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arXiv:quant-ph/9710032

Is Quantum Mechaincs Non-Local?

William George Unruh

Published Oct 10, 1997• 0 citations
arXivHTMLPDF

Abstract

Stapp has recently argued from a version of the Hardy type experiments that quantum mechanics must be non-local, independent of any additional assumptions like realism or hidden variables. I argue that either his conclusions do not follow from his assumptions, or that his assumptions are not true of quantum mechanics and can be interpreted as assigning an unwarranted level of reality to the value of certain quantum attributes.

DOI
10.48550/arxiv.quant-ph/9710032

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Stapp has recently argued from a version of the Hardy type experiments that quantum mechanics must be non-local, independent of any additional assumptions like realism or hidden variables. I argue that either his conclusions do not follow from his assumptions, or that his assumptions are not true of quantum mechanics and can be interpreted as assigning an unwarranted level of reality to the value of certain quantum attributes.
The debate about the non-locality of quantum mechanics is old, but still lively. Numerous people use non-locality as (bad) shorthand for quantum entanglement. But some have a long-standing commitment to the validity of this characterization. This paper examines two separate streams in this debate. The first is the arguments of Stapp, and especially his recent paper where he simplifies his contractual argument in the Hardy situation to argue for the non-locality of quantum mechanics. He has maintained his contention that an analysis of a Hardy-type correlation between two spatially separated observers proves that quantum mechanics itself is non-local, without any additional assumption of realism or hidden variables. In the second section, I try to carefully examine the Bell argument in the CHSH variant to see where the difference between the quantum and classical situations differ. Asher Peres was one of the great physicists of the late 20th century, especially for his intense concern with the fundamental nature of quantum mechanics. His courage in devoting his life to an area many considered "philosophical" (i.e. non-physical) paved the way for the rest of us to reveal our interests and confusions about this area. I am not sure that he would agree with everything in this paper, but I offer it as a tribute to him.
In the paper the proof of the non-locality of quantum mechanics, given recently by H. Stapp and D. Bedford, and appealing to the GHZ example, is analyzed. The proof does not contain any explicit assumption of realism, but instead it uses formal methods and techniques of the Lewis calculus of counterfactuals. To ascertain the validity of the proof, a formal semantic model for counterfactuals is constructed. With the help of this model it can be shown that the proof is faulty, because it appeals to the unwarranted principle of Elimination of Eliminated Conditions (EEC). As an additional way of showing unreasonableness of the assumption (EEC), it is argued that yet another alleged and highly controversial proof of non-locality of QM, using the Hardy example, can be made almost trivial with the help of (EEC). Next the question is considered whether the validity of the proof in the GHZ case can be restored by adopting the assumption of partial realism. It is argued that although this assumption makes the crucial step of the original reasoning valid, it nevertheless renders another important transition unjustified, therefore the entire reasoning collapses.
I s it possible to bring experiments to bear on metaphysical theses such as realism? In recent developments in quantum mechanics particularly associated with the late John Bell it has been claimed that a certain type of realism, what is known as local realism, has indeed been refuted by a series of experiments, culminating in those carried out by Alain Aspect and his collaborators in Paris in 1982. Crudely local realism means in this context that atomic and subatomic entities, the subject matter of quantum mechanics, possess definite sharp values for all their attributes at all times, and, in addition, these attributes cannot be affected instantaneously by operations such as measurements performed on other microentities at different spatial locations from the one whose attributes are in question. In other words, realism is supplemented with a denial of the possibility of instantaneous action-at-a-distance. Now relativity theory, the other great pillar of modern theoretical physics, is standardly understood as committed to such a denial. So an experimental refutation of local realism would force us to give up either locality (the no-instantaneous-action-at-a-distance principle) or the realist thesis itself. The first horn of this dilemma is closed off by appeal to relativity theory, and so the conclusion of the argument would appear to be the refutation of realism.
A recent proof [H. P. Stapp, Am. J. Phys. 65, 300 (1997)], formulated in the symbolic language of modal logic, claims to show that contemporary quantum theory, viewed as a set of rules that allow us to calculate statistical predictions among certain kinds of observations, cannot be imbedded in any rational framework that conforms to the principles that (1) the experimenters' choices of which experiments they will perform can be considered to be free choices, (2) outcomes of measurements are unique, and (3) the free choices just mentioned have no backward-in-time effects of any kind. This claim is similar to Bell's theorem, but much stronger, because no reality assumption alien to quantum philosophy is used. The paper being commented on [W. Unruh, Phys. Rev. A 59, 126 (1999)] argues that some such reality assumption has been ``smuggled'' in. That argument is examined here and shown, I believe, to be defective.
The conceptually puzzling features of quantum mechanics as a statistical theory all have their source in the impossibility of relating the probability assignments defined by the quantum state to distributions over determinate values of the physical magnitudes. While some interpretations of quantum mechanics, as well as “hidden variable” modifications of the theory, have proposed several constructions for assigning values to magnitudes (beyond the value assignments defined by the quantum state alone), a variety of theorems exist which impose severe restrictions on such theoretical constructions. This note will deal with Bell's proof (in [2]), that any hidden variable theory satisfying a physically reasonable locality condition is characterized by an inequality which is inconsistent with the quantum statistics. Bell's result has initiated a series of experiments designed to refute the entire class of local hidden variable theories. We show that Bell's inequality actually characterizes a feature of hidden variable theories which is much weaker than locality in the sense considered physically motivated.