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Annals of Science

Statistical and causal concepts in Einstein's early thought

Patrick H. Byrne

Published Mar 1, 1980• 3 citations
Publisher

Abstract

Summary Albert Einstein's attitude towards quantum mechanics—and statistical physics in general—was a puzzle to many of his contemporaries, and has remained a puzzle to the present. Though he made many significant contributions to statistical physics, he continually refused to regard that branch of science as fundamental. The present essay demonstrates that his attitude towards statistical physics was formed during his earliest investigations—between 1901 and 1903. In particular, it is shown that in Einstein's view, statistical laws are based upon non-statistical (causal) assumptions. This view influenced much of his later thinking. A few illustrations are offered, concluding with a discussion of his opposition to quantum mechanics.

DOI
10.1080/00033798000200201

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Summary Albert Einstein's attitude towards quantum mechanics—and statistical physics in general—was a puzzle to many of his contemporaries, and has remained a puzzle to the present. Though he made many significant contributions to statistical physics, he continually refused to regard that branch of science as fundamental. The present essay demonstrates that his attitude towards statistical physics was formed during his earliest investigations—between 1901 and 1903. In particular, it is shown that in Einstein's view, statistical laws are based upon non-statistical (causal) assumptions. This view influenced much of his later thinking. A few illustrations are offered, concluding with a discussion of his opposition to quantum mechanics.
This is an account of Einstein's work and thoughts on the quantum theory. The following topics will be discussed: The light-quantum hypothesis and its gradual evolution into the photon concept. Early history of the photoelectric effect. The theoretical and experimental reasons why the resistance to the photon was stronger and more protracted than for any other particle proposed to date. Einstein's position regarding the Bohr-Kramers-Slater suggestion, the last bastion of resistance to the photon. Einstein's analysis of fluctuations around thermal equilibrium and his proposal of a duality between particles and waves, in 1909 for electromagnetic radiation (the first time this duality was ever stated) and in January 1925 for matter (prior to quantum mechanics and for reasons independent of those given earlier by de Broglie). His demonstration that long-known specific heat anomalies are quantum effects. His role in the evolution of the third law of thermodynamics. His new derivation of Planck's law in 1917 which also marks the beginning of his concern with the failure of classical causality. His role as one of the founders of quantum statistics and his discovery of the first example of a phase transition derived by using purely statistical methods. His position as a critic of quantum mechanics. Initial doubts on the consistency of quantum mechanics (1926-1930). His view maintained from 1930 until the end of his life: quantum mechanics is logically consistent and quite successful but it is incomplete. His attitude toward success. His criterion of objective reality. Differences in the roles relativity and quantum theory played in Einstein's life. His vision regarding quantum theory in the context of a unified field theory. His last autobiographical sketch, written a few months before his death, concluding with a statement about the quantum theory, a subject to which (by his own account) he had given more thought than even to general relativity.
Albert Einstein made fundamental contributions to the development of quantum mechanics. However, he was never satisfied with the quantum worldview. In fact, during most of his life he attempted to find inconsistencies and paradoxes within quantum mechanics. His famous quote "God does not play dice" shows how disturbing was to Einstein one of the most important aspects of quantum mechanics: non-determinism. In this paper we will present the basic concepts of quantum mechanics, we will describe Einstein's attempts to destroy it and we will discuss why we can nowadays state that, in this regard, Albert Einstein was not right.
Time in quantum theory By 1920, the spectacular confirmation of general relativity, during the solar eclipse of 1919, had made Einstein a household name. Not only did relativity theory (both special and general) upset the long-received Newtonian ideas of space and time, it also stimulated a widespread ‘operationalist’ attitude to physical theories. Physical quantities came to be seen as inextricably interwoven with our means of measuring them, in the sense that any limits on our means of measurement were taken to imply limits on the definability, or ‘meaningfulness’, of the physical quantities themselves. In particular, Einstein's relativity paper of 1905 – with its operational analysis of simultaneity – came to be widely regarded as a model for the new operationalist approach to physics. Not surprisingly, then, as the puzzles continued to emerge from atomic experiments, in the 1920s a number of workers suggested that the concepts of space and time would require still further revision in the atomic domain. Thus, Campbell (1921, 1926) suggested that the puzzles in atomic physics could be removed if the concept of time was given a purely statistical significance: ‘time, like temperature, is a purely statistical conception, having no meaning except as applied to statistical aggregates’ (quoted in Beller 1999, p. 97).
This chapter first discusses statistical techniques and concepts — including probability, probability distribution, average and expectation value, and uncertainty — that are relevant to quantum mechanics. The physical interpretation of probability in quantum mechanics is then discussed. It is argued that by adopting the statistical interpretation, one can think clearly about quantum mechanics without committing to any of the various physical interpretations, and without tackling the conceptual hurdles that they present. The history and substance of interpretational issues in quantum mechanics is then briefly discussed, the point being to introduce these profound, unresolved questions without taking sides in ongoing scientific debates. The chapter closes with a personal reflection on Albert Einstein, the most revered and fascinating figure in physics, and the one most famously at odds with the conventional interpretation of quantum mechanics.
Einstein did not contribute significantly to the quantum mechanics we are familiar with, but he did contribute to its theoretical foundations. In a seminal theory on black body radiation, he used two physically distinct sets of coordinates, a classical set to describe the continuity of heat energy with Maxwell Boltzmann statistics and an atomic set to describe discrete energy states required by the Planck radiation law. His methods are extended here to reveal that matrix mechanics is an incomplete description of atomic structure. In addition to the discrete energy states of the diagonal matrix elements, classically derived components of kinetic energy are necessary. We conclude that the diagonalized matrix elements and eigenvalues of the Schrödinger equation both describe characteristics of the steady states, but the physical variables they describe are different, because they are measured with respect to different coordinate systems. Einstein’s assumptions lead to a resolution of the measurement problem by introducing statistical laws at the microscopic level.