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Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

A relativistic retrocausal model violating Bell's inequality

Dustin Lazarovici

Published Nov 19, 2014• 6 citations
Publisher

Abstract

We present a simple model demonstrating that time-symmetric (advanced + retarded) relativistic interactions can account for statistical correlations violating the Bell inequalities while avoiding conspiracies as well as the commitment to instantaneous (direct space-like) influences. We provide an explicit statistical analysis of the model while highlighting some of the difficulties arising from retrocausal effects. Finally, we discuss how this account fits into the framework of Bell's theorem.

DOI
10.1098/rspa.2014.0454

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We present a simple model demonstrating that time-symmetric (advanced + retarded) relativistic interactions can account for statistical correlations violating the Bell inequalities while avoiding conspiracies as well as the commitment to instantaneous (direct space-like) influences. We provide an explicit statistical analysis of the model while highlighting some of the difficulties arising from retrocausal effects. Finally, we discuss how this account fits into the framework of Bell's theorem.
The possibility of using retrocausality to obtain a fundamentally relativistic account of the Bell correlations has gained increasing recognition in recent years. It is not known, however, the extent to which these models can make use of their relativistic properties to account for relativistic effects on entangled systems. We consider here a hypothetical relativistic Bell experiment, where one of the wings experiences time-dilation effects. We show that the retrocausal Brans model ( Found. Phys. , 49 (2), 2019) can be easily generalized to analyse this experiment, and that it predicts less separation of eigenpackets in the wing experiencing the time-dilation. This causes the particle distribution patterns on the photographic plates to differ between the wings—an experimentally testable prediction of the model. We discuss the difficulties faced by other hidden variable models in describing this experiment, and their natural resolution in our model due to its relativistic properties. In particular, we discuss how a ψ -epistemic interpretation may resolve several difficulties encountered in relativistic generalizations of de Broglie–Bohm theory and objective state reduction models. Lastly, we argue that it is not clear at present, due to technical difficulties, if our prediction is reproduced by quantum field theory. We conclude that if it is, then the retrocausal Brans model predicts the same result with great simplicity in comparison. If not, the model can be experimentally tested.
The precision with which we can measure operators that do not commute with conserved quantities is limited by the need to preserve the associated global symmetries. We show how to construct a local hidden-variable model that violates Bell inequalities by interpreting this measurement error as altering the measure space of the hidden variables. This provides a physically-motivated example of a supermeasured model, where the statistical independence assumption used to form Bell inequalities is violated without there being a causal dependence of the measurement settings on the hidden variables (superdeterminism) or a causal dependence of the hidden variables on the measurement settings (retrocausality). The model also gives subtly different predictions to quantum mechanics, that could be tested experimentally.
Abstract Bell's theorem revealed that a local hidden-variable model cannot completely reproduce the quantum mechanical predictions. Bell's inequality provides an upper bound under the locality and reality assumptions that can be violated by correlated measurement statistics of quantum mechanics. Greenberger, Horne, and Zeilinger (GHZ) gave a more compelling proof of Bell's theorem without inequalities by considering perfect correlations rather than statistical correlations. In this work, we present a temporal analogue of GHZ argument that establishes Bell's theorem in time without inequalities .
Bell's theorem revealed that a local hidden-variable model cannot completely reproduce the quantum mechanical predictions. Bell's inequality provides an upper bound under the locality and reality assumptions that can be violated by correlated measurement statistics of quantum mechanics. Greenberger, Horne, and Zeilinger (GHZ) gave a more compelling proof of Bell's theorem without inequalities by considering perfect correlations rather than statistical correlations. This work presents a temporal analog of the GHZ argument that establishes Bell's theorem in time without inequalities.
Abstract We show that the ability to consider counterfactual situations is a necessary assumption of Bell’s theorem, and that, to allow Bell inequality violations while maintaining all other assumptions, we just require certain measurement choices be counterfactually restricted, rather than the full removal of counterfactual definiteness. We illustrate how the counterfactual definiteness assumption formally arises from the statistical independence assumption. Counterfactual restriction therefore provides a way to interpret statistical independence violation different to what is typically assumed (i.e. that statistical independence violation means either retrocausality or superdeterminism). We tie counterfactual restriction to contextuality, and show the similarities to that approach.