Probabilities and certainties within a causally symmetric model

TL;DR

This paper explores a causally symmetric, retrocausal interpretation of quantum mechanics that derives the Born rule, assigns definite spins to particles, and maintains Lorentz invariance without nonlocality.

Contribution

It introduces a causally symmetric model that reproduces quantum probabilities, assigns definite properties via boundary conditions, and preserves Lorentz invariance against Bell's theorem.

Findings

Derives the Born rule within the causally symmetric model.

Assigns definite spin values to particles with boundary conditions.

Maintains Lorentz invariance without nonlocality.

Abstract

This paper is concerned with the causally symmetric version of the familiar de Broglie-Bohm interpretation, this version allowing the spacelike nonlocality and the configuration space ontology of the original model to be avoided via the addition of retrocausality. Two different features of this alternative formulation are considered here. With regard to probabilities, it is shown that the model provides a derivation of the Born rule identical to that in Bohm's original formulation. This derivation holds just as well for a many-particle, entangled state as for a single particle. With regard to "certainties", the description of a particles spin is examined within the model and it is seen that a statistical description is no longer necessary once final boundary conditions are specified in addition to the usual initial state, with the particle then possessing a definite (but hidden) value for every spin component at intermediate times. These values are consistent with being the components of a single, underlying spin vector. The case of a two-particle entangled spin state is also examined and it is found that, due to the retrocausal aspect, each particle possesses its own definite spin during the entanglement, independent of the other particle. In formulating this picture, it is demonstrated how such a realistic model can preserve Lorentz invariance in the face of Bell's theorem and avoid the need for a preferred reference frame.