On the CSL Scalar Field Relativistic Collapse Model

TL;DR

This paper discusses a relativistic CSL collapse model using a scalar field, providing solutions for the density matrix and analyzing collapse behavior and energy production, highlighting its theoretical soundness despite physical limitations.

Contribution

It introduces a relativistic CSL model with a scalar field operator and provides explicit solutions for the density matrix in different Hamiltonian scenarios.

Findings

Collapse favors eigenstates close to initial Gaussian states

Particle production dominates the density matrix over time

Model is theoretically sound but not physically viable due to energy increase

Abstract

The CSL dynamical collapse structure, adapted to the relativistically invariant model where the collapse-generating operator is a one-dimensional scalar field $\hat\phi(x,t)$ (mass $m$) is discussed. A complete solution for the density matrix is given, for an initial state $|\psi,0\rangle=\frac{1}{\sqrt{2}}[|L\rangle+|R\rangle]$ when the Hamiltonian $\hat H$ is set equal to 0, and when $\hat H$ is the free field Hamiltonian. Here $|L\rangle, |R\rangle$ are coherent states which represent clumps of particles, with mean particle number density $N\chi_{i}^{2}(x)$, where $\chi_{1}(x),\chi_{1}(x) $ are gaussians of width $\sigma>>m^{-1}$ with mean positions separated by distance $>>\sigma$. It is shown that, with high probability, the solution for $\hat H=0$ (identical to the short time solution for $\hat H\neq 0$) favors collapse toward eigenstates of the scalar field whose eigenvalues are close to $\sim\chi_{i}(x)$. Thus, this collapse dynamics results in essentially one clump of particles. However, eventually particle production dominates the density matrix since, as is well known, the collapse generates energy/sec-volume of every particle momentum in equal amounts. Because of the particle production, this is not an experimentally viable physical theory but, as is emphasized by the discussion, it is a sound relativistic collapse model, with sensible collapse behavior.