A Relativistic Dynamical Collapse Model

TL;DR

This paper introduces a Lorentz-invariant relativistic collapse model based on a quantum scalar field, analyzing its dynamics, parameters, and implications for mass change over cosmic timescales.

Contribution

It develops a relativistic dynamical collapse model using a quantum scalar field with a Lorentz-invariant formalism and explores its physical implications and parameter choices.

Findings

Collapse rate matches non-relativistic CSL with specific parameters

Vacuum state remains unexcited in this model

Mass change over universe's age can be acceptable with certain parameter choices

Abstract

A model is discussed where all operators are constructed from a quantum scalar field whose energy spectrum takes on all real values. The Schr\"odinger picture wave function depends upon space and time coordinates for each particle, as well as an inexorably increasing evolution parameter $s$ which labels a foliation of space-like hypersurfaces. The model is constructed to be manifestly Lorentz invariant in the interaction picture. Free particle states and interactions are discussed in this framework. Then, the formalism of the CSL (Continuous Spontaneous Localization) theory of dynamical collapse is applied. The collapse-generating operator is chosen to to be the particle number space-time density. Unlike previous relativistically invariant models, the vacuum state is not excited. The collapse dynamics depends upon two parameters, a parameter $\Lambda$ which represents the collapse rate/volume and a scale factor $\ell$. A common example of collapse dynamics, involving a clump of matter in a superposition of two locations, is analyzed. The collapse rate is shown to be identical to that of non-relativistic CSL when the GRW-CSL choice of $\ell=a=10^{-5}$cm, is made, along with $\Lambda=\lambda/a^{3}$ (GRW-CSL choice $\lambda=10^{-16}s^{-1}$). However, it is also shown that the change of mass of a nucleon over the age of the universe is then unacceptably large. The case where $\ell$ is the size of the universe is then considered. It is shown that the collapse behavior is satisfactory and the change of mass over the age of the universe is acceptably small, when $\Lambda= \lambda/\ell a^{2}$.