Einstein's Interpretation of Quantum Mechanics L. E. Ballentine Citation: American Journal of Physics 40, 1763(1972); doi: 10.1119/1.1987060 View online: https://doi.org/10.1119/1.1987060 View Table of Contents: http://aapt.scitation.org/toc/ajp/40/12 Published by the American Association of Physics Teachers Articles you may be interested in Einstein’s opposition to the quantum theory American Journal of Physics 58, 673 (1990); 10.1119/1.16399 Probability theory in quantum mechanics American Journal of Physics 54, 883 (1986); 10.1119/1.14783 The Shaky Game: Einstein, Realism and the Quantum Theory American Journal of Physics 56, 571 (1988); 10.1119/1.15540 QUANTUM MEASUREMENTS American Journal of Physics 85, 5 (2017); 10.1119/1.4967925 Einstein’s boxes American Journal of Physics 73, 164 (2005); 10.1119/1.1811620 Development of concepts in the history of quantum theory American Journal of Physics 43, 389 (1975); 10.1119/1.9833 an Association of Physics Teachers Explore the AAPT Career Center - access hundreds of physics education and other STEM teaching jobs at two-year and four-year colleges and universities. http://jobs.aapt.org December 1972 Einstein’s Interpretation of Quantum Mechanics L. E. BALLENTINE his own interpretation of the theory are less well Physics Department known. Indeed, Heisenberg’s essay “The Develop­ Simon Fraser University ment of the Interpretation of the Quantum Burnaby, B.C., Canada Theory,”2 in which he replied in detail to many (Received 23 May 1972; revised 27 June 1972) critics of the Copenhagen interpretation, takes no account of Einstein’s specific arguments. Einstein Einstein’s arguments concerning the interpretation of is said merely to belong to a group which “ex­ quantum mechanics are reviewed and contrasted with cer­ presses rather its general dissatisfaction with the tain misconceptions regarding his attitude toward the quantum theory, without making definite counter­ theory. He considered Born’s statistical interpretation to be proposals, either physical or philosophical in the only satisfactory one, and he was not a supporter of nature.” We shall see that this latter remark is hidden-variable theories such as that of Bohm. His criticism of the interpretation accepted, at least tacitly, by many certainly false. physicists was that the quantum state function does not Einstein’s attitude is best expressed in his provide a description of an individual system but rather of “Reply to Criticisms,”3 to which we shall return an ensemble of similar systems. This criticism was not later. There he sums up his argument as follows based merely upon his famous remark that God does not play dice, but upon some definite physical arguments (p. 671): which did not assume determinism. One arrives at very implausible theoretical conceptions, if one attempts to maintain the thesis that the statistical quantum theory is in principle capable of producing a complete description of an individual physical system. On the other hand, those difficulties of theoretical interpretation disappear, if one views the quantum-mechanical description as the description of ensembles of systems. We see here that he did indeed make a definite INTRODUCTION counterproposal to the Copenhagen interpretation, and that he regarded quantum mechanics as a What was Einstein’s attitude toward the satisfactory theory provided one gives up the claim statistical quantum theory? A widespread myth that a quantum state function constitutes a (difficult to trace but quite real) holds that he complete description of an individual system. misunderstood or rejected quantum mechanics on How, then, could such ignorance, misinforma­ rather vague philosophical grounds, that he dis­ tion, and pernicious myths about Einstein have regarded the statistical quantum theory merely come to be? Presumably it is because he did not because he did not believe in a God who plays dice. participate actively in the development of the new In a preface to a British Broadcasting Corporation quantum mechanics (after 1925) except as a series1 about Einstein, Christopher Sykes speaks critic, and because he did not publish a systematic of, “The main and most pernicious [myth] account of quantum theory from his own point of concerns the last phase of his life . (the view. But from his publications and his cor­ period spent in the United States of America) respondence with contemporary physicists, we when he was sometimes regarded as a man of can obtain a clear picture of his attitude toward enfeebled energy and even decaying mind. quantum mechanics. That Einstein criticized the Copenhagen inter­ We shall frequently refer to The Bom—Einstein pretation of quantum mechanics is well known, Letters (BEL)4 and to Letters on Wave Mechanics although the nature of his critical arguments and (LWM).6 A useful bibliography of Einstein’s A JP Volume Ifi / 1763 writing is contained in Ref. 3, and a more complete continuously, whereas Bom gave an interpreta­ list has been compiled by Boni, Russ, and Law­ tion in terms of discrete events and transition rence.8 probabilities. In fact, the interpretation of quantum theory was not at all settled at that time FIRST IMPRESSION and it was to be the main topic of discussion at the Modern quantum mechanics originated in 1925 Solvay Conference the following year. from two independent starting points, Heinsen- berg’s “matrix mechanics” and Schrodinger’s THE SOLVAY CONFERENCE “wave mechanics.” Although the two formalisms The Fifth Solvay Conference, held in Brussels were shown to be equivalent by Schrodinger in from 24 to 29 October 1927, provided an op­ 1926, they appeared to be very different in their portunity for the leading physicists of the day to original form. discuss the new quantum theory. Einstein’s only Now Einstein had earlier suggested that contribution to the official proceedings was one Louis deBroglie’s thesis, which postulated waves comment in the general discussion.11 He considered associated with material particles, should be taken the situation pictured in Fig. 1. Let S be a screen seriously. So it is not at all surprising that he with a small opening 0, and let P be a photographic responded favorably to Schrodinger’s paper. film in the form of a large hemisphere. Suppose Somewhat surprising is his remark,7 “I am con­ that electrons fall on S and that some of them vinced that you have made a decisive advance pass through 0. Because of the smallness of the with your formulation of the quantum condition, opening 0, the deBroglie-Schrodinger wave just as I am equally convinced that the Heisen­ appropriate to the quantum mechanical descrip­ berg-Born route is off the track.”7 tion will be diffracted at 0, and a spherical wave Here he was referring to the fact that, if two will propagate towards P. noninteracting systems are regarded as one system, Einstein then distinguished two possible points then their energies are clearly additive according of view. to Schrodinger’s theory. Einstein believed (in­ correctly) that the same was not true in the Idea I:1* “The deBroglie-Schrodinger waves matrix formalism. We may presume that he was do not correspond to a single electron, but to a not aware of Schrodinger’s demonstration8 of cloud of electrons extended in space. The theory equivalence between the two formalisms because does not give any information about the individual that paper was published on 4 May 1926. processes, but only about the ensemble of an Earlier, in a letter9 to Mrs. Born dated 7 March infinity of elementary processes.” 1926, Einstein had said, “The Heisenberg-Born Idea I I : “The theory has the pretention to be a concepts leave us all breathless, and have made a complete theory of individual processes.” Al­ deep impression on all theoretically oriented though the particle may initially be described by people.” But on 4 December 1926 he wrote to a small wave packet, the wave will be diffracted Born,10 “Quantum mechanics is certainly impos­ at 0, and will cover the whole of the film P. ing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the ‘old one.’ I, at any rate, am convinced that He is not playing at dice.” No doubt the publication of Schrodinger’s work between these two letters influenced Einstein to change his attitude, but since the equivalence of the two formalisms had been demonstrated this is hardly a sufficient reason. Here we must remember that a formalism requires a physical interpretation before it becomes til a theory. Schrodinger interpreted the | ^ |2 as a Fig. 1. Electrons incident on screen S at 0 are diffracted real extended charge distribution which evolves and recorded on the photographic film P. 1764 / December 1972 Einstein’s Interpretation of Quantum Mechanics According to Idea I, purely statistical, | ^ |2 that allowed by Heisenberg’s uncertainty relations. expresses the probability that a particle of the Although Einstein did not succeed in producing an cloud should exist at a particular place. example, it is known today that in certain situa­ According to Idea II, | ^ |2 expresses the tions it is possible to measure two noncommuting probability that at a certain instant one and the observables simultaneously with a precision same particle is found at the specified place. Hence unrestricted by Heisenberg’s relations, but con­ it should be possible for one particle to be detected trary to the belief held in 1927, the foundations at two or more places on the film. This objectionable of quantum mechanics are not shaken by this conclusion can be avoided only if we suppose there fact.15 For quantum mechanics, properly under­ is a very peculiar action-at-a-distance mechanism stood, does not prohibit or restrict simultaneous which prevents the extended wave from producing measurement of noncommuting observables, but an action at more than one place on the film.