Matter Density and Relativistic Models of Wave Function Collapse

TL;DR

This paper proposes a new relativistic law for matter density in wave function collapse models, resolving conflicts between different Lorentz frames and aligning with experimental results.

Contribution

It introduces a relativistic matter density law based on the wave function's past light cone, addressing a key relativity issue in collapse models.

Findings

The proposed law is consistent with all known experiments.

It resolves conflicts between Lorentz frames in relativistic models.

The model extends non-relativistic collapse theories to a relativistic context.

Abstract

Mathematical models for the stochastic evolution of wave functions that combine the unitary evolution according to the Schroedinger equation and the collapse postulate of quantum theory are well understood for non-relativistic quantum mechanics. Recently, there has been progress in making these models relativistic. But even with a fully relativistic law for the wave function evolution, a problem with relativity remains: Different Lorentz frames may yield conflicting values for the matter density at a space-time point. We propose here a relativistic law for the matter density function. According to our proposal, the matter density function at a space-time point x is obtained from the wave function psi on the past light cone of x by setting the i-th particle position in |psi|^2 equal to x, integrating over the other particle positions, and averaging over i. We show that the predictions that follow from this proposal agree with all known experimental facts.