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AIP conference proceedings

Supercorrelation, an interpretation of quantum non-locality

Louis Vervoort

Published Jan 1, 2012• 1 citation
Publisher

Abstract

It will be shown that in a highly correlated, but local, universe the Bell inequality can be violated. To that end, we study well-known model systems, namely spin lattices, in which locality and correlation are simply verified. Our universe may be a similar, correlated universe, in which nonlocality is only apparent. To corroborate this claim, it will be shown that an arbitrarily weak correlation between λ and the analyzer settings - in agreement with 'free will' - is sufficient for reproducing the quantum correlations.

DOI
10.1063/1.4773174

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It will be shown that in a highly correlated, but local, universe the Bell inequality can be violated. To that end, we study well-known model systems, namely spin lattices, in which locality and correlation are simply verified. Our universe may be a similar, correlated universe, in which nonlocality is only apparent. To corroborate this claim, it will be shown that an arbitrarily weak correlation between λ and the analyzer settings - in agreement with 'free will' - is sufficient for reproducing the quantum correlations.
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Starting from the late 60's many experiments have been performed to verify the violation Bell's inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell's inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical grounds (not discussed in the present paper) and the experiment discussed below has been devised to support these theoretical arguments. We emphasize that the goal of our experiment is not to reproduce classically the EPR correlations but to prove that there exist perfectly local classical dynamical systems violating Bell's inequality.
Bell's theorem is 50 years old. Still there is a controversy about its implications. Much of it has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities requires just locality assumption, and nothing more. Violations of the inequalities are then interpreted as ``nonlocality'' or ``quantum nonlocality''. We show that such claims are unfounded and that every derivation of Bell's inequalities requires a premise -- in addition to locality and freedom of choice -- which is either assumed tacitly, or unconsciously, or is embedded in a single compound condition (like Bell's ``local causality''). The premise is equivalent to the assumption of existence of additional variables which do not appear in the quantum formalism (in form of determinism, or joint probability for outcomes of all conceivable measurements, or ``additional causes`'', or ``hidden variables'', ``complete description of the state'' or counterfactual definiteness, etc.). A certain irony is that perhaps the main message of violation of Bell's inequalities is that our notion of locality should be based on an operationally well-defined no-signalling condition, rather than on local causality.
The empirical proof of Bell inequality violations was a landmark moment for research into quantum foundations. It commits us to a universe without strict relativistic locality or requires that we escape through a potential loophole like many-worlds or superdeterminism. In this work, we consider a sequential, single-spin experiment whose auto-correlations match the two-spin entangled correlations of a Bell scenario. We use a counterfactual equivalence between the two to argue that Bell-type correlations are actually just a different implementation of the sequential experiment. This comports well with the counterfactual basis of the original EPR argument, and explains any apparent non-locality as a consequence of indirectly measuring quantities that do not have predefined values, due to the state-altering nature of sequential spin measurements.
J.S. Bell's remarkable 1964 theorem showed that any theory sharing the empirical predictions of orthodox quantum mechanics would have to exhibit a surprising – and, from the point of view of relativity theory, very troubling – kind of nonlocality. Unfortunately, even still on this 50th anniversary, many commentators and textbook authors continue to misrepresent Bell's theorem. In particular, one continues to hear the claim that Bell's result leaves open the option of concluding either nonlocality or the failure of some unorthodox “hidden variable” (or “determinism” or “realism”) premise. This mistaken claim is often based on a failure to appreciate the role of the earlier 1935 argument of Einstein, Podolsky, and Rosen in Bell's reasoning. After briefly reviewing this situation, I turn to two alternative versions of quantum theory – the “many worlds” theory of Everett and the quantum Bayesian interpretation of Fuchs, Schack, Caves, and Mermin – that purport to provide actual counterexamples to Bell's claim that nonlocality is required to account for the empirically verified quantum predictions. After analyzing each theory's grounds for claiming to explain the EPR–Bell correlations locally, however, one can see that (despite a number of fundamental differences) the two theories share a common for-all-practical-purposes (FAPP) solipsistic character. This dramatically undermines such theories’ claims to provide a local explanation of the correlations and thus, by concretizing the ridiculous philosophical lengths to which one must go to elude Bell's own conclusion, reinforces the assertion that nonlocality really is required to coherently explain the empirical data. Introduction Fifty years ago, in 1964 [1], John Stewart Bell first proved the theorem that has become widely known as “Bell's Theorem” but that Bell himself instead referred to as the “locality inequality theorem” [2]. In Bell's own view, the theorem showed that the empirical predictions of local theories will be constrained by Bell's inequality (or as Bell himself preferred to call it, the “locality inequality”). Hence, nonlocality is a necessary feature of any theory that shares the empirical predictions of standard quantum mechanics.
We address the problem of detecting non-locality in coupled N level systems in the language of spin. Through a number of examples, we show that non-locality can be detected via a violation of the standard Bell inequality, irrespective of what N is, with correlations from observables of order k ~ 2s in the fundamental spin operators. We further show that, contrarily, if the order k is frozen, then non-locality eludes a detection when s >> k, leading to a weak classical limit. Armed with these results, we proceed to characterize observables that 'genuinely' reflect non-locality in higher dimensions, and demonstrate that one needs to go beyond the standard set-ups such as Stern-Gerlach and those with correlations involving measurement of spin projections along quantization axes.