2023/04/03 by Ashmeet Singh, Oliver Friedrich, Singh, Ashmeet +1
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2304.01263
openalex publication_date 2023/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
We study gravitational back-reaction within the Page-Wootters formulation of quantum mechanics by treating time as a quantum degree of freedom. Our model introduces a distinction between global coordinate time, represented as a relational quantum observable, and proper time, measured by internal quantum degrees of freedom of physical systems. By coupling mass-energy with coordinate time through a Wheeler-DeWitt-like constraint, we demonstrate the natural emergence of gravitational time dilation. In the presence of a massive object this agrees with time dilation in a Schwarzchild metric at leading order if the interaction strength is taken to be representative of the gravitational coupling G. Additionally, when two particles independently couple to the time coordinate, a Newtonian gravitational interaction arises in the low-energy limit, showing how gravitational potential can emerge from non-interacting quantum systems. Our approach also reveals renormalization features, potentially softening high-energy divergences and suggesting that particles in superposition might introduce quantum corrections to gravitational time dilation.