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A Local \(\psi \)-Epistemic Retrocausal Hidden-Variable Model of Bell Correlations with Wavefunctions in Physical Space

  • Indrajit SenEmail author
Article

Abstract

We construct a local \(\psi \)-epistemic hidden-variable model of Bell correlations by a retrocausal adaptation of the originally superdeterministic model given by Brans. In our model, for a pair of particles the joint quantum state \(|\psi _e(t)\rangle \) as determined by preparation is epistemic. The model also assigns to the pair of particles a factorisable joint quantum state \(|\psi _o(t)\rangle \) which is different from the prepared quantum state \(|\psi _e(t)\rangle \) and has an ontic status. The ontic state of a single particle consists of two parts. First, a single particle ontic quantum state \(\chi (\vec {x},t)|i\rangle \), where \(\chi (\vec {x},t)\) is a 3-space wavepacket and \(|i\rangle \) is a spin eigenstate of the future measurement setting. Second, a particle position in 3-space \(\vec {x}(t)\), which evolves via a de Broglie–Bohm type guidance equation with the 3-space wavepacket \(\chi (\vec {x},t)\) acting as a local pilot wave. The joint ontic quantum state \(|\psi _o(t)\rangle \) fixes the measurement outcomes deterministically whereas the prepared quantum state \(|\psi _e(t)\rangle \) determines the distribution of the \(|\psi _o(t)\rangle \)’s over an ensemble. Both \(|\psi _o(t)\rangle \) and \(|\psi _e(t)\rangle \) evolve via the Schrodinger equation. Our model exactly reproduces the Bell correlations for any pair of measurement settings. We also consider ‘non-equilibrium’ extensions of the model with an arbitrary distribution of hidden variables. We show that, in non-equilibrium, the model generally violates no-signalling constraints while remaining local with respect to both ontology and interaction between particles. We argue that our model shares some structural similarities with the modal class of interpretations of quantum mechanics.

Keywords

Retrocausality 3D wavefunctions Local causality Bell’s theorem Modal interpretations 

Notes

Acknowledgements

I would like to thank my thesis advisor Antony Valentini for stimulating discussions and helpful suggestions throughout this work, and for encouragement to work on retrocausality. I would also like to thank Ken Wharton for several helpful comments and discussions on an earlier draft of the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Kinard Laboratory, Department of Physics and AstronomyClemson UniversityClemsonUSA

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