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Quantum Physics Without Quantum Philosophy Detlef Dürr • Sheldon Goldstein • Nino Zanghì Quantum Physics Without Quantum Philosophy 2123 Authors Dr. Detlef Dürr Sheldon Goldstein Mathematisches Institut Department of Mathematics, Rutgers Universität München State University of New Jersey München, Germany Piscataway New Jersey, USA Nino Zanghì Istituto Nazionale Fisica Nucleare, Sezione di Genova (INFN) Università di Genova, Genova, Italy ISBN 978-3-642-30689-1 ISBN 978-3-642-30690-7 (eBook) DOI 10.1007/978-3-642-30690-71 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2012952411 © Springer-Verlag Berlin Heidelberg 2013 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Foreword In an ideal world, this book would not occasion any controversy. It provides the artic- ulation and analysis of a physical theory, presented with more clarity and precision than is usual in a work of physics. A reader might start out predisposed towards the theory, or skeptical, or neutral, but should in any case be impressed by the pellucid explication. The theory, in various incarnations, postulates exact physical hypotheses about what exists in the world, and precise, universal, mathematically defined laws that determine how those physical entities behave. Large, visible objects (such as planets, or rocks, or macroscopic laboratory equipment) are postulated to be collec- tions of small objects (particles). Since the theory specifies how the small objects behave, it automatically implies how the large, visible objects behave. It is then just a matter of analysis to determine what the theory predicts about the outcomes of experiments and other sorts of observable phenomena, and to compare these predic- tions with empirical data. So long as those predictions prove accurate (they do), the theory must be regarded as a candidate for the true theory of the physical universe. It has to face competition from other empirically accurate theories, and there might be disputes over which of the various contenders is the most promising. But a fair competition requires that all the contestants be judged on their merits, which de- mands that each be clearly and sympathetically presented. This book supplies such a presentation. Unfortunately, we do not live in an ideal world. On certain topics, cool rational judgment is hard to find, and quantum mechanics is one of those topics. For reasons rooted in the tortuous history of the theory1, clear and straightforward physical the- ories that can account for the phenomena treated by quantum mechanics are viewed with suspicion, if not downright hostility. These phenomena, it is said, admit of no clear or “classical” explanation, and anyone who thinks that they do has not appre- ciated the revolutionary character of the quantum world. In order to “understand” quantum phenomena, it is said, we must renounce classical logic, or amend classical probability theory, or admit a plethora of invisible universes, or recognize the cen- tral role that conscious observers play in production of the physical world. Lest the 1 A useful account of that history may be found in the book of James Cushing [1]. v vi Foreword reader think I am exaggerating, there are many clear examples of each of these. The Many Worlds interpretation posits that whenever quantum theory seems to present a probability, there is in fact a multiplicity: Schrödinger’s cat splits into a myriad of cats in each experiment, some of which are alive and some dead. Defenders of the “consistent histories” approach insist that classical logic must be abandoned: in some cases, the claim P can be true and the claim Q can be true but the conjunction “P and Q” be not only not true, but meaningless.2 David Mermin, in a famous article on Bell’s theorem [2], asserts that “[w]e now know that the moon is demonstrably not there when nobody looks.” These sorts of extraordinary claims should not be dismissed out of hand. Perhaps the world is so strange that “classical” modes of thought are incapable of compre- hending it. But extraordinary claims require extraordinary proof. And one would hope that such extreme positions would only be advocated if one were certain that nothing less radical could be correct. Surely, one imagines, these sorts of claims would not be made if some clear, precise theory that uses classical probability theory and classical logic, a theory that postulates only one, commonplace world in which observers are just complicated physical systems interacting by the same physical laws as govern everything else, actually existed. Surely, one imagines, respected physicists would not be driven to these extreme measures unless no alternative were available. But such an alternative is available, and has been for almost as long as the quantum theory itself has existed. It was first discovered by Louis de Broglie, and later rediscovered by David Bohm. It goes by the names “pilot wave theory” and “causal interpretation” and “ontological interpretation” and “Bohmian mechanics.” It is the main subject of this book. How could the most prominent physicists of the last century have failed to rec- ognize the significance of Bohmian mechanics? This is a fascinating question, but subsidiary to our main task. The important thing is to become convinced that they did fail to recognize its significance. Consider one example. In his classic Lectures on Physics, Richard Feynman introduces his students to quantum theory by means of an experiment: In this chapter, we shall tackle immediately the mysterious behavior in its most strange form. We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot explain the mystery in the sense of “explaining” how it works. We will tell you how it works. In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics. [3, p. 37-2] The experiment Feynman describes is the two-slit interference experiment for elec- trons.An electron beam, shot through a barrier with two holes in it, forms interference bands on a distant screen. The bands are formed by individual marks on the screen, one for each electron. They form even when the intensity of the beam is so low that only one electron at a time passes through the device. What does Feynman find so mysterious about this phenomenon? He considers the most straightforward, obvious attempt to understand it: “The first thing we would say 2 Cf. Omnes [4] or Griffiths [5]. Foreword vii is that since they come in lumps, each lump, which we may as well call an electron, has come either through hole 1 or hole 2. [3, p. 37–6 ]” This leads him to what he calls Proposition A: Each electron either goes through hole 1 or it goes through hole 2. [3, p. 37-6] The burden of Feynman’s argument is then to show that Proposition A is false: it is not the case that each electron goes through exactly one of the two holes. In order to prove this, he suggests that we “check this idea by experiment.” First, block up hole 2 and count the number of electrons that arrive at each part of the screen, yielding a distribution P1. Then, block up hole 1 and count the arrival rates to get another distribution P2. Finally, note that the distribution of electrons on the screen when both holes are open, P12, is not the sum of P1 and P2. This is an empirical result that cannot be denied. But what, exactly, does it imply? Feynman asserts that these phenomena simply cannot be explained if we accept Proposition A: It is all quite mysterious. And the more you look at it, the more mysterious it seems. Many ideas have been concocted to try to explain the curve for P12 in terms of individual electrons going around in complicated ways through the holes. None of them has succeeded. None of them can get the right curve for P12 in terms of P1 and P2. [3. p. 37–6] The reader should now turn to p. 13 of the introduction and study the diagram to be found on that page. The diagram depicts the trajectories of individual electrons in the two-slit experiment according to Bohmian mechanics. Note that each electron does go through exactly one slit, validating Proposition A. Note also that the trajectories do not look particularly “complicated.” And the visual simplicity of the diagram fails to convey the mathematical simplicity of the exact equations: the trajectories of the electrons are guided by the wavefunction in the simplest, most straightforward possi- ble way. Feynman’s claim about the impossibility of understanding this experiment consistent with electrons following continuous trajectories, and hence consistent with Proposition A, is flatly false. It had been known to be false since 1927, when de Broglie first presented the pilot wave theory, and its falsity was reinforced in 1952 when Bohm published the theory again.

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