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Clearing Up Mysteries

  1. Jan 13, 2005 #1
    Ed Jaynes, in "CLEARING UP MYSTERIES - THE ORIGINAL GOAL" tells us
    his thinking on EPR and the foundation of QM:

    "BACKGROUND OF EPR
    Quantum Mechanics (QM) is a system of mathematics that was not developed to express any particular physical ideas, in the sense that the mathematics of relativity theory expresses the ideas of Einstein, or that of genetics expresses the ideas of Mendel. Rather, it grew empirically, over about four decades, through a long series of trial-and-error steps. But QM has two difficulties; firstly, like all empirical equations, the process by which it was found gives no clue as to its meaning. QM has the additional difficulty that its predictions are incomplete, since in general it gives only probabilities instead of definite predictions, and it does not indicate what extra information would be required to make definite predictions.

    Einstein and Schroedinger saw this incompleteness as a defect calling for correction in some future more complete theory. Niels Bohr tried instead to turn it into a merit by fitting it into his philosophy of complementarity, according to which one can have two different sets of concepts, mutually incompatible, one set meaningful in one situation, the complementary set in another. As several of his early acquaintances have testified (Rozental, 1964), the idea of complementarity had taken control of his mind years before he started to study quantum physics.

    Bohr's "Copenhagen Theory" held that, even when the QM state vector
    gives only probabilities, it is a complete description of reality in the sense that nothing more can ever be known; not because of technological limitations, but as a matter of fundamental principle. It seemed to Einstein that this completeness claim was a gratuitous addition, in no way called for by the facts; and he tried to refute it by inventing thought experiments which would enable one to get more information than Bohr wished us to have. Somehow, the belief has been promulgated that Bohr successfully answered all of Einstein's objections.

    But when we examine Bohr's arguments, we find a common logical structure; always they start by postulating that the available measurement apparatus is subject to his "uncertainty" limitations; and then by using only classical physics (essentially, only Liouville's theorem) they come to the conclusion that such an apparatus could not be used for Einstein's purpose. Bohr's foregone conclusion is always assured by his initial postulate, which simply
    appears out of nowhere. In our view, then, the issue remains open and we must raise our standards of logic before there can be any hope of resolving it.

    Leslie Ballentine (1970) analyzed the Bohr and Einstein positions and
    showed that much of the chanting to the effect that "Bohr won,
    Einstein lost" is sustained by quoting Einstein's views and attributing them to Bohr. Virtually all physicists who do real quantum-mechanical calculations interpret their results in the sense of Einstein, according to which a pure state represents an ensemble of similarly prepared systems and is thus an incomplete description of an individual system. Bohr's completeness claim has never played any functional role in applications, and in that sense it is indeed
    gratuitous.

    CONFRONTATION OR RECONCILIATION?
    Put most briefly, Einstein held that the QM formalism is incomplete and that it is the job of theoretical physics to supply the missing parts; Bohr claimed that there are no missing parts. To most, their positions seemed diametrically opposed; however, if we can understand better what Bohr was trying to say, it is possible to reconcile their positions and believe them both. Each had an important truth to tell us.

    But Bohr and Einstein could never understand each other because they
    were thinking on different levels. When Einstein says QM is incomplete, he means it in the ontological sense; when Bohr says QM is complete, he means it in the epistemological sense. Recognizing this, their statements are no longer contradictory. Indeed, Bohr's vague, puzzling sentences - always groping for the right word, never finding it - emerge from the fog and we see their underlying sense, if we keep in mind that Bohr's thinking is never on the ontological level traditional in physics. Always he is discussing not Nature, but
    our information about Nature. But physics did not have the vocabulary
    for expressing ideas on that level, hence the groping.

    Paul Dirac, who was also living here in St. John's College at the time when he and Harold Jeffreys were doing their most important work side by side, seems never to have realized what Jeffreys had to offer him: probability theory as the vehicle for expressing epistemological notions quantitatively. It appears to us that, had either Bohr or Dirac understood the work of Jeffreys, the recent history of theoretical physics might have been very different. They would have had the language and technical apparatus with which Bohr's ideas
    could be stated and worked out precisely without mysticism. Had they
    done this, and explained clearly the distinction between the ontological and epistemological levels, Einstein would have understood it and accepted it at once.

    Needless to say, we consider all of Einstein's reasoning and conclusions correct on his level; but on the other hand we think that Bohr was equally correct on his level, in saying that the act of measurement might perturb the system being measured, placing a limitation on the information we can acquire and therefore on the predictions we are able to make. There is nothing that one could object to in this conjecture, although the burden of proof is on the person who makes it. But we part company from Bohr when this metamorphoses without explanation into a claim that the limitation on
    the predictions of the present QM formalism are also - in exact, minute detail - limitations on the measurements that can be made in the laboratory!

    Like Einstein, we can see no justification at all for this gratuitous assumption. We need a more orderly division of labour; it is simply not the proper business of theoretical physics to make pronouncements about what can and what cannot be measured in the laboratory, any more than it would be for an experimenter to issue proclamations about what can and cannot be predicted in the theory.

    The issue of what kind of limitation on measurement really exists - or indeed, whether any limitation at all exists - is still logically an open question, that belongs to the province of the experimenter; but we may be able to settle it soon in the quantum optics laboratory, thanks to the spectacular recent advances in experimental techniques such as those by H.Walther and coworkers (Rempe et al, 1987) as discussed by Knight (1987) and in the Scientific American (June 1987, p. 25).

    We believe that to achieve a rational picture of the world it is necessary to set up another clear division of labour within theoretical physics; it is the job of the laws of physics to describe physical causation at the level of ontology, and the job of probability theory to describe human inferences at the level of
    epistemology. The Copenhagen theory scrambles these very different
    functions into a nasty omelette in which the distinction between reality and our knowledge of reality is lost.

    Although we agree with Bohr that in different circumstances (different states of knowledge) different quantities are predictable, in our view this does not cause the concepts themselves to fade in and out; valid concepts are not mutually incompatible. Therefore, to express precisely the effect of disturbance by measurement, on our information and our ability to predict, is not a philosophical problem calling for complementarity; it is a technical problem calling for probability theory as expounded by Jeffreys, and information theory. Indeed, we know that toward the end of his life, Bohr showed an interest in information theory.

    EPR
    But to return to the historical account; somehow, many physicists became persuaded that the success of the QM mathematical formalism proved the correctness of Bohr's private philosophy, even though hardly any - even among his disciples - understood what that philosophy was. All the attempts of Einstein, Schroedinger, and others to point out the patent illogic of this were rejected and sneered at; it is a worthy project for future psychologists to explain why.

    The Einstein-Podolsky-Rosen (EPR) article of 1935 is Einstein's major effort to explain his objection to the completeness claim by an example that he thought was so forceful that nobody could miss the point. Two systems, S1 and S2, that were in interaction in the past are now separated, but they remain jointly in a pure state. Then EPR showed that according to QM an experimenter can measure a quantity q1 in S1, whereupon he can predict with certainty the value of q2 in S2. But he can equally well decide to measure a quantity p1 that does not commute with q1; whereupon he can predict with certainty the value of p2 in S2.

    The systems can be so far apart that no light signal could have traveled between them in the time interval between the S1 and S2 measurements. Therefore, by means that could exert no causal influence on S2 according to relativity theory, one can predict with certainty either of two noncommuting quantities, q2 and p2. EPR concluded that both q2 and p2 must have had existence as definite physical quantities before the measurements; but since no QM state vector is capable of representing this, the state vector cannot be the whole story.

    Since today some think that merely to verify the correlations experimentally is to refute the EPR argument, let us stress that EPR did not question the existence of the correlations, which are to be expected in a classical theory. Indeed, were the correlations absent, their argument against the QM formalism would have failed. Their complaint was that, with physical causation unavailable, only instantaneous psychokinesis (the experimenter's free-will decision which experiment to do) is left to control distant events, the
    forcing of S2 into an eigenstate of either q2 or p2. Einstein called this "a spooky kind of action at a distance".

    To understand this, we must keep in mind that Einstein's thinking is always on the ontological level; the purpose of the EPR argument was to show that the QM state vector cannot be a representation of the "real physical situation" of a system. Bohr had never claimed that it was, although his strange way of expressing himself often led others to think that he was claiming this.

    From his reply to EPR, we find that Bohr's position was like this: "You may decide, of your own free will, which experiment to do. If you do experiment E1 you will get result R1. If you do E2 you will get R2. Since it is fundamentally impossible to do both on the same system, and the present theory correctly predicts the results of either, how can you say that the theory is incomplete? What more can one ask of a theory?"

    While it is easy to understand and agree with this on the epistemological level, the answer that I and many others would give is that we expect a physical theory to do more than merely predict experimental results in the manner of an empirical equation; we want to come down to Einstein's ontological level and understand what is happening when an atom emits light, when a spin enters a Stern-Gerlach magnet, etc. The Copenhagen theory, having no answer to any question of the form:

    "What is really happening when - - - ?",

    forbids us to ask such questions and tries to persuade us that it is philosophically naive to want to know what is happening. But I do want to know, and I do not think this is naive; and so for me QM is not a physical theory at all, only an empty mathematical shell in which a future theory may, perhaps, be built."

    The entire paper may be found at:
    http://bayes.wustl.edu/etj/articles/cmystery.pdf

    All the best
    John B.
     
    Last edited: Jan 13, 2005
  2. jcsd
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