Modified Sch\"odinger dynamics with attractive densities

TL;DR

This paper proposes a deterministic modification to the Schr"odinger equation that suppresses macroscopic density fluctuations, ensuring unique macroscopic states without stochastic processes, aligning the wave function more closely with physical reality.

Contribution

It introduces a new deterministic dynamics with an attraction term based on de Broglie-Bohm positions, avoiding stochastic collapse models and ensuring macroscopic uniqueness.

Findings

Automatically ensures macroscopic uniqueness

Suppresses macroscopic density fluctuations

Aligns wave function with physical reality

Abstract

The linear Schr\"{o}dinger equation does not predict that macroscopic bodies should be located at one place only. Quantum mechanics textbooks generally solve the problem by introducing the projection postulate, which forces definite values to emerge during position measurements; many other interpretations have also been proposed.\ Here, in the same spirit as the GRW and CSL theories, we modify the Schr\"{o}dinger equation in a way that efficiently cancels macroscopic density fluctuations in space.\ Instead of introducing the stochastic dynamics of GRW or CSL, we assume a deterministic dynamics that includes an attraction term towards the density in space of the de Broglie-Bohm position of particles. This automatically ensures macroscopic uniqueness, so that the state vector can be considered as a direct representation of physical reality.