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Bell's Theorem Cannot Close the Loophole of Spatial Locality

Ramzi Suleiman

Published Nov 1, 2015• 0 citations
OpenAlex

Abstract

Bell's Theorem prescribes that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. However, Bell's proof presupposes that particles which are distanced from each other in space become spatially disconnected. However, the theoretical possibility for the existence of spatial locality between separated particles had never been refuted empirically. Here I show that Doppler-like local-realistic relativity theories, which predict that the relativistic length of a body distancing from an observer's rest-frame will stretch rather than contract, could maintain spatial locality between particles, even when the particles are distanced enough to ensure that information about the outcomes of one particle is passed to the other particle faster than light. This implies that local and realistic theories which belong to the aforementioned Doppler-like theories could not be disqualified a priori by Bell's Theorem.

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Bell's Theorem prescribes that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. However, Bell's proof presupposes that particles which are distanced from each other in space become spatially disconnected. However, the theoretical possibility for the existence of spatial locality between separated particles had never been refuted empirically. Here I show that Doppler-like local-realistic relativity theories, which predict that the relativistic length of a body distancing from an observer's rest-frame will stretch rather than contract, could maintain spatial locality between particles, even when the particles are distanced enough to ensure that information about the outcomes of one particle is passed to the other particle faster than light. This implies that local and realistic theories which belong to the aforementioned Doppler-like theories could not be disqualified a priori by Bell's Theorem.
Bell's theorem prescribes that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. However, Bell's theorem presupposes that particles that are distanced from each other become spatially disconnected. Yet studies have never experimentally confirmed the possibility of spatial locality between distanced particles. Here, I show that Bell’s theorem cannot forbid an infinite set of local-deterministic relativity theories that violate Lorentz's contraction for distancing bodies. This result in itself cannot guarantee a theory from this set of theories to successfully reproduce the predictions of quantum theory, but until the spatial locality loophole is satisfactorily closed, experiments should be decided the fate of such theories.
In a recent Nature article, Hensen et al. reported that they have accomplished a loophole-free test of Bell's theorem. The authors speculated that further improvements in their experimental design could settle an 80 years debate in favor of quantum theory's stance that entanglement is action at a distance. We direct attention to a spatial aspect of locality, not considered by Bell's Theorem nor by any of its experimental tests. We refer to the possibility that two particles distancing from each other could remain spatially disconnected, even when they have distanced enough to ensure that information between them was transmitted faster than the velocity of light. We show that any local-deterministic relativity theory which violates Lorentz's contraction for distancing bodies can maintain spatial locality. We briefly note that the recently proposed Information Relativity Theory satisfies the aforementioned condition, and that it predicts and explains several quantum phenomena, despite being local and deterministic. We conclude by arguing that quantum entanglement is not nonlocal and that the unnoticed spatial dimension of locality is in fact the hidden variable conjectured in the seminal EPR paper.
Bell's Theorem prescribes that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. However the theorem presupposes that distanced physical systems become spatially disconnected. This presupposition, although in agreement with our intuition, has never been confirmed experimentally. As a result Bell's Theorem prohibits only temporal locality, but not spatial locality between distanced particles. Here, I show that any local-deterministic relativity theory that violates Lorentz's contraction for distancing bodies cannot be forbidden by Bell's inequality. I further show that the predictions of a recently proposed local and deterministic Information Relativity Theory, are consistent with quantum theory and quantum thermodynamics, and reproduce the same results for key quantum phenomena, including matter-wave duality, quantum criticality and phase transition, formation of Bose-Einstein condensate, and quantum entanglement. The theory assumes that observers who are in inertial motion with respect to each other with relative velocity v, communicate information about physical observables using an information carrier with known velocity (vc) which satisfies vc > v. No other presumptions are made. For velocities satisfying v << vc all the theory transformations reduce to Galileo-Newton laws. The theory is simple and is also beautiful due to its Golden Ratio symmetries. More importantly, the theory is scale independent with respect to the investigated physical systems' dimensions and the velocity of the information carrier, which renders it applicable to the dynamics of moving bodies in all inertial physical systems.
In a recent Nature article Hensen et al. reported that they have accomplished a loophole-free test of Bell's theorem. The authors speculated that further improvements in their experimental design could settle an 80 year debate in favor of quantum theory's stance that entanglement is action at a We direct attention to a spatial aspect of locality, not considered by Bell's Theorem or by any of its experimental tests. We refer to the possibility that two distanced particles could remain spatially disconnected, even when distanced enough to ensure that information between them was transmitted faster than the velocity of light. We show that any local-deterministic relativity theory which violates Lorentz's contraction for distancing bodies can maintain spatial locality at any distance. We conclude that until the loophole of spatial locality is closed by future experiments, the news about the death of locality will remain greatly exaggerated.
Introduction Fifty years after the publication of Bell's theorem, there remains some controversy regarding what the theorem is telling us about quantum mechanics, and what the experimental violations of Bell inequalities are telling us about the world. This chapter represents my best attempt to be clear about what I think the lessons are. In brief: There is some sort of nonlocality inherent in any quantum theory, and, moreover, in any theory that reproduces, even approximately, the quantum probabilities for the outcomes of experiments. But not all forms of nonlocality are the same; there is a distinction to be made between action at a distance and other forms of nonlocality, and I will argue that the nonlocality needed to violate the Bell inequalities need not involve action at a distance. Furthermore, the distinction between forms of nonlocality makes a difference when it comes to compatibility with relativistic causal structure. The Bell locality condition is a condition which, if satisfied, renders possible a completely local account of the correlations between outcomes of spatially separated experiments. Bell's theorem tells us that the probabilities that we compute from quantum mechanics do not admit of such an account. Modulo auxiliary assumptions that, in my opinion, should be noncontroversial, this yields the conclusion that there must be something nonlocal about any theory that yields the quantum mechanical probabilities or anything close to them. One way to violate the Bell locality condition – and this is the way that any deterministic theory must do it – is via straightforward action at a distance. However, we should also consider the possibility of a stochastic theorywith probabilistic laws that involve irreducible correlations. The sort of nonlocality inherent in such a theory involves relations between events that are significantly different from causal relations as usually conceived. Perhaps surprisingly, such a theory, unlike its deterministic cousins, need not invoke a distinguished relation of distant simultaneity. This makes a difference for the situation of the two sorts of theories vis-a-vis relativity. Though a deterministic theory can achieve the appearance of being relativistic, at the level of observable phenomena, it can do so only by introducing a preferred foliation and with it a causal structure at odds with relativistic causal structures. Things are otherwise with dynamical collapse theories.
Bell's theorem states that some quantum correlations can not be represented by classical correlations of separated random variables. It has been interpreted as incompatibility of the requirement of locality with quantum mechanics. We point out that in fact the space part of the wave function was neglected in the proof of Bell's theorem. However this space part is crucial for considerations of property of locality of quantum system. Actually the space part leads to an extra factor in quantum correlations and as a result the ordinary proof of Bell's theorem fails in this case. We present a criterium of locality in a realist theory of hidden variables. It is argued that predictions of quantum mechanics for Gaussian wave functions can be consistent with Bell's inequalities and hence Einstein's local realism is restored in this case.