Arrival-time distributions as a probe of the preferred foliation in relativistic Bohmian mechanics

TL;DR

This paper proposes an experimental method to detect the preferred foliation in relativistic Bohmian mechanics by analyzing arrival-time distributions, potentially revealing superluminal signaling.

Contribution

It introduces an experimental protocol to empirically detect the preferred foliation in relativistic Bohmian models using arrival-time statistics.

Findings

Arrival-time distributions depend on measurement order relative to the foliation.

The proposed experiment could reveal the preferred foliation.

Superluminal signaling may be possible under certain conditions.

Abstract

Relativistic extensions of de Broglie-Bohm theory postulate a preferred foliation of space-time, an additional structure essential for defining simultaneous configurations on Minkowski space-time, but conventionally believed to be empirically undetectable at quantum equilibrium. In this paper, we outline an experimental protocol for empirically detecting the preferred foliation, which is assumed to be flat for simplicity. Building on the arrival-time distributions for spin-1/2 particles predicted by Das and D\"urr, we show that in an EPRB-type experiment with spacelike-separated spin and arrival-time measurements, the observed arrival-time statistics will depend crucially on the temporal order of these measurements relative to the preferred foliation of space-time. This dependence offers a potential experimental signature of the preferred foliation postulated by relativistic Bohmian models. Moreover, it implies the possibility of superluminal signaling.