Einstein, Bohr, and Bell

Soon after the appearance of the papers of Heisenberg, Born, and Jordan introducing matrix mechanics (the first formulation of quantum mechanics) in the summer and fall of 1925, Einstein wrote in a letter to his old friends Max and Heidi Born (in March of 1926) that “the Heisenberg-Born concepts leave us all breathless and have made a deep impression on all theoretically-oriented people. Instead of a dull resignation, there is now a singular tension in us sluggish people”. Just two months later, inspired by “brief but infinitely far-seeing remarks by Einstein” on statistical gas theory and the de-Broglie wave-particle duality, Schrodinger published in May 1926 his paper on wave mechanics, which seemed at first to give an alternative way of accounting for quantum phenomena. Einstein was appreciative, saying “Schrodinger has come out with a pair of wonderful papers on the quantum rules”. However, it soon became clear that matrix mechanics and wave mechanics were just two mathematically equivalent ways of formulating the same theory. Furthermore, in June 1926, Born published a paper arguing that the square of the wave function represents not the energy of a field in the classical sense, but rather a probability density.

Einstein wrote to Born in December 1926 that although the new quantum mechanics gives many good results, an “inner voice” told him it wasn’t the right path (“not the real Jacob”, i.e., not destined to be the progenitor of the future of physics). He later said “this theory holds no useful point of departure for future development”. Einstein held to this belief for the rest of his life, despite the tremendous successes that followed for the quantum theory. Already in 1909 Einstein had predicted that the next step in physics would be some kind of union between wave and particle concepts, so one might have expected him to rejoice at the discovery of quantum mechanics, but in February of 1927 he was still saying that the correct synthesis had “thus far exceeded the mental powers of physicists”. A month later, to cement the indeterminacy of quantum mechanics (which Einstein disliked), Heisenberg published the uncertainty principle. At the Solvay conference in October of that year Einstein said almost nothing during the formal meetings, but in private discussions he attempted to point out inconsistencies in quantum mechanics or ways of defeating the uncertainty principle. Each of his scenarios was resolved by Bohr, including a particularly difficult one involving a clock suspended in a gravitational field. Thereafter Einstein accepted that quantum mechanics did not contain any inconsistency, but he continued to believe that it was the wrong path, because he held that it could not be a complete theory.

The first published expression of Einstein’s main point of dissatisfaction with quantum mechanics was the famous paper of Einstein, Podolsky, and Rosen (EPR) in 1935. This paper was actually written primarily by Podolsky, based on discussions with Einstein and Rosen, and Einstein later commented that he thought the essential idea had gotten “smothered by the formalism”. Einstein later wrote his own explanations of the essential idea. To describe his mature view of the subject, we refer to the explanation he gave in his autobiographical notes written in 1949. He considers a system consisting of two spatially-separated partial systems S₁ and S₂. According to quantum mechanics, the total system is completely described by a wave function ψ₁₂. Now, if we make a complete measurement of S₁, the results of that measurement, together with ψ₁₂, determine an entirely definite wave function ψ₂ that completely describes S₂. However, the character of ψ₂ depends on what kind of measurement we performed on S₁. As Einstein said, all quantum theoreticians agree on this. Einstein’s objection is that he believes the real factual state of S₂ should be independent of what kind of measurement we (freely?) choose to perform on S₁, because these two system are spatially separate. Hence quantum mechanics implies a lack of separability between space-like separated events. He said

One can escape from this conclusion only by either assuming that the measurement of S₁ (telepathically) changes the real situation of S₂, or by denying independent real situations as such to things which are spatially separated from each other. Both alternative appear to me entirely unacceptable.

It is often said that Niels Bohr showed that Einstein’s reasoning was incorrect, but in fact Bohr agreed with Einstein’s reasoning, and merely argued that Einstein was wrong to regard the second alternative as unacceptable. Bohr wrote

Of course there is no question of a mechanical disturbance of the system under investigation during the last stage of the measuring procedure. But even at this stage there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system... [Einstein’s] argumentation does not justify the conclusion that quantum mechanical description is essentially incomplete...

Bohr does not say Einstein’s argumentation is wrong, but merely that it does not force us to conclude that the quantum mechanical description is incomplete. When Bohr says (or obscurely implies the possibility that) the choice of what measurement to perform on S₁ influences the conditions which define the possible types of predictions for the future behavior of S₂, he is denying the independence of the situations for the spatially separate systems. In other words, he is adopting the second of Einstein’s two alternatives. On the other hand, Bohr’s use of the qualifier “mechanical” also obscurely leaves open the possibility that he may wish to invoke the telepathic influence of Einstein’s first alternative. In either case, Bohr is conceding the correctness of Einstein’s analysis, and simply contends that one or both of Einstein’s alternatives are acceptable, whereas Einstein regards both as unacceptable.

Since Bohr was equivocal about which of the two alternatives he believed was correct, it is difficult to address his position succinctly. The idea of non-mechanical influence (telepathy) is not considered to be very plausible by most people (even those who think they agree with Bohr), since it is difficult if not impossible to reconcile with Lorentz invariance, so we tend to assume that Bohr held to the second alternative, i.e., denying that spatially separate systems have definite separable states. This enabled Bohr to maintain that the quantum mechanical is complete, whereas Einstein believed it must be incomplete.

If one agreed with Einstein that quantum mechanics is incomplete, one way (though not necessarily the only way) of formulating a complete theory would be to propose some additional variables, outside the scope of the usual quantum mechanical formalism, that would give a complete description of a physical system, and that would satisfy Einstein’s requirement for separability of space-like separated systems. This approach is sometimes called “hidden variables”, although the name is somewhat misleading, since the variables need not be hidden – they are merely outside the usual formalism. In subsequent years the debate between Einstein and Bohr was sometimes presented as an argument over the existence or viability of hidden variables - although Einstein himself never explicitly advocated “hidden variables”. (In an appendix to his paper “Einstein-Podolsky-Rosen experiments”, John Bell discussed the question of whether Einstein was a proponent of “hidden variables”. Bell argued that he was.)

In the 1960s John Bell re-examined the Bohr-Einstein debate, and in particular considered whether hidden variables could possibly provide a complete description of physical systems and processes, consistent with quantum mechanics, but satisfying Einstein’s requirement for separability. He based his analysis on a version of the original EPR scenario devised by David Bohm. Consider two entangled electrons, emitted from a common origin in opposite directions toward two experimenters at distant locations. Each experimenter has a spin measuring device, which he can orient at will to measure the incoming electron’s spin (Up or Down) along any axis he chooses. For simplicity, let’s agree that they will measure only along one of three directions, 0, 120, or 240 degrees. Each experimenter finds that, whichever direction he measures, half the electrons are spin UP and half are spin DOWN. Each experimenter keeps a record of his measurements, noting the angle he selected and the result (UP or DOWN) that he measured for each incoming electron. When the experimenters get together later to compare their results, they find that (in accord with quantum mechanics) every time the two experimenters happened to measure a pair of entangled electrons along the same direction, they always got opposite results (one UP and one DOWN), and whenever they measured in different directions they got the same result (both UP or both DOWN) 3/4 of the time. Assuming the experimenters can choose their respective measurement angles “freely”, and assuming no superluminal influences, Bell argued that these results are impossible to reconcile with the assumption that the electrons have definite and separable states, even if we postulate hidden variables.

He argued as follows:  If we measure Particle 1 along the 0 degree axis and find UP, then a measurement of Particle 2 along the 0 degree axis must find DOWN. Thus Particle 2 must be prepared to show DOWN at 0 degrees whenever Particle 1 is prepared to show UP at 0 degrees, and vice versa.  If we insist that the particles have separable states, this perfect anti-correlation in the results at equal angles implies that the particles must be prepared at their common point of departure to yield definite correlated results for each possible measurement angle. Bell argued that there is no other way for separable particles to yield perfect anti-correlation whenever they are measured at equal angles (assuming that the choices of measurement angles are free and independent). But this leads to a contradiction with quantum mechanics (and with experimental results) when we consider the results at unequal measurement angles. By simple algebra we can show that there is no way for the eight possible pre-arranged pairs of results (for three measurement angles) to be assigned probabilities such that the particles always give opposite results when measured in the same direction and such that they give the same results 3/4 of the time when measured at unequal angles. Bell says this rules out hidden variables as a way of giving a complete and separable description of events, so we are left with only the two “spooky” alternatives identified by Einstein – telepathy or non-separability – alternatives that Bohr embraced but Einstein considered unacceptable.

The term “non-separable” needs careful definition. Sometimes people substitute “non-local” for “non-separable”, but this leads to confusion, because the term non-local is properly defined as involving superluminal conveyance of energy and/or information, whereas everyone agrees that quantum mechanics does not entail non-locality in this sense. (As noted above, even Bohr said “there is no question of a mechanical disturbance”.) The fact to be explained is a consistent pattern of correlations between spatially separate events that cannot be explained by any known causal effect, even though these correlations do not entail any superluminal conveyance of energy or information. This is a subtle kind of non-separability, never contemplated before the advent of quantum mechanics.

As Bell himself acknowledged, his analysis is based firmly on the assumption that the choices of measurement angles for the two particles are free and independent. In his paper “Free variables and Local Causality” he discussed the possibility that this freedom might be illusory, and hence it might be possible to rescue what he called local causality. Bell was not sympathetic to this view, and argued that simple randomized choices could serve, for all practical purposes, as free variables, unless we posit some pervasive conspiracy. However, he recognized that this could not be ruled out: “A theory may appear in which such conspiracies inevitably occur, and these conspiracies may then seem more digestible than the non-localities of other theories.”

Another possibility, one that Bell never mentioned explicitly, is to invoke temporal symmetry, also sometimes called “backward causation”. The basic concept of locality in a metrical sense could be expressed as the requirement for all causation to be conveyed across null intervals (rather than spacelike intervals), but this doesn’t rule out advanced null intervals. It is conceivable that quantum correlations are enforced by causal effects propagated symmetrically along both advanced and retarded null intervals. The idea that the emission of a lightlight signal is conditions on its absorption has a long history, and was discussed by Tetrode, Einstein, Ehrenfest, and others during the early days of relativity.

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