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

TL;DR

The paper confronts the problem of gravity-induced wave-function collapse by introducing a non-local gravitational self-energy inspired by string-theoretic T-duality into the Schrödinger–Newton framework. This regularizes the gravitational potential at short distances and makes the evolution nonlinear, sourcing a gravitational self-energy that depends on the quantum state. A key result is a model-independent collapse timescale that scales as the inverse square of the mass, with gravity-induced phases arising between inertial and freely falling frames. The work argues for a deterministic, non-stochastic mechanism for gravity-related collapse, distinct from the Diosi–Penrose stochastic models, and outlines potential experimental paths to test the predicted gravitational phases and collapse dynamics.

Abstract

We incorporate non-local gravitational self-energy, motivated by string-inspired T-duality, into the Schrödinger-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.