Thursday, 15 October 2015

Bohr's Reply to EPR (Part II)

In Part I, I claimed that Bohr simply took for granted the conclusion that EPR argue for, namely, that quantum mechanics does not yield a complete description of physical reality,  and that where they part ways is the unargued-for suggestion that a more complete theory is possible.

If this is right, why isn't it clear to every reader of Bohr's reply to EPR?

The reason, I think, is that it wasn't clear in Bohr's own mind.  When I read Bohr, it often seems to me that he is conflating two distinct questions.  One is the question of whether there could be a theory whose state-descriptions go beyond what is allowed by quantum mechanics.  The other is whether we might ever be in a position to know more about the state of a quantum system than is allowed by the uncertainty relations.

They aren't the same question. Think of classical mechanics.  In classical mechanics, a complete state-description is a specification of precise values of all the system's dynamical variables.  For systems composed of many molecules, it would be hopeless to even come close to knowing the precise state of the system, and so we resort to probability distributions over the set of precise states.  It is irrelevant, for the way the theory is used, whether these limitations on knowledge of the precise state are pragmatic limitations, or limitations in principle.

Einstein's view was that quantum wave functions had a status similar to the probability distributions used in classical statistical mechanics; they represented incomplete knowledge of a precise state that would occur in some other theory (not necessarily classical).   If anyone, prior to Einstein's death, presented a good argument for why one shouldn't think of quantum states in this way, I haven't seen it.  No such argument is found in Bohr's reply to EPR.

Though I don't understand Bohr's response to Einstein, I do understand what Einstein attributes to Bohr as a reply, in his Replies to Critics in the Schilpp volume.  There are two ways to reject the conclusion of an argument. One is to find a flaw in the reasoning; the other is to accept the reasoning that leads from premises to conclusion, and to reject one or more of the premises.  Bohr's reply to EPR reads as if he thinks he's found a flaw in the reasoning; he says he's detected an ambiguity in the EPR reality criterion, an ambiguity fatal to the argument.  But in the Replies, Einstein has Bohr reject a premise of the argument.

Of the "orthodox" quantum theoreticians whose positions I know, Niels Bohr's seems to me to come nearest to doing justice to the problem.  Translated into my own way of putting it, he argues as follows:
If the partial systems A and B form a total system which is described by its ψ-function ψ/(AB), there is no reason why any mutually independent existence (state of reality) should be ascribed to the partial systems A and B viewed separately, not even if the partial systems are spatially separated from each other at the particular time under consideration.

So: I understand that as a potential reply to EPR, though I also think that it would be incumbent on someone who replied that way to answer Einstein's challenge, at the end of the Dialectica article, to point to some phenomenon that suggests that we should reject the premise.

As it appears to me, there can be no doubt that the physicists who hold the quantum mechanical manner of description to be, in principle, definitive, will react to these considerations as follows: They will drop requirement II of the independent existence of the physical realities which are present in different portions of space; they can rightly appeal to the fact that the quantum-theory nowhere makes explicit use of this requirement.

I grant this, but note: if I consider the physical phenomena with which I am acquainted, and especially those which are so successfully comprehended by means of quantum-mechanics, then, nevertheless, I nowhere find a fact which makes it appear to me probable that one has to give up requirement II. (Einstein 1948, translation in Howard 1985)

I don't think that Bohr, or anyone else, answered that challenge in Einstein's lifetime.


Einstein, Albert (1948). Quanten-mechanik und wirklichkeit. Dialectica 2, 320–324

Einstein, Albert (1949).  Remarks concerning the essays brought together in this co-operative volume, in P.A. Schilpp, ed., Albert Einstein: Philosopher-Scientist (Chicago: Open Court Press), 665–688.

Howard, Don (1985). “Einstein on Locality and Separability.” Studies in History and Philosophy of Science  16, 171–201.


  1. So why isn't the answer to that last challenge simply entanglement, itself? I think that that was the reaction of most of those on Bohr's side. It was certainly Pauli's view, as expressed in his correspondence with Heisenberg in the summer of 1935.

  2. The question at issue was how to think about entanglement. Classical probability distributions can have correlations between separated systems: Bertlmann's socks.

    Should quantum correlations be understood as analogous? Does Pauli provide a good reason why one shouldn't think of the quantum correlations between separated systems as correlations a la Bertlmann's socks, that is, as arising from probability distributions over more specific states that attribute definite values to the quantities in question? (Or else more specific states on which these quantities are uncorrelated?)

    Not a rhetorical question; I don't have the correspondence ready-to-hand, and will have to go look at it

  3. Yes, but classical correlations don't give you the Bell inequalities. I don't recall a place where Pauli says explicitly that classical probability distributions won't give you the quantum correlations, but in my reading of the literature, this was a commonplace, certainly after 1925 (i.e., post Einstein-Bose). Pauli discusses entanglement at length (though, of course, not by that name) in his 1933 Handbuch article. In his correspondence with Heisenberg in the summer of 1935, he even goes so far as to sketch out - conceptually - the Jarrett/Shimony distinction between parameter and outcome independence. I discussed the latter in my contribution to the first Festschrift for Abner. I have discussed the former in many talks, including this one devoted entirely to the 1933 Handbuch article:

    1. Yes, classical correlations don't give you violation of the Bell Inequalities, and so we now know that there's a serious obstacle to the sort of theory Einstein had in mind. That's the reason for the qualification "in Einstein's lifetime" in the last sentence of the blog post.

      I'll re-read your paper in the Shimony festschrift. If indeed, there were cogent arguments that early that quantum correlations couldn't come from probability distributions over states that attribute definite values to locally measurable quantities, that's interesting. But I want to see it.

    2. I've looked at those slides, and at your article in the Shimony festschrift.

      You'll have to help me out here, because I'm not seeing what Pauli's answer to the Einstein Dialectica challenge could be. What reason could Pauli give for not regarding quantum entangled states as statistical mixtures of product states of a more comprehensive theory that satisfies the Trennungsprinzip?

      Occurrence of correlations isn't sufficient: in classical stat mech, if a system has interacting subsystems, the canonical distribution doesn't factor into a product of distributions for those subsystems.

      Does Pauli have an analogue of Bell's theorem?

  4. My impression is that Bohr does not want to accept Einstein's argument, but also does not want to reject the premise he needs to reject, i.e. Einstein's implicit appeal to locality. That why he explicitly says that there is no "mechanical disturbance" of one part of the entangled pair due to an experiment carried out on the other part, but wants to insist that nonetheless there is some obscure other sort of quasi-conceptual "disturbance" sufficient to block Einstein's appeal to the reality criterion. For if Bohr agrees that there is no sort of disturbance at all, and the one system is physically unchanged by the distant experiment, then he has to concede that not only is the quantum description incomplete, but that the complete description would predetermine the outcome both a position and a momentum measurement. So all the talk of complementarity as a deep physical principle goes away. Non-locality is the price Bohr has to pay to maintain a deep non-classical role for complementarity, and he does not want to pay it. But if he says there is no non-local physical effect at all, Einstein has him trapped. Hence the incoherent waffling.

    1. But, as the passage Wayne quotes from Einstein's "Responses" in the 1949 Schilpp volume makes clear, Einstein thought that Bohr was explicitly rejecting the assumption of the mutual independence of the two systems. Do you think that Einstein misunderstood Bohr?

    2. I have to admit that I don't know what to make of that. I do understand what Einstein attributes to Bohr, but I don't see it in the published articles, either in 1935 or 1949.

      Is Einstein perhaps referring to private conversations? Or is he being overly charitable, attributing to Bohr what he thinks a defender of QM ought to say?

      In the Dialectica article, he doesn't attribute the rejection of Assumption II to anyone, but says that "there can be no doubt that the physicists who hold the quantum mechanical manner of description to be, in principle, definitive, will react to these considerations" by rejecting the Assumption.

      There, he doesn't say that anybody has responded in this way.