Relativistic Dynamical Collapse Model for a Scalar Field

TL;DR

This paper extends the CSL dynamical collapse model to a relativistic scalar field, ensuring relativistic invariance, probability normalization, and no vacuum energy production, with collapse toward eigenstates over time.

Contribution

It introduces a relativistic generalization of the CSL collapse model for scalar fields, maintaining key physical properties and invariance.

Findings

The modified Schrödinger equation is relativistically invariant.

Probabilities for all collapse outcomes sum to one.

No energy is produced from the vacuum during collapse.

Abstract

A natural generalization of the CSL (Continuous Spontaneous Localization) theory of dynamical collapse is applied to a relativistic quantum scalar field $\phi({\bf x},t)$. It is shown that the modified Schr\"odinger equation is relativistically invariant, that the probabilities associated to all possible values of the classical scalar random field $w({\bf x},t)$ (which determines the eventual state of collapse) add up to 1, that there is no energy production out of the vacuum and, in the limit of large time, the collapse is toward eigenstates of $\phi({\bf x},0)$.