy initially, 2P_Glealer-StoryEverTold_Atirdd 250 12/16116 3:06 PIA EFTA00286172 Spanking the Vacuum 251 are easier to accelerate to high energies. In 2976 a proton accelerator at the European Organization for Nuclear Research (CERN) in Geneva, the Super Proton Synchrotron (SPS), had just been commissioned as a conventional fixed-target accelerator operating with a proton beam at goo GeV. However, another accelerator at Fermilab, near Chicago, had already achieved proton beams of soo GeV by the time the SPS turned on. In June of that year, physicists Carlo Rubbia, Peter McIntyre, and David Cline made a bold suggestion at a neutrino conference: convert- ing the SPS at CERN into a machine that collided protons with their antiparticles—antiprotons—would allow CERN to potentially produce W's and Z's. Their bold idea was to use the same circular tunnel to accelerate pro- tons in one direction, and antiprotons in another. Since the two par- ticles have opposite electric charges, the same accelerating mechanism would have opposite effects on each particle. So a single accelerator could in principle produce two high-energy beams circulating in op- posite directions. The logic of such a proposal was clear, but its implementation was not. In the first place, given the strength of the weak interaction, the pro- duction of even a few W and Z particles would require the collision of hundreds of billions of protons and antiprotons. But no one had ever pro- duced and collected enough antiprotons to make an accelerator beam. Next, you might imagine that with two beams traversing the same tunnel in opposite directions, particles would be colliding all around the tunnel and not in the detectors designed to measure the products of the collisions. However, this is far from the case. The cross section of even a small tunnel compared to the size of the region over which a proton and an antiproton might collide is so huge that the problem is quite the op- posite. It seemed impossible to produce enough antiprotons and ensure that both they and the protons in the proton beam would be sufficiently compressed so that when the two beams were brought together, steered by powerful magnets, any collisions at all would be observed. 2P_GrealestSlontEverTald_AC.indd 251 12/16116 3:06 PIA EFTA00286173 252 THE GREATEST STORY EVER TOLD-SO FAR Convincing the CERN directorate to transform one of the world's most powerful accelerators, built in a circular tunnel almost eight ki- lometers around at the French-Swiss border, into a new kind of collider would have been difficult for many people, but Carlo Rubbia, a bombastic force of nature, was up to the task. Few people who got in Rubbia's way were likely to be happy about it afterward. For eighteen years he jetted every week between CERN and Harvard, where he was a professor. His office was two floors down from mine, but I knew when he was in town because I could hear him. Moreover, Rubbia's idea was good, and in pro- moting it he was really suggesting to CERN that the SPS move up from an "also-ran" machine to the most exciting accelerator in the world. As Sheldon Glashow said to the CERN directorate when encouraging them to move forward, to you want to walk, or do you want to fly?" Still, to fly one needs wings, and the creation of a new method to pro- duce, store, accelerate, and focus a beam of antiprotons fell to a brilliant accelerator physicist at CERN, Simon van der Meer. His method was so clever that many physicists who first heard about it thought it violated some fundamental principles of thermodynamics. The properties of the particles in the beam would be measured at one place in the circular tunnel, then a signal would be sent for magnets farther down the tun- nel to give many small kicks over time to the particles in the beam as they passed by, thus slightly altering the energies and momenta of any wayward particles so that they would eventually all get focused into a narrow beam. The method, called stochastic cooling, helped make sure particles that were wandering away from the center of the beam would be sent back into the middle. Together van der Meer and Rubbia pushed forward, and by 1981 the collider was working as planned, and Rubbia assembled the largest phys- ics collaboration ever created and built a large detector capable of sort- ing through billions of collisions of protons and antiprotons to search for a handful of possible W and Z particles. Rubbia's team was not the only one hunting for a W and a Z, however. Another detector collabora- 2P_GrealesiSleryEverTold_AC.indd 262 12/16116 3:06 PIA EFTA00286174 Spanking the Vacuum 253 tion had been assembled and was also built at CERN. Redundancy for such an important observation seemed appropriate. Unearthing a signal from the immense background in these experi- ments was not easy. Remember that protons are made of more than one quark, and in a single proton-antiproton collision a lot of things can happen. Moreover, the W's and Z's would not be observed directly, but via their decays—in the case of the W, into electrons and neutrinos. Neutrinos would not be directly observed, either. Rather the experimen- talists would tally up the total energy and momentum of each outgoing particle in a candidate event and look for large amounts of "missing en- ergy," which would signal that a neutrino had been produced. By December 1982, a W candidate event had been observed by Rub- bia and his colleagues. Rubbia was eager to publish a paper based on this single event, but his colleagues were more cautious, for good reason. Rubbia seemed to have a history of making discoveries that weren't al- ways there. In the meantime he leaked details of the event to a number of colleagues around the world. Over the next few weeks his "UM" collaboration obtained evidence for five more W candidate events, and the UAI physicists designed sev- eral far more stringent tests to ascertain with high confidence that the candidates were real. On January 2o, 1983, Rubbia presented a memora- ble and masterful seminar at CERN announcing the result. The stand- ing ovation he received made it clear that the physics community was convinced. A few days later Rubbia submitted a paper to the journal Physics Letters announcing the discovery of six W events. The W had been discovered with precisely the predicted mass. The search was not over, however. The Z remained to be seen. Its predicted mass was slightly higher than that of the W, and its signal was therefore slightly harder to obtain. Nevertheless, within a month or so of the W announcement, evidence for Z events began to come in from both experiments, and on the basis of a single clear event, on May 27 that year Rubbia announced its discovery. 2P_Glealer-StoryEverTold_Atirdd 253 12/16116 3:06 PIA EFTA00286175 254 THE GREATEST STORY EVER TOLD-SO FAR The gauge bosons of the electroweak model had been found. The sig- nificance of these discoveries for solidifying the empirical basis of the Standard Model was underscored when, just slightly over a year after making the announcement, Rubbia and his accelerator colleague van der Meer were awarded the Nobel Prize in Physics. While the teams that had built and operated both the accelerator and the detectors were huge, few could deny that without Rubbia's drive and persistence and van der Meer's ingenious invention the discovery would not have been possible. One big Holy Grail now remained: the purported Higgs particle. Un- like the W and Z bosons, the mass of the Higgs is not fixed by the the- ory. Its couplings to matter and to the gauge bosons were predicted, as these couplings allow the background Higgs field that presumably exists in nature to break the gauge symmetry and give mass not to just the W and the Z, but also to electrons, muons, and quarks—indeed to all the fundamental particles in the Standard Model save the neutrino and the photon. However, neither the Higgs particle mass nor the strength of its self-interactions was separately determined in advance by then existing measurements. Only their ratio was fixed by the theory in terms of the measured strength of the weak interaction between known particles. Given conservative estimates of the possible magnitude of the Higgs self-interaction strength, the Higgs particle mass was conservatively es- timated to lie within a range of 2 to 2,000 GeV. What set the upper limit was that, if the Higgs self-coupling is too big, then the theory becomes strongly interacting and many of the calculations performed using the simplest picture of the Higgs break down. Aside from their necessary role in breaking the electroweak sym- metry and giving other elementary particles masses, these quantitative details were therefore largely undetermined by experiments up to that time—which is probably why Sheldon Glashow in the 3.98os referred to the Higgs as the "toilet" of modern physics. Everyone was aware of its necessary existence, but no one wanted to talk about the details in public. 2P_GrealetaleryEverTold_AC.indd 254 12/16116 3:06 PIA EFTA00286176 Spanking the Vacuum 255 That the Standard Model didn't fix in advance many of the details of the Higgs sector didn't dissuade many theorists from proposing models that "predicted" the Higgs mass based on some new theoretical ideas. In the early 1980s, each time accelerators increased their energies, new physics papers would come out predicting a Higgs would be discov- ered when the machine was turned on. Then a new threshold would be reached, and nothing would be observed. To explore all the available parameter space to see if the Higgs existed, a radically new accelerator would clearly have to be built. I was convinced during all this time that the Higgs didn't exist. The spontaneous symmetry breaking of the electroweak gauge symmetry did certainly occur—the W and the Z exist and have mass—but adding a fundamental new scalar field designed by recipe specifically to per- form this task seemed contrived to me. First, no other fundamental sca- lar field had ever been observed to exist in nature's particle menagerie. Second, I felt that with all of the unknown physics yet to be discovered at small scales, nature would have developed a much more ingenious and unexpected way of breaking the gauge symmetry. Once one posits the Higgs particle, then the next obvious question is "Why that?" or more specifically "Why just the right dynamics to cause it to condense at that scale, and with that mass?" I thought that nature would find a way to break the theory in a less ad hoc fashion, and I expressed this conviction fairly strongly when I was interviewed for my eventual posi- tion at the Society of Fellows at Harvard after getting my PhD. Let's recall now what the existence of the Higgs implies. It requires not just a new particle in nature but an invisible background field that must exist throughout all of space. It also implies that all particles— not just the W and the Z particles but also electrons and quarks—are massless in the fundamental theory. These particles that interact with the Higgs background field then experience a kind of resistance to their motion that slows their travel to less than the speed of light—just as a swimmer in molasses will move more slowly than a swimmer in water. 2P_Glealer-StoryEverTold_Atirdd 255 12/16116 3:06 PIA EFTA00286177 256 THE GREATEST STORY EVER TOLD-SO FAR Once they are moving at sub-light-speed, the particles behave as if they are massive. Those particles that interact more strongly with this back- ground field will experience a greater resistance and will act as if they are more massive, just as a car that goes off the road into mud will be harder to push than if it were on the pavement, and to those pushing it, it will seem heavier. This is a remarkable claim about the nature of reality. Remembering that in superconductors the condensate that forms is a complicated state of bound pairs of electrons, I was skeptical that things would work out so much more simply and cleanly on fundamental scales in empty space. So how to explore such a remarkable claim? We use the central prop- erty of quantum field theory that was exploited by Higgs himself when he proposed his idea. For every new field in nature, at least one new type of elementary particle must exist with that field. How, then, to produce the particles if such a background field exists throughout space? Simple. We spank the vacuum. By this I mean that if we can focus enough energy at a single point in space, we can excite real Higgs particles to emerge and be measured. One can picture this as follows. In the language of elementary particle physics, using Feynman diagrams, we can think of a virtual Higgs par- ticle emerging from the background Higgs field, giving mass to other particles. The left diagram corresponds to particles such as quarks and electrons scattering off a virtual Higgs particle and being deflected, thus experiencing resistance to their forward motion. The right diagram rep- resents the same effect for particles such as the W and the Z. We can then simply turn this picture around: 2P_Glealer-StoryEverrold_Atirdd 258 12/16,I6 3:06 PIA EFTA00286178 Spanking the Vacuum 257 In this case energetic particles such as W's and Z's or quarks and/or antiquarks or electrons and/or positrons appear to emit virtual Higgs particles and recoil. If the energies of the incoming particles are large enough, then the emitted Higgs could be a real particle. If they aren't, the Higgs would be a virtual particle. Now remember that if the Higgs gives mass to particles, then the particles it interacts with most strongly will be the particles that get the largest masses. In turn this means that the particles most likely to spit out a Higgs are the incident particles with the heaviest masses. That means that light particles such as electrons are probably not a good bet to directly create Higgs particles in an accelerator. Instead we can imag- ine creating an accelerator with enough energy so that we can create heavy virtual particles that will spit out Higgs particles, either virtual or real. The natural candidates are then protons. Build an accelerator or a collider starting with protons and accelerate them to high enough en- ergies to produce enough virtual heavy constituents so as to produce Higgs particles. The Higgs particles, virtual or real, being heavy, will quickly decay into the lighter particles that the Higgs interacts with most strongly—once again either the top or bottom quarks or W's and Z's. These will in turn decay into other particles. The trick would be to consider events with the smallest number of outgoing particles that could be cleanly detected, then determine their energies and momenta precisely and see if one could reconstruct a se- ries of events traceable to a single massive intermediate particle with the predicted interactions of a Higgs particle. No small task! These ideas were already clear as early as 1977, even before the dis- 2P_GlealerASIonEverTold_Aairdd 251 12/16116 3:06 PIA EFTA00286179 258 THE GREATEST STORY EVER TOLD-SO FAR covery of the top quark itself (since the bottom quark had already been discovered, and all the other quarks came in weak pairs—up and down, charm and strange—clearly another quark had to exist, although it took until 199s to discover it, a whopping um times heavier than the proton). But knowing what was required and actually building a machine ca- pable of doing the job were two different things. 2P_GlealestStoryEverrold_Atirdd 258 12/16116 3:06 PIA EFTA00286180 Chapter 21 GOTHIC CATHEDRALS OF THE TWENTY-FIRST CENTURY The price of wisdom is above rubies. -JOB 28:18 Accelerating protons to high enough energies to explore the full range of possible Higgs masses was well beyond the capabilities of any machine in 1978—when all the other predictions of the elec- troweak theory were confirmed—or in 1983 when the W and the Z had been discovered. An accelerator at least an order of magnitude more powerful than the most powerful machine then in existence was re- quired. In short, not a collider, but a supercollider. The United States, which for the entire period since the end of the Second World War had dominated science and technology, had good reason to want to build such a machine. After all, CERN in Geneva had emerged by 1984 as the dominant particle physics laboratory in the world. American pride was so hurt when both the W and the Z particles were discovered at CERN that six days after the press conference an- nouncing the Z discovery, the New York Times published an editorial titled "Europe 3, U.S. Not Even Z-Zerol Within a week after the Z discovery, American physicists decided to 259 2P_Glealer-StoryEverTold_Atirdd 259 12/16116 3:06 PIA EFTA00286181 260 THE GREATEST STORY EVER TOLD-SO FAR cancel construction of an intermediate-scale accelerator in Long Island and go for broke. They would build a massive accelerator with a center- of-mass energy almost one hundred times greater than the CERN SPS machine. To do so they would need new superconducting magnets, and so their brainchild was named the Superconducting Super Col- lider (SSC). After the project was proposed by the US particle physics commu- nity in 2983, the traditional scramble proceeded among many different states to get a piece of the enormous fiscal pie for its construction and management. After much political and scientific wrangling a site just south of Dallas, Texas, in Waxahachie, was chosen. Whatever the moti- vation, Texas seemed particularly appropriate, as everything about the project, which was approved in 1987 by President Reagan, was supersize. The huge underground tunnel would have been eighty-seven kilo- meters around, the largest tunnel ever constructed. The project would be twenty times bigger than any other physics project ever attempted. The proposed energy of collisions, with two beams each having an en- ergy twenty thousand times the mass of the proton, would be about one hundred times larger than the collision energy of the machine at CERN that had discovered the W and the Z. Ten thousand superconducting magnets, each of unprecedented strength, would have been required. Cost overruns, lack of international cooperation, a poor US economy, and political machinations eventually led to SSC's demise in October 1993. I remember the time well. I had recently moved from Yale to be- come chair of the Physics Department at Case Western Reserve Uni- versity, with a mandate to rebuild the department and hire twelve new faculty members over five years. The first year we advertised, in 1993-94, we received more than two hundred applications from senior scientists who had been employed at the SSC and who were now without a job or any prospects. Many of them were very senior, having left full professor- ships at distinguished universities to spearhead the effort. It was sad, and more than half of those people had to leave the field altogether. 2P_Glealer-StoryEverTold_Atincld 280 12/18118 308 PIA EFTA00286182 Gothic Cathedrals of the Twenty-first Century 281 The anticipated cost of the project when it was canceled had risen from 54.4 billion at its inception in 2987 to about $12 billion in 1993. While this was, and still is, a large amount of money, one can debate the merits of killing the project. Two billion dollars had already been spent on it, and twenty-four kilometers of tunnel had been completed. The decision to kill the project was not black-and-white, but a num- ber of things could have played a bigger role in considerations—from the opportunity costs of losing a fair fraction of the talented accelera- tor physicists and particle physics experimentalists in the country to the many new breakthroughs that might have resulted from the expen- ditures on high-tech development that would have contributed to our economy. Moreover, had the SSC been built and functioned as planned, we may have had answers more than a decade ago to experimental ques- tions we are still addressing. Would knowing the answers have changed anything we might have done in the meantime? We'll probably never know. The $12 billion would have been spent over some ten to fifteen years during construction and the commencement of operations, which makes the cost in the range of Si billion per year. In the federal budget this is not a large amount. My own political views are well known, so it may not be surprising for me to suggest, for example, that the United States would have been just as secure had it cut the bloated US defense budget by this amount, far less than 2 percent of its total each year. More- over, the entire cost of the SSC would have probably been comparable to the air-conditioning and transportation costs of the disastrous 2003 Iraq invasion, which decreased our net security and well-being. I can't help referring once again to Robert Wilson's testimony before Congress regarding the Fermilab accelerator: "It has nothing to do directly with defending our country except to help make it worth defending! These are political questions, however, not scientific ones, and in a democracy, Congress, representing the public, has the right and respon- sibility to oversee priorities for expenditures on large public projects. 2P_GlealerASIonEverTold_Atindd 261 12/16116 3:06 PIA EFTA00286183 282 THE GREATEST STORY EVER TOLD-SO FAR The particle physics community, perhaps too used to a secure inflow of money during the Cold War, did not do an adequate job of inform- ing the public and Congress what the project was all about. It is not surprising that in hard economic times the first thing to be cut would be something that seemed so esoteric. I wondered at the time why it was necessary to kill the project, rather than suspend funding until the economy improved or until technological developments might have re- duced its cost. Neither the tunnel (now filling with water) nor the lab- oratory buildings (now occupied by a chemical company) were going anywhere. Despite these developments in the United States, CERN was moving forward with a new machine, the Large Electron-Positron (LEP) Col- lider, designed to explore in detail the physics of the W and the Z par- ticles, at the urging of its newest Nobel laureate, the indomitable Carlo Rubbia. He became the laboratory's director in 1989, the same year the new machine came online. A twenty-seven-kilometer-long circular tunnel was dug about a hundred meters underground around the old SPS machine, which was now used to inject electrons and positrons into the bigger ring, where they were further accelerated to huge energies. Located on the outskirts of Geneva, the new machine was large enough to cross under the Jura Mountains into France. European nations are more familiar with build- ing tunnels than the United States is, and when the tunnel was com- pleted, the two ends met up to within one centimeter. Moreover CERN, as an international collaboration of many countries, did not significantly eat into the GDP of any one country. The new machine ran successfully for more than a decade, and after the demise of the SSC in the United States, the huge LEP tunnel was considered for the creation of a miniversion of the SSC—not quite as powerful but still energetic enough to explore much of the parameter space where the long-sought Higgs particle might exist. Some competi- tion came from a machine at Fermilab, called the Tevatron, which had 2P_Glealer-StoryEverTold_Atincld 282 12/16116 3:06 PIA EFTA00286184 Gothic Cathedrals of the Twenty-first Century 263 been running since 1976 and in 1984 came online as the world's most energetic proton-antiproton machine. By 1986, the collision energy of protons and antiprotons circulating around the 6.s-kilometer ring of superconducting magnets at Fermilab was almost two thousand times the equivalent rest mass energy of the proton. As significant as this was, it was not sufficient to probe most of the available parameter space for the Higgs, and a discovery at the Tevatron would have required nature to have been kind. The Tevatron did garner one great success, the long-anticipated discovery, in 1995, of the mam- moth top quark, 175 times the mass of the proton, and the most massive particle yet discovered in nature. With no clear competition therefore, within fourteen months of the demise of the SSC the CERN council approved the construction of a new machine, the Large Hadron Collider, in the LEP tunnel. Design and development of the machine and detectors would take some time to complete, so the LEP machine would continue to operate in the tunnel for almost another six years before having to close down for reconstruc- tion. It would then take almost another decade to complete construc- tion of the machine and the particle detectors to be used in the search for the Higgs and/or other new physics. That is, if a working machine and viable detectors could be con- structed. This would be the most complicated engineering task humans had ever undertaken. The design specifications for superconducting magnets, computing facilities, and many other aspects of the machine and detectors called for technology far exceeding anything then avail- able. Conceptual design of the machine took a full year, and another year later two of the main experimental detector collaboration pro- posals were approved. The United States, with no horses in this race, was admitted as an "observer" state to CERN, allowing US physicists to become key players in detector development and design. In 1998 con- struction of the cavern to hold one of the two major detectors, the CMS 2P_GlealerASIonEverTold_Atincld 263 12/16116 3:06 PIA EFTA00286185 284 THE GREATEST STORY EVER TOLD-SO FAR detector, was delayed for six months as workers discovered fourth- century Gallo-Roman ruins, including a villa and surrounding fields, on the site. Four and a half years later, the huge caverns that would house both main detectors underground were completed. Over the next two years, 1,232 huge magnets, each fifteen meters long and weighing thirty-five tons, were lowered fifty meters below the surface in a special shaft and delivered to their final destinations using a specially designed vehicle that could travel in the tunnel. A year after that, the final pieces of each of the two large detectors were lowered into place, and at 10:28 M., September 10, 2008, the machine officially turned on for the first time. Two weeks later, disaster struck. A short occurred in one of the mag- net connectors, causing the associated superconducting magnet to go normal, releasing a huge amount of energy and resulting in mechanical damage and release of some of the liquid helium cooling the machine. The damage was extensive enough that a redesign and examination of every weld and connection in the LHC was required, taking more than a year to complete. In November of 2009 the LHC was finally turned back on, but because of design concerns, it was set to run at seven thou- sand times the center-of-mass energy of the proton, instead of fourteen thousand. On