Constraints on the noise in dynamical reduction models

TL;DR

This paper investigates how the choice of the Heaviside function value at zero affects predictions in collapse models, constraining the properties of the noise field to ensure probability conservation.

Contribution

It demonstrates that only a specific value of the Heaviside function at zero ensures particle number conservation in collapse models, constraining the noise field's physical properties.

Findings

Only a single Heaviside value preserves particle number.

Constraints on the noise field depend on the Heaviside function choice.

Physical properties of the noise are essential for consistent collapse models.

Abstract

The dynamics of a quantum system with internal degrees of freedom undergoing spontaneous collapse in the position basis are analysed; e.g., neutral mesons or neutrinos. Surprisingly, the value of the Heaviside function $\theta(x)$ at $x=0$ that can in general be chosen in the interval [0,1] leads to different physical predictions. For the QMUPL (Quantum Mechanics with Universal Position Localization) model only a single value leads to probabilities conserving the particle number. Herewith the physical properties of the noise field can be constrained. This opens a road to study the physical properties of the noise field essential for collapse models.