Quantum mechanics without spacetime III: a proposal for a non-linear Schrodinger equation

TL;DR

This paper proposes a non-linear modification to the Schrödinger equation that depends on particle mass, potentially explaining wave-function collapse and remaining consistent with current experimental tests.

Contribution

It introduces a mass-dependent non-linear correction to the Schrödinger equation, suggesting a possible mechanism for wave-function collapse near a critical mass scale.

Findings

Corrections are negligible for masses far from the critical value.

Significant corrections occur near the critical mass, affecting energy levels.

Current experiments do not rule out these non-linear corrections.

Abstract

It is proposed that the Schrodinger equation for a free point particle has non-linear corrections which depend on the mass of the particle. It is assumed that the corrections become extremely small when the mass is much smaller or much larger than a critical value (the critical value being related to but smaller than Planck mass). The corrections become significant when the mass is close to this critical value and could play a role in explaining wave-function collapse. It appears that such corrections are not ruled out by present day experimental tests of the Schrodinger equation. Corrections to the energy levels of a harmonic oscillator are calculated.