Relativistic Collapse Model with Quantised Time Variables

TL;DR

This paper introduces a relativistic collapse model where position and time are fundamental operators, providing a covariant framework with state evolution and collapse mechanisms consistent with quantum probabilities.

Contribution

It presents a novel relativistic collapse model with quantised time variables, ensuring Poincaré covariance and energy conservation in expectation.

Findings

Model achieves Poincaré covariance.

States can have definite mass and configuration.

Collapse dynamics follow Born rule probabilities.

Abstract

A relativistic collapse model for distinguishable particles is presented. Position and time, for each particle, are the fundamental operators of the theory. The Schr\"odinger equation is of the CSL form, with a Hermitian Hamiltonian and an anti-Hermitian, white-noise dependent, Hamiltonian. It generates state vector evolution parametrised by an "evolution parameter". It is shown how this can be interpreted as an evolving state in spacetime with collapses satisfying Born rule probabilities, and how certain choices of collapse generating operators lead to states of definite mass and definite configuration in spacetime. The model is Poincar\'e covariant and conserves energy in expectation.