Stress Tensor for Quantized Random Field and Wave Function Collapse

TL;DR

This paper develops a symmetric energy-momentum tensor for the quantized random field in collapse models, enabling analysis of its gravitational effects and energy conservation within a quantum collapse framework.

Contribution

It introduces a conserved energy-momentum tensor for the quantized random field in collapse models, facilitating gravitational studies of the field's energy density.

Findings

Constructed a symmetric, conserved energy-momentum tensor for the random field.

Analyzed the field's energy density in particle interactions and cosmological models.

Explored the gravitational implications of the random field's energy.

Abstract

The continuous spontaneous localization (CSL) theory of dynamical wave function collapse is an experimentally testable alternative to non-relativistic quantum mechanics. In it, collapse occurs because particles interact with a classical random field. However, particles gain energy from this field, i.e., particle energy is not conserved. Recently, it has been shown how to construct a theory dubbed "completely quantized collapse" (CQC) which is predictively equivalent to CSL. In CQC, a quantized random field is introduced, and CSL's classical random field becomes its eigenvalue. In CQC, energy is conserved, which allows one to understand that energy is conserved in CSL, as the particle's energy gain is compensated by the random field's energy loss. Since the random field has energy, it should have gravitational consequences. For that, one needs to know the random field's energy density. In this paper, it is shown how to construct a symmetric, conserved, energy-momentum-stress-density tensor associated with the quantized random field, even though this field obeys no dynamical equation and has no Lagrangian. Then, three examples are given involving the random field's energy density. One considers interacting particles, the second treats a "cosmological" particle creation model, the third involves the gravity of the random field.