EINSTEIN AND THE QUANTUM
EINSTEIN AND THE QUANTUM
THE QUEST OF THE VALIANT SWABIAN
A. DOUGLAS STONE
PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD
Copyright © 2013 by Princeton University Press
Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540
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Jacket photograph: Albert Einstein reading. Courtesy of The Hebrew University of Jerusalem / Corbis Historical Images. Personality rights of ALBERT EINSTEIN are used with permission of The Hebrew University of Jerusalem. Represented exclusively by GreenLight.
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Library of Congress Cataloging-in-Publication Data
Stone, A. Douglas, 1954–
Einstein and the quantum : the quest of the valiant Swabian / A. Douglas Stone.
pages cm
Includes bibliographical references and index.
ISBN 978-0-691-13968-5 (hardback)
1. Einstein, Albert, 1879–1955. 2. Physicists—Biography. 3. Quantum theory. 4. Science—History. I. Title.
QC16.E5S76 2013
530.12—dc23 2013013162
British Library Cataloging-in-Publication Data is available
This book has been composed in Verdigris MVB
Printed on acid-free paper. ∞
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
This book is dedicated to my father, Alan, who has been my intellectual inspiration, and to my wife, Mary, who has been my emotional inspiration.
Science as something already in existence, already completed, is the most objective, most impersonal thing that we humans know. Science as something coming into being, as a goal, however, is just as subjectively, psychologically conditioned, as all other human endeavors.
—ALBERT EINSTEIN, 1932
CONTENTS
Acknowledgments ix
INTRODUCTION A Hundred Times More Than Relativity Theory 1
CHAPTER 1 “An Act of Desperation” 5
CHAPTER 2 The Impudent Swabian 15
CHAPTER 3 The Gypsy Life 21
CHAPTER 4 Two Pillars of Wisdom 26
CHAPTER 5 The Perfect Instruments of the Creator 36
CHAPTER 6 More Heat Than Light 44
CHAPTER 7 Difficult Counting 51
CHAPTER 8 Those Fabulous Molecules 62
CHAPTER 9 Tripping the Light Heuristic 70
CHAPTER 10 Entertaining the Contradiction 80
CHAPTER 11 Stalking the Planck 86
CHAPTER 12 Calamity Jeans 94
CHAPTER 13 Frozen Vibrations 103
CHAPTER 14 Planck’s Nobel Nightmare 111
CHAPTER 15 Joining the Union 122
CHAPTER 16 Creative Fusion 129
CHAPTER 17 The Importance of Being Nernst 141
CHAPTER 18 Lamenting the Ruins 149
CHAPTER 19 A Cosmic Interlude 160
CHAPTER 20 Bohr’s Atomic Sonata 168
CHAPTER 21 Relying on Chance 181
CHAPTER 22 Chaotic Ghosts 193
CHAPTER 23 Fifteen Million Minutes of Fame 204
CHAPTER 24 The Indian Comet 215
CHAPTER 25 Quantum Dice 228
CHAPTER 26 The Royal Marriage: E = mc2 = hν 241
CHAPTER 27 The Viennese Polymath 254
CHAPTER 28 Confusion and Then Uncertainty 268
CHAPTER 29 Nicht diese Töne 279
Appendix 1: The Physicists 287
Appendix 2: The Three Thermal Radiation Laws 291
Notes 295
References 319
Index 325
ACKNOWLEDGMENTS
This project began after I gave several public lectures at Aspen and at Yale on Einstein, Planck, and the beginning of quantum theory, when it became clear that most of this story was completely unknown both to the interested layman and to most working physicists. While several eminent historians of science, T. S. Kuhn, Martin Klein, Abraham Pais, and John Stachel for example, have written excellent but relatively technical works analyzing various facets of Einstein’s work on quantum theory, no book for the general reader had attempted to synthesize all this into a complete picture. I have tried to fill that void with this book, while making it a fun read along the way. The book is based on the Collected Papers of Albert Einstein and the large body of outstanding historiography that has been produced on the history of quantum theory, blended with material from a number of biographies of Einstein, with a particular debt to the recent ones by Albrecht Folsing and Walter Isaacson. While I chose not to footnote quotations in the text, all their sources are identified in extensive notes at the back of the book.
I want to thank the late Martin Klein for his encouragement at the very early stages of this project, and Walter Isaacson for his generous advice and assistance, which was so important to a first-time author. I am very grateful to my editor, Ingrid Gnerlich, for her critical reading of the manuscript and useful guidance, and to Deborah Chasman, who made key suggestions for improving my initial draft. I also want to thank Samantha Hasey and Eric Henney at Princeton University Press, who helped with the final stages of preparation for publication. Barbara Wollf at the Albert Einstein Archive of the Hebrew University in Jerusalem was very generous with her advice and experience relating to the copyright permissions I was seeking, and Andy Shimp helped me navigate the library systems at Yale and retrieve difficult-to-find items. Both my father, Alan Stone, and my wife, Mary Schwab Stone, read the work with a keen eye and helped me immeasurably, not the least in keeping up my enthusiasm for the project. My son, Will Stone, found time between his journalistic pursuits to work as my editorial assistant in assembling the final version of the manuscript.
EINSTEIN AND THE QUANTUM
INTRODUCTION
A HUNDRED TIMES MORE THAN RELATIVITY THEORY
“Let’s see if Einstein can solve our problem.” This was not an idea I had ever entertained, much less verbalized, during my previous twenty-six years doing research in quantum physics. Physicists don’t read the works of the great masters of earlier generations. We learn physics from weighty textbooks in which the ideas are stated with cold-blooded logical inevitability, and the history that is mentioned is sanitized to eliminate the passions, egos, and human frailties of the great “natural philosophers.” After all, since physical science (we believe) is a cumulative discipline, why shouldn’t we downplay or even censor the missteps and misunderstandings of our predecessors? It is daunting enough to attempt to master and then extend the most complex concepts produced by the human mind, such as the bizarre description of the atomic world provided by quantum theory. Wouldn’t telling the real human history of discovery just confuse people?
Thus, while I had studied history and philosophy of science avidly as an undergraduate, I had not read a single word written by Einstein during my actual career as a research physicist. I was of course aware that Einstein had contributed to the subject of quantum physics. Even freshman physics students learn that Einstein explained the photoelectric effect and said something fundamental about the quantized nature of light. And both atomic and solid-state physics (my specialty) have specific equations of quantum theory named for Einstein. So clearly the guy did something important in the subject. But the most familiar fact about Einstein and quantum mechanics is that he just didn’t like it. He refused to use the theory in its final form. And troubled by the fundamental indeterminism of quantum mechanics, he famously dismissed its worldview with the phrase “God does not play dice.”
Despite its esoteric
-sounding name, quantum mechanics represents arguably the greatest achievement of human understanding of nature. By the end of the nineteenth century progress in physical science was stymied by the most basic problem: what are the fundamental constituents of matter, and how do they work? The existence of atoms was fairly well established, but they were clearly much too small to be observed in any direct manner. Hints were emerging from indirect probes that the microscopic world did not obey the settled laws of macroscopic Newtonian physics; but would scientists ever be able to understand and predict the properties of objects and forces so far from our everyday experience? For decades the answer was in doubt, until a theory emerged, a theory that has now withstood almost a century of tests and extensions. That theory has wrung human knowledge from the deep interior of the atomic nucleus and from the vacuum of intergalactic space. It is the theory that most physicists use every day in their work. This is the theory that Einstein rejected. Thus most physicists think of Einstein as playing a significant but still secondary role in this intellectual triumph.
I might have continued with this conventional view of Einstein and quantum physics for my entire career, if not for a coincidental intersection of my own research with that of the great man. I am interested in quantum systems, which if they were not microscopic but were scaled up in size to everyday proportions, would behave “chaotically.” In physics this is a technical term; it means that very small differences in the initial state of a system lead to large differences in the final state, similar to the way a pencil, momentarily balanced on its point, will fall to the left or right when nudged by the smallest puff of air. I was searching (with one of my PhD students) for a good explanation of the difficulty that arises when mixing this sort of unstable situation with quantum theory. I recalled hearing that Einstein had written something related to this in 1917 and, almost as a lark, I suggested that we see if this work were relevant to our task.
Well the joke was on us. When we finally got our hands on the paper, we quickly realized that Einstein had put his finger on the essence of the problem and had delineated when it has a solution, before the invention of the modern quantum theory. Moreover, Einstein wrote with great lucidity about the subject, so that it seemed as if he were speaking directly to us, a century later. There was nothing dated or quaint about the analysis. For the first time in a long while, I found myself thinking, “Wow, this man really was a genius.”
This experience piqued my interest in the actual history of Einstein and quantum theory, and as I delved into the subject I came to a stunning realization. It was Einstein who had introduced almost all the revolutionary ideas underlying quantum theory, and who saw first what these ideas meant. His ultimate rejection of quantum theory was akin to Dr. Frankenstein’s shunning of the monster he had originally created for the betterment of mankind. Had Einstein not done so, in all likelihood he would be seen as the father of the modern theory.
This is not a view that one could extract from any of the popular biographies of Einstein, where the focus is always on his development of relativity theory. Nonetheless, I discovered to my surprise that, for much of Einstein’s scientifically productive career, he was obsessed with solving the problems of quantum theory, not relativity theory. He commented to his friend the Nobel laureate Otto Stern, “I have thought a hundred times as much about the quantum problems as I have about Relativity Theory.”
It is crucial to understand that while relativity theory is an important part of modern physics, for most of us quantum mechanics is the theory of everything. Quantum mechanics explains the periodic table of the elements, the nuclear reactions that power the sun, and the greenhouse effect that leads to global warming. The quantum theory of radiation and electrical conduction underlies all of modern information technology. Moreover, quantum mechanics has already subsumed part of relativity theory (the “special theory”). The goal of modern string theorists and their well-publicized “theory of everything” is to have quantum mechanics gobble up all of general relativity as well. Since quantum mechanics is the big kahuna, it behooves us to appreciate the role of Einstein in the “other” revolution of twentieth-century physics, the quantum one.
To understand Einstein’s seminal role in this revolution, it is necessary to understand what had come before him. In this subject he had exactly one predecessor, the eminent German physicist Max Planck, of whom we will learn much below. Planck was the first major figure to recognize Einstein’s seminal 1905 work on relativity theory, and he became Einstein’s greatest champion in the world of science and one of his closest personal friends. But Einstein’s work in the quantum theory—that was another matter. Sometimes it is easier to recognize the genius that doesn’t paint in your own style. Planck had not worked on the problems that were solved by relativity theory, but he had worked on the quantum theory. In fact Planck, not Einstein, is universally regarded as its originator, based on his work on heat radiation in December 1900. Planck, a truly admirable man of science, indeed achieved something of incalculable significance as the new century began. But what it was, and what it meant, are not as clear as the textbooks maintain.
At the moment that Planck was making his historic advance the young Einstein, just graduated from the Zurich Polytechnic, was coming to a bitter realization: he was not wanted in the world of academic physics. Already engaged to his classmate Mileva Maric, as his travails, both practical and scientific, multiplied, he maintained a bold self-confidence. This was exemplified by a humorous nickname he chose for himself in his letters to Mileva: the “Valiant Swabian,” after the swashbuckling crusader-knight invented by the Swabian romantic poet Ludwig Uhland. Einstein had just submitted his first research paper to the Annalen der Physik; it was on liquid interfaces and proposed a novel (but simplistic) picture of the forces between atoms. This would signify the beginning of his lifelong quest to understand the laws of physics on the atomic scale.
CHAPTER 1
“AN ACT OF DESPERATION”
On the evening of Friday, October 19, 1900, Max Planck, the world’s leading expert on the science of heat, was experiencing a physicist’s worst nightmare. Little more than a year earlier, he had staked his considerable reputation on a theory that purported to solve the outstanding problem of his field: the relationship between heat and light. Tonight at this meeting of the German Physical Society, the hall filled by the men who had been Planck’s closest colleagues for over a decade, another scientist would announce publicly what Planck already knew—that the theory he had worked on for the past five years was almost certainly in error. This theory, which built on the work of his close friend Wilhelm Wien, was expressed in terms of a mathematical formula known as the Planck-Wien radiation law.
One of the scientists who had discovered the failure of the Planck-Wien law, Ferdinand Kurlbaum, was scheduled to speak first that night. A friend and close colleague of Planck’s, Kurlbaum had no plan to attack Planck’s theory on mathematical or logical grounds. Planck after all was the world’s greatest expert on this topic and universally respected for his deep understanding of thermodynamics (the physics of heat flow and energy). Kurlbaum would simply present the hard data he and his collaborator, Henrich Rubens, had painstakingly collected to test the predictions of the Planck-Wien theory. The data would show (to quote Richard Feynman) that “Nature had a different way of doing things.”
If Planck had been an experimenter himself, like Rubens and Kurlbaum, his reputation would have been less in jeopardy on that night. But Planck was a new breed of physicist, a theoretical physicist, with no laboratory or instruments. The theorist’s job was (and is) simply to predict and understand physical systems, from stars and planets to atoms and molecules, using mathematical deductions from known and accepted physical laws. Very rarely (experience tells us about twice a century) theorists may also successfully propose some amendments to the laws of physics; but mostly they are master craftsmen, whose reputation depends on how well they use their intellectual tools. There had of course b
een great theory-building physicists before Planck: Isaac Newton, James Clerk Maxwell, and Ludwig Boltzmann, to name three of relevance to our story, but only at the end of the nineteenth century had the division of labor been formally recognized by academe, and the theoretical physicist, who divined nature by thought alone, became a recognized species. When Planck had taken up his post at the University of Berlin in 1889, it was the only chair of theoretical physics in Germany, and one of only a handful in the world.
Because a theorist has no measurements to report and no inventions to demonstrate, he is judged solely on whether his theoretical predictions describe important phenomena and are confirmed by experiment. An experimenter can go into the lab and make a great discovery without necessarily knowing what he is looking for, sometimes without even recognizing the discovery when it is first found. Many a Nobel Prize has been awarded for just such serendipity. In short, a good experimentalist can also be lucky. A good theorist, on the other hand, has to be right. Experimentalists are playing poker; theorists are playing chess. Chess games are not lost by “bad luck.” The problem for Planck that night was that he had made a serious error in the contest with Nature, which was being exposed by Kurlbaum just now as Planck waited for his turn to speak. He needed to come up with an endgame that would preserve, at least temporarily, his reputation as a theorist.
So what was the problem on which the estimable Professor Planck had stumbled? It was the deceptively simple question of how much a heated object glows. The great Scottish physicist James Clerk Maxwell had demonstrated in 1865 that visible light and radiant heat are different expressions of the same physical phenomenon—the propagation of electrical and magnetic energy through empty space at the speed of light. The difference between visible radiation (i.e., “light”) and thermal radiation is only their wavelength. For light, that length is about one-half of a millionth of a meter; for thermal radiation it is twenty times larger, or about ten millionths of a meter (which is still about eight times smaller than the width of a human hair). Such radiation arises when energy, originally stored in atoms (matter), is emitted; it can then be transmitted as an electromagnetic wave over large distances and be reabsorbed by matter.1 In any enclosed space this happens over and over until the electromagnetic (EM) radiation and the matter share the energy in a balanced manner (they are “in equilibrium”).
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