# No Signalling and Unknowable Bohmian Particle Positions

## TL;DR

This paper demonstrates that in Bohmian mechanics, the only accessible information about particle positions, compatible with no-signalling, is their distribution given by the wave function, highlighting the non-locality and unknowability of exact positions.

## Contribution

It shows that in simple quantum models, Bohmian particle positions cannot be known precisely or prepared independently, due to non-locality and no-signalling constraints.

## Key findings

- Particle positions follow the wave function distribution |ff(x)|^2.
- Exact positions cannot be prepared independently from the wave function.
- Knowledge of precise positions would enable faster-than-light signaling.

## Abstract

We exhibit in a model with simple dynamics, specifically a particle in a square box or two particles in one dimensional boxes, that if an experimenter can prepare the initial wave function of a system, the maximal information about the positions of Bohmian particles that is compatible with "no signalling" is that they are distributed according to $|\psi(x)|^2$. In particular, the positions cannot be prepared independently from the wave function. Any sharper "actual" position of the particle must be inaccessible since it could be used to send signals instantaneously. This is a consequence of the non-local character of the Bohmian dynamical law.