Spontaneous wave function collapse from non-local gravitational self-energy

TL;DR

This paper explores how non-local gravitational self-energy influences wave function collapse, suggesting gravity-induced instability of superpositions and deriving a spontaneous collapse time related to mass.

Contribution

It introduces a non-local gravitational self-energy into the Schrödinger-Newton equation, linking gravity with wave function collapse in a novel way.

Findings

Wave functions in different frames differ by a gravitational phase shift.

Collapse time is inversely proportional to the system's mass.

Spontaneous collapse arises from tension between quantum superposition and gravity.

Abstract

We incorporate non-local gravitational self-energy, motivated by string-inspired T-duality, into the Schr\"odinger-Newton equation. In this framework spacetime has an intrinsic non-locality, rendering the standard linear superposition principle only an approximation valid in the absence of gravitational effects. We then invert the logic by assuming the validity of linear superposition and demonstrate that such superpositions inevitably become unstable once gravity is included. The resulting wave-function collapse arises from a fundamental tension between the equivalence principle and the quantum superposition principle in a semiclassical spacetime background. We further show that wave functions computed in inertial and freely falling frames differ by a gravitationally induced phase shift containing linear and cubic time contributions along with a constant global term. These corrections produce a global phase change and lead to a spontaneous, model-independent collapse time inversely proportional to the mass of the system.