Hidden variables and nonlocality in quantum mechanics

Most physicists hold a skeptical attitude toward a 'hidden variables' interpretation of quantum theory, despite David Bohm's successful construction of such a theory and John S. Bell's strong arguments in favor of the idea. The first reason for doubt concerns certain mathematical theorems (von Neumann's, Gleason's, Kochen and Specker's, and Bell's) which can be applied to the hidden variables issue. These theorems are often credited with proving that hidden variables are indeed 'impossible', in the sense that they cannot replicate the predictions of quantum mechanics. Many who do not draw such a strong conclusion nevertheless accept that hidden variables have been shown to exhibit prohibitively complicated features. The second concern is that the most sophisticated example of a hidden variables theory--that of David Bohm--exhibits non-locality, i.e., consequences of events at one place can propagate to other places instantaneously. However, neither the mathematical theorems in question nor the attribute of nonlocality detract from the importance of a hidden variables interpretation of quantum theory. Nonlocality is present in quantum mechanics itself, and is a required characteristic of any theory that agrees with the quantum mechanical predictions.;We first discuss the earliest analysis of hidden variables--that of von Neumann's theorem--and review John S. Bell's refutation of von Neumann's 'impossibility proof'. We recall and elaborate on Bell's arguments regarding the theorems of Gleason, and Kochen and Specker. According to Bell, these latter theorems do not imply that hidden variables interpretations are untenable, but instead that such theories must exhibit contextuality, i.e., they must allow for the dependence of measurement results on the characteristics of both measured system and measuring apparatus. We demonstrate a new way to understand the implications of both Gleason's theorem and Kochen and Specker's theorem by noting that they prove a result we call "spectral incompatibility". We develop further insight into the concepts involved in these two theorems by investigating a special quantum mechanical experiment first described by David Albert. We review the Einstein-Podolsky-Rosen paradox, Bell's theorem, and Bell's later argument that these imply that quantum mechanics is irreducibly nonlocal.;The paradox of Einstein, Podolsky, and Rosen was generalized by Erwin Schrodinger in the same paper where his famous 'cat paradox' appeared. We show that Schrodinger's conclusions can be derived using a simpler argument--one which makes clear the relationship between the quantum state and the 'perfect correlations' exhibited by the system. We use Schrodinger's EPR analysis to derive a wide variety of new quantum nonlocality proofs. These proofs share two important features with that of Greenberger, Horne, and Zeilinger. First, they are of a deterministic character, i.e., they are 'nonlocality without inequalities' proofs. Second, the quantum nonlocality results we develop may be experimentally verified so that one need only observe the 'perfect correlations' between the appropriate observables. This latter feature serves to contrast these proofs with EPR/Bell nonlocality, the laboratory confirmation of which demands not only the observation of perfect correlations, but also the observations required to test whether 'Bell's inequality' is violated. The 'Schrodinger nonlocality' proofs we give differ from the GHZ proof in that they apply to two-component composite systems, while the latter involves a composite system of at least three-components. In addition, some of the Schrodinger proofs involve classes of observables larger than that addressed in the GHZ proof. (Abstract shortened by UMI.).