What is Einstein's statistical interpretation, or, is it Einstein for whom Bell's theorem tolls?

Abstract

Einstein regarded the quantum theory as descriptively incomplete. What he meant was that, in typical cases, the probabilistic assertions provided by the theory for an individual quantum system do not exhaust all the relevant and true physical assertions about the system. Put briefly, according to Einstein, the typical statistical story told by quantum theory is not the whole story. Einstein arrived at this doctrine by means of a dialectical strategy that involved several beautiful and simple 'in-principle' applications of the theory, elegant thought experiments of a kind characteristic of Einstein's genius for physical insight. His strategy was to show how the alternative idea, the idea of the completeness of quantum theory, was forced into puzzling and unnatural interpretations for these special applications. By switching from completeness to incompleteness everything was supposed to 'click' into place: the fly, as it were, was to be let out of the bottle. Certainly Einstein never thought he was offering strict counterexamples to the theory itself. Nor, I believe, did he think he had strictly proved his case for incompleteness, or actually refuted the idea of completeness. Rather, he felt that the dialectical strategy showed his conception to have a powerful intuitive appeal vis-a-vis its competitor. The final stage of that strategy involved showing how the idea of incompleteness could ground a specific understanding of quantum theory, one that would make intelligible the puzzling thought experiments. That understanding comprises what is sometimes called Einstein's 'statistical interpretation' of the state functions of quantum theory; in his own words "the ~O-function is to be understood as the description not of a single system but of an ensemble of systems.' (Schilpp, 1949, p. 671). Using this idea the seeming-paradoxes generated by the alternative conception (that the ~O-function is a complete description of the single system) were supposed to disappear. From his earliest public comments on the interpretation of quantum mechanics, in the Solvay conference of 1927, down through his last papers on the subject in the 1940s and early 50s, Einstein referred to the ensemble interpretation of the state function in language virtually identical to that just cited. 1 So far as I have been able to ascertain, the same is true of his unpublished remarks. This concept of an ensemble interpretation was clearly the cornerstone of his own understanding of the quantum theory. Writing to Born in 1953, he described this concept as "the only one which does justice to the mechanism of the probabilistic quantum theory." (Born, 1971, p. 209). It is, therefore, remarkable although (curiously) scarcely ever remarked upon, that nowhere at all does Einstein say in any detail just exactly what this ensemble interpretation amounts to. In particular, he never does so for the very applications that are supposed to be treated by this interpretation 'more naturally' than by its competitor. Although it would be intriguing to speculate on the reasons behind Einstein's cryptic brevity here, and even more intriguing to think about the reluctance of his many commentators on the subject to deal with this fact, I shall defer the pleasure of those speculations, just now, in favor of another. For what, after all, was Einstein's ensemble interpretation? As just noted, there is very little textual material available on which to base an answer. One only finds a couple of vague phrases in one article, and a couple of very similar ones in the others. Despite the scant data, however, the literature seems to have settled on a standard answer. ~ This answer, the so-called 'statistical interpretation,' has been faced with difficulties at least since 1935, difficulties known to Einstein and simply ignored by him. 3 Recently these difficulties have been sharply focused, and have received a good deal of attention, through the work of John Bell. 4 Bell showed that, in principle (at least), the statistical interpretation is actually numerically inconsistent with the quantum theory when applied to coupled systems, the most favorite of Einstein's provocative examples. If the standard answer is Einstein's, then it appears that his interpretation of the quantum theory has been refuted. This conclusion is, I think, the received opinion. Given what little Einstein actually had to say on the matter and given his complete aplomb in the face of earlier