# Local de Broglie-Bohm Trajectories from Entangled Wavefunctions

## TL;DR

This paper proposes a local interpretation of entangled particle trajectories in quantum mechanics using retarded wavefunctions, challenging the nonlocal view and suggesting experimental ways to test locality loopholes.

## Contribution

It introduces a local model for entangled particles using retarded wavefunctions that can violate Bell's inequality without detector inefficiencies.

## Key findings

- Local model can violate Bell's inequality with retarded wavefunctions.
- Local interpretation is possible for non-ultra-relativistic particles.
- Magnetic field changes can create detector loopholes in experiments.

## Abstract

We present a local interpretation of what is usually considered to be a nonlocal de Broglie-Bohm trajectory prescription for an entangled singlet state of massive particles. After reviewing various meanings of the term ``nonlocal'', we show that by using appropriately retarded wavefunctions (i.e., the locality loophole) this local model can violate Bell's inequality, without making any appeal to detector inefficiencies. We analyze a possible experimental configuration appropriate to massive two-particle singlet wavefunctions and find that as long as the particles are not ultra-relativistic, a locality loophole exists and Dirac wave(s) can propagate from Alice or Bob's changing magnetic field, through space, to the other detector, arriving before the particle and thereby allowing a local interpretation to the 2-particle de Broglie-Bohm trajectories. We also propose a physical effect due to changing magnetic fields in a Stern-Gerlach EPR setup that will throw away events and create a detector loophole in otherwise perfectly efficient detectors, an effect that is only significant for near-luminal particles that might otherwise close the locality loophole.