Einstein's Dice and Schrödinger's Cat

How Two Great Minds Battled Quantum Randomness to Create a Unified Theory of Physics


By Paul Halpern

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“A fascinating and thought-provoking story, one that sheds light on the origins of . . . the current challenging situation in physics.” — Wall Street Journal

When the fuzzy indeterminacy of quantum mechanics overthrew the orderly world of Isaac Newton, Albert Einstein and Erwin Schröger were at the forefront of the revolution. Neither man was ever satisfied with the standard interpretation of quantum mechanics, however, and both rebelled against what they considered the most preposterous aspect of quantum mechanics: its randomness. Einstein famously quipped that God does not play dice with the universe, and Schröger constructed his famous fable of a cat that was neither alive nor dead not to explain quantum mechanics but to highlight the apparent absurdity of a theory gone wrong. But these two giants did more than just criticize: they fought back, seeking a Theory of Everything that would make the universe seem sensible again.

In Einstein’s Dice and Schröger’s Cat, physicist Paul Halpern tells the little-known story of how Einstein and Schröger searched, first as collaborators and then as competitors, for a theory that transcended quantum weirdness. This story of their quest-which ultimately failed-provides readers with new insights into the history of physics and the lives and work of two scientists whose obsessions drove its progress.

Today, much of modern physics remains focused on the search for a Theory of Everything. As Halpern explains, the recent discovery of the Higgs Boson makes the Standard Model-the closest thing we have to a unified theory- nearly complete. And while Einstein and Schröger failed in their attempt to explain everything in the cosmos through pure geometry, the development of string theory has, in its own quantum way, brought this idea back into vogue. As in so many things, even when they were wrong, Einstein and Schröger couldn’t help but get a great deal right.


Einstein's Dice and Schrödinger's Cat

Einstein's Dice and Schrödinger's Cat

How Two Great Minds Battled Quantum Randomness to Create a Unified Theory of Physics

Paul Halpern, PhD

A Member of the Perseus Books Group New York

Copyright © 2015 by Paul Halpern

Published by Basic Books,A Member of the Perseus Books Group

All rights reserved. Printed in the United States of America. No part of this book may be reproduced in any manner whatsoever without written permission except in the case of brief quotations embodied in critical articles and reviews. For information, address Basic Books, 250 West 57th Street, New York, NY 10107.

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Designed by Pauline Brown

Library of Congress Cataloging-in-Publication Data

Halpern, Paul, 1961–

Einstein's dice and Schrödinger's cat : how two great minds battled quantum randomness to create a unified theory of physics / Paul Halpern, PhD.

pages cm

Includes bibliographical references and index.

ISBN 978-0-465-04065-0 (e-book) 1. Quantum chaos. 2. Quantum theory—Philosophy. 3. Physics—Philosophy. 4. Unified field theories. 5. Einstein, Albert, 1879–1955. 6. Schrödinger, Erwin, 1887–1961. I. Title.

QC174.17.C45H35 2015



10 9 8 7 6 5 4 3 2 1

Dedicated to the memory of Max Dresden, my PhD advisor, whose passion for the history of twentieth-century physics was truly inspiring

Well who am I? (This question is meant in general, the "I" not referring just to the present writer.) The Image of God, gifted with power of thought to try and understand His world. However naive my attempt at this may be, I do have to value it higher than scrutinizing Nature for the purpose of inventing a device to . . . say, avoid splashing my spectacles in eating a grapefruit, or other very handy conveniences of life.

—Erwin Schrödinger, "The New Field Theory"



introduction Allies and Adversaries

chapter one The Clockwork Universe

chapter two The Crucible of Gravity

chapter three Matter Waves and Quantum Jumps

chapter four The Quest for Unification

chapter five Spooky Connections and Zombie Cats

chapter six Luck of the Irish

chapter seven Physics by Public Relations

chapter eight The Last Waltz: Einstein's and Schrödinger's Final Years

conclusion Beyond Einstein and Schrödinger: The Ongoing Search for Unity

Further Reading




I would like to acknowledge the outstanding support of my family, friends, and colleagues in helping me see this project to completion. Thanks to the faculty and staff of the University of the Sciences, including Helen Giles-Gee, Heidi Anderson, Suzanne Murphy, Elia Eschenazi, Kevin Murphy, Brian Kirschner, and Jim Cummings, and to my colleagues in the Department of Math, Physics, and Statistics and the Department of Humanities, for supporting my research and writing. I am grateful for the camaraderie of the history of science community, including the APS Forum on the History of Physics, the Philadelphia Area Center for History of Science, and the AIP Center for History of Physics. The warm support of the Philadelphia Science Writers Association, including Greg Lester, Michal Mayer, Faye Flam, Dave Goldberg, Mark Wolverton, Brian Siano, and Neil Gussman, is most appreciated. Thanks to historians of science David C. Cassidy, Diana Buchwald, Tilman Sauer, Daniel Siegel, Catherine Westfall, Robert Crease, and Peter Pesic for useful suggestions and to Don Howard for offering helpful references. I greatly appreciate the help of Schrödinger's family, including Leonhard, Arnulf, and Ruth Braunizer, in addressing questions about his life and work. I'm grateful to musician Roland Orzabal and philosopher Hilary Putnam for kindly answering questions about their work. Thanks to science writer Michael Gross for his friendly advice on German culture and language. I appreciate the encouragement of David Zitarelli, Robert Jantzen, Linda Dalrymple Henderson, Roger Stuewer, Lisa Tenzin-Dolma, Jen Govey, Cheryl Stringall, Tony Lowe, Michael LaBossiere, Peter D. Smith, Antony Ryan, David Bood, Michael Erlich, Fred Schuepfer, Pam Quick, Carolyn Brodbeck, Marlon Fuentes, Simone Zelitch, Doug Buchholz, Linda Holtzman, Mark Singer, Jeff Shuben, Jude Kuchinsky, Kris Olson, Meg and Woody Carsky-Wilson, Carie Nguyen, Lindsey Poole, Greg Smith, Joseph Maguire, Doug DiCarlo, Patrick Pham, and Vance Lehmkuhl. I offer my sincere appreciation to Ronan and Joe Mehigan for their photographs of Schrödinger locations in Dublin. Thanks to the Princeton University Library Manuscripts Division for permission to peruse the Albert Einstein Duplicate Archives and other research materials and to the American Philosophical Society Library for access to the Archive for the History of Quantum Physics. Many thanks to Barbara Wolff and the Albert Einstein Archives in Jerusalem for reviewing my quotes from Einstein's correspondence to Schrödinger. Thanks to the Royal Irish Academy for information about their proceedings. I thank the John Simon Guggenheim Foundation for a 2002 fellowship, during which I first encountered the Einstein-Schrödinger correspondence.

Thanks to my editor, T. J. Kelleher, for his outstanding guidance and useful suggestions, and to the staff of Basic Books, including Collin Tracy, Quynh Do, Betsy DeJesu, and Sue Warga, for their help. I thank my marvelous agent, Giles Anderson, for his enthusiastic support.

Special thanks to my wife, Felicia; my sons, Eli and Aden; my parents, Bernice and Stanley Halpern; my in-laws, Arlene and Joseph Finston; Richard, Anita, Jake, Emily, Alan, Beth, Tessa, and Ken Halpern; Aaron Stanbro; Lane and Jill Hurewitz; Shara Evans; and other family members for all their love, patience, advice, and support.


Allies and Adversaries

This is the tale of two brilliant physicists, the 1947 media war that tore apart their decades-long friendship, and the fragile nature of scientific collaboration and discovery.

When they were pitted against each other, each scientist was a Nobel laureate, well into middle age, and certainly past the peak of his major work. Yet the international press largely had a different story to tell. It was a familiar narrative of a seasoned fighter still going strong versus an upstart contender hungry to seize the trophy. While Albert Einstein was extraordinarily famous, his every pronouncement covered by the media, relatively few readers were conversant with the work of Austrian physicist Erwin Schrödinger.

Those following Einstein's career knew that he been working for decades on a unified field theory. He hoped to extend the work of nineteenth-century British physicist James Clerk Maxwell in uniting the forces of nature through a simple set of equations. Maxwell had provided a unified explanation for electricity and magnetism, called electromagnetic fields, and identified them as light waves. Einstein's own general theory of relativity described gravity as a warping of the geometry of space and time. Confirmation of the theory had won him fame. However, he didn't want to stop there. His dream was to incorporate Maxwell's results into an extended form of general relativity and thereby unite electromagnetism with gravity.

Every few years, Einstein had announced a unified theory to great fanfare, only to have it quietly fail and be replaced by another. Starting in the late 1920s, one of his primary goals was a deterministic alternative to probabilistic quantum theory, as developed by Niels Bohr, Werner Heisenberg, Max Born, and others. Although he realized that quantum theory was experimentally successful, he judged it incomplete. In his heart he felt that "God did not play dice," as he put it, couching the issue in terms of what an ideal mechanistic creation would be like. By "God" he meant the deity described by seventeenth-century Dutch philosopher Baruch Spinoza: an emblem of the best possible natural order. Spinoza had argued that God, synonymous with nature, was immutable and eternal, leaving no room for chance. Agreeing with Spinoza, Einstein sought the invariant rules governing nature's mechanisms. He was absolutely determined to prove that the world was absolutely determined.

Exiled in Ireland in the 1940s after the Nazi annexation of Austria, Schrödinger shared Einstein's disdain for the orthodox interpretation of quantum mechanics and saw him as a natural collaborator. Einstein similarly found in Schrödinger a kindred spirit. After sharing ideas for unification of the forces, Schrödinger suddenly announced success, generating a storm of attention and opening a rift between the men.

You may have heard of Schrödinger's cat—the feline thought experiment for which the general public knows him best. But back when this feud took place, few people outside of the physics community had heard of the cat conundrum or of him. As depicted in the press, he was just an ambitious scientist residing in Dublin who might have landed a knockout punch on the great one.

The leading announcer was the Irish Press, from which the international community learned about Schrödinger's challenge. Schrödinger had sent them an extensive press release describing his new "theory of everything," immodestly placing his own work in the context of the achievements of the Greek sage Democritus (the coiner of the term "atom"), the Roman poet Lucretius, the French philosopher Descartes, Spinoza, and Einstein himself. "It is not a very becoming thing for a scientist to advertise his own discoveries," Schrödinger told them. "But since the Press wishes it, I submit to them."1

The New York Times cast the announcement as a battle between a maverick's mysterious methods and the establishment's lack of progress. "How Schrödinger has proceeded we are not told," it reported.2

For a fleeting moment it seemed that a Viennese physicist whose name was then little known to the general public had beaten the great Einstein to a theory that explained everything in the universe. Perhaps it was time, puzzled readers may have thought, to get to know Schrödinger better.

A Gruesome Conundrum

Today, what comes to mind for most people who have heard of Schrödinger are a cat, a box, and a paradox. His famous thought experiment, published as part of a 1935 paper, "The Present Situation in Quantum Mechanics," is one of the most gruesome devised in the history of science. Hearing about it for the first time is bound to trigger gasps of horror, followed by relief that it is just a hypothetical experiment that presumably has never been attempted on an actual feline subject.

Schrödinger proposed the thought experiment in 1935 as part of a paper that investigated the ramifications of entanglement in quantum physics. Entanglement (the term was coined by Schrödinger) is when the condition of two or more particles is represented by a single quantum state, such that if something happens to one particle the others are instantly affected.

Inspired in part by dialogue with Einstein, the conundrum of Schrödinger's cat presses the implications of quantum physics to their very limits by asking us to imagine the fate of a cat becoming entangled with the state of a particle. The cat is placed in a box that contains a radioactive substance, a Geiger counter, and a sealed vial of poison. The box is closed, and a timer is set to precisely the interval at which the substance would have a 50–50 chance of decaying by releasing a particle. The researcher has rigged the apparatus so that if the Geiger counter registers the click of a single decay particle, the vial would be smashed, the poison released, and the cat dispatched. However, if no decay occurs, the cat would be spared.

According to quantum measurement theory, as Schrödinger pointed out, the state of the cat (dead or alive) would be entangled with the state of the Geiger counter's reading (decay or no decay) until the box is opened. Therefore, the cat would be in a zombielike quantum superposition of deceased and living until the timer went off, the researcher opened the box, and the quantum state of the cat and counter "collapsed" (distilled itself) into one of the two possibilities.

From the late 1930s until the early 1960s the thought experiment was little mentioned, except sometimes as a classroom anecdote. For instance, Columbia University professor and Nobel laureate T. D. Lee would tell the tale to his students to illustrate the strange nature of quantum collapse.3 In 1963, Princeton physicist Eugene Wigner mentioned the thought experiment in a piece he wrote about quantum measurement and extended it into what is now referred to as the "Wigner's friend" paradox.

Renowned Harvard philosopher Hilary Putnam—who learned about the conundrum from physicist colleagues—was one of the first scholars outside of the world of physics to analyze and discuss Schrödinger's thought experiment.4 He described its implications in his classic 1965 paper "A Philosopher Looks at Quantum Mechanics," published as a book chapter. When the paper was mentioned the same year in a Scientific American book review, the term "Schrödinger's cat" entered the realm of popular science. Over the decades that followed, it crept into culture as a symbol of ambiguity and has been mentioned in stories, essays, and verse.

Despite the public's current familiarity with the cat paradox, the physicist who developed it still isn't well known otherwise. While Einstein has been an icon since the 1920s, the very emblem of a brilliant scientist, Schrödinger's life story is scarcely familiar. That is ironic because the adjective "Schrödinger's"—in the sense of a muddled existence—could well have applied to him.

A Man of Many Contradictions

The ambiguity of Schrödinger's cat perfectly matched the contradictory life of its creator. The bookish, bespectacled professor maintained a quantum superposition of contrasting views. His yin-yang existence began in his youth when he learned German and English from different family members and was raised bilingual. With ties to many countries but a supreme love of his native Austria, he never felt comfortable with either nationalism or internationalism and preferred avoiding politics altogether.

An enthusiast of fresh air and exercise, he would drown others in the smoke from his omnipresent pipe. At formal conferences, he'd walk in dressed like a backpacker. He'd call himself an atheist and talk about divine motivations. At one point in his life he lived with both his wife and another woman who was the mother of his first child. His doctoral work was a mixture of experimental and theoretical physics. During the early part of his career he briefly considered switching to philosophy before veering back to science. Then came whirlwind shifts between numerous institutions in Austria, Germany, and Switzerland.

As physicist Walter Thirring, who once worked with him, described, "It was like he was always being chased: from one problem to another by his genius, from one country to another by the political powers in the twentieth century. He was a man full of contradictions."5

At one point in his career, he argued vehemently that causality should be rejected in favor of pure chance. Several years later, after developing the deterministic Schrödinger equation, he had second thoughts. Perhaps there are causal laws after all, he argued. Then physicist Max Born reinterpreted his equation probabilistically. After fighting that reinterpretation, he started to sway back toward the chance conception. Later in life, his philosophical roulette wheel landed once again in the direction of causality.

In 1933, Schrödinger heroically gave up an esteemed position in Berlin because of the Nazis. He was the most prominent non-Jewish physicist to leave of his own accord. After working in Oxford, he decided to move back to Austria and became a professor at the University of Graz. But then, strangely enough, after Nazi Germany annexed Austria, he tried to cut a deal with the government to keep his job. In a published confession, he apologized for his earlier opposition and proclaimed his loyalty to the conquering power. Despite his pandering, he had to leave Austria anyway, moving on to a prominent position at the newly founded Dublin Institute for Advanced Studies. Once on neutral ground, he recanted his self-renunciation.

"He demonstrated impressive civil courage after Hitler came to power in Germany and . . . left the most prominent German professorship in physics," noted Thirring. "As the Nazis caught up with him, he was forced into a pathetic show of solidarity with the terror regime."6

Quantum Comrades

Einstein, who had been a colleague and dear friend in Berlin, stuck by Schrödinger all along and was delighted to correspond with him about their mutual interests in physics and philosophy. Together they battled a common villain: sheer randomness, the opposite of natural order.

Schooled in the writings of Spinoza, Schopenhauer—for whom the unifying principle was the force of will, connecting all things in nature—and other philosophers, Einstein and Schrödinger shared a dislike for including ambiguities and subjectivity in any fundamental description of the universe. While each played a seminal role in the development of quantum mechanics, both were convinced that the theory was incomplete. Though recognizing the theory's experimental successes, they believed that further theoretical work would reveal a timeless, objective reality.

Their alliance was cemented by Born's reinterpretation of Schrödinger's wave equation. As originally construed, the Schrödinger equation was designed to model the continuous behavior of tangible matter waves, representing electrons in and out of atoms. Much as Maxwell constructed deterministic equations describing light as electro­magnetic waves traveling through space, Schrödinger wanted to create an equation that would detail the steady flow of matter waves. He thereby hoped to offer a comprehensive accounting of all of the physical properties of electrons.

Born shattered the exactitude of Schrödinger's description, replacing matter waves with probability waves. Instead of physical properties being assessed directly, they needed to be calculated through mathematical manipulations of the probability waves' values. In doing so, he brought the Schrödinger equation in line with Heisenberg's ideas about indeterminacy. In Heisenberg's view, certain pairs of physical quantities, such as position and momentum (mass times velocity) could not be measured simultaneously with high precision. He encoded such quantum fuzziness in his famous uncertainty principle: the more precisely a researcher measures a particle's position, the less precisely he or she can know its momentum—and the converse.

Aspiring to model the actual substance of electrons and other particles, not just their likelihoods, Schrödinger criticized the intangible elements of the Heisenberg-Born approach. He similarly eschewed Bohr's quantum philosophy, called "complementarity," in which either wavelike or particlelike properties reared their heads, depending on the experimenter's choice of measuring apparatus. Nature should be visualizable, he rebutted, not an inscrutable black box with hidden workings.

As Born's, Heisenberg's, and Bohr's ideas became widely accepted among the physics community, melded into what became known as the "Copenhagen interpretation" or orthodox quantum view, Einstein and Schrödinger became natural allies. In their later years, each hoped to find a unified field theory that would fill in the gaps of quantum physics and unite the forces of nature. By extending general relativity to include all of the natural forces, such a theory would replace matter with pure geometry—fulfilling the dream of the Pythagoreans, who believed that "all is number."

Portrait of Albert Einstein in his later years. Courtesy of the University of New Hampshire, Lotte Jacobi Collection, and the AIP Emilio Segre Visual Archives, donated by Gerald Holton.

Schrödinger had good reason to be much indebted to Einstein. A talk by Einstein in 1913 help spark his interest in pursuing fundamental questions in physics. An article Einstein published in 1925 referenced French physicist Louis de Broglie's concept of matter waves, inspiring Schrödinger to develop his equation governing the behavior of such waves. That equation earned Schrödinger the Nobel Prize, for which Einstein, among others, had nominated him. Einstein endorsed his appointment as a professor at the University of Berlin and as a member of the illustrious Prussian Academy of Sciences. Einstein warmly invited Schrödinger to his summer home in Caputh and continued to offer guidance in their extensive correspondence. The EPR thought experiment, developed by Einstein and his assistants Boris Podolsky and Nathan Rosen to illustrate murky aspects of quantum entanglement, along with a suggestion by Einstein about a quantum paradox involving gunpowder, helped inspire Schrödinger's cat conundrum. Finally, the ideas developed by Schrödinger in his quest for unification were variations of proposals by Einstein. The two theorists frequently corresponded about ways to tweak general relativity to make it mathematically flexible enough to encompass other forces besides gravity.

Portrait of a Fiasco

Dublin's Institute for Advanced Studies, where Schrödinger was the leading physicist throughout the 1940s and early 1950s, was modeled directly on Princeton's Institute for Advanced Study, where Einstein had played the same role since the mid-1930s. Irish press reports often compared the two of them, treating Schrödinger as Einstein's Emerald Isle equivalent.

Erwin Schrödinger, in midlife, relaxing outdoors. Photo by Wolfgang Pfaundler, Innsbruck, Austria, courtesy AIP Emilio Segre Visual Archives

Schrödinger took every opportunity to mention his connection with Einstein, going so far as to reveal some of the contents of their private correspondence when it suited his purpose. For example, in 1943, after Einstein wrote personally to Schrödinger that a certain model for unification had been the "tomb of his hopes" in the 1920s, Schrödinger exploited that statement to make it look like he had succeeded where Einstein had failed. He read the letter publicly to the Royal Irish Academy, bragging that he had "exhumed" Einstein's hopes through his own calculations. The lecture was reported in the Irish Times, capped by the misleading headline "Einstein Tribute to Schroedinger."7

At first Einstein graciously chose to ignore Schrödinger's boasts. However, the press reaction to a speech Schrödinger gave in January 1947 claiming victory in the battle for a theory of everything proved too much. Schrödinger's bold statement to the press asserting that he had achieved the goal that had eluded Einstein for decades (by developing a theory that superseded general relativity) was flung in Einstein's face, in hopes of spurring a reaction.

And react he did. Einstein's snarky reply reflected his deep displeasure with Schrödinger's overreaching assertions. In his own press release, translated into English by his assistant Ernst Straus, he responded: "Professor Schroedinger's latest attempt . . . can . . . be judged only on the basis of its mathematical qualities, but not from the point of view of 'truth' and agreement with facts of experience. Even from this point of view, it can see no special advantages—rather the opposite."8

The bickering was reported in newspapers such as the Irish Press, which conveyed Einstein's admonition that it is "undesirable . . . to present such preliminary attempts to the public in any form. It is even worse when the impression is created that one is dealing with definite discoveries concerning physical reality."9

Humorist Brian O'Nolan, writing in the Irish Times


  • A New Scientist Best Read of 2015
  • "Entertaining and evocative."—New Scientist
  • "[Told] with humor and concision."—Nature
  • "This book can be put on the reading list of those who have enjoyed The Theory of Everything and want to know more."—Physics World
  • "A highly approachable book that will appeal to readers...who are interested in physics, the history of science, and the human and political aspects of scientists and their work."—Library Journal
  • "That's a lot to cover in a single book, and the author masters this challenge most thoroughly."—MAA Reviews
  • "As a fan of popular science books and someone who has used phrases such as 'God does not play dice' and 'Schrodinger's Cat' in my songs, I found Paul Halpern's book illuminating and entertaining."—Roland Orzabal, co-founding member of Tears for Fears

On Sale
Apr 14, 2015
Page Count
288 pages
Basic Books

Paul Halpern

About the Author

Paul Halpern is a professor of physics at Saint Joseph’s University and the author of eighteen popular science books, including Flashes of Creation, The Quantum Labyrinth, Einstein's Dice and Schrodinger's Cat, and Synchronicity. He is the recipient of a Guggenheim Fellowship and is a Fellow of the American Physical Society. He lives near Philadelphia, Pennsylvania.  

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