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

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.

💡 Research Summary

The paper proposes a novel mechanism for spontaneous wave‑function collapse by incorporating a non‑local gravitational self‑energy, motivated by string‑theoretic T‑duality, into the Schrödinger‑Newton framework. The authors begin by recalling the measurement problem and the long‑standing debate over whether collapse is a fundamental physical process or an emergent phenomenon. They note that gravity‑induced collapse models, especially those of Diòsi and Penrose, attribute the instability of macroscopic superpositions to a conflict between the equivalence principle and quantum superposition when different mass distributions generate distinct spacetime geometries.

Building on T‑duality, the authors introduce a minimal length scale (l_{0}=2L) and a modified propagator that regularizes the Newtonian potential: \