# The effect of time-dilation on Bell experiments in the retrocausal Brans model

## TL;DR

This paper extends the retrocausal Brans model to a relativistic Bell experiment with time-dilation, predicting observable differences in particle distributions that can be tested experimentally, highlighting the model's relativistic advantages.

## Contribution

It generalizes the retrocausal Brans model to account for relativistic effects like time-dilation in Bell experiments, providing testable predictions and discussing implications for other hidden variable theories.

## Key findings

- The model predicts less separation of eigenpackets under time-dilation.
- Particle distribution patterns differ between wings in the experiment.
- The model's predictions are experimentally testable.

## Abstract

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 generalised 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 $\psi$-epistemic interpretation may resolve several difficulties encountered in relativistic generalisations 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.