Emergence of Gravitational Potential and Time Dilation from Non-interacting Systems Coupled to a Global Quantum Clock

• URL: http://arxiv.org/abs/2304.01263v2
• Date: Thu, 16 Oct 2025 20:34:28 GMT
• Title: Emergence of Gravitational Potential and Time Dilation from Non-interacting Systems Coupled to a Global Quantum Clock
• Authors: Ashmeet Singh, Oliver Friedrich,
• Abstract summary: We study gravitational back-reaction within the Page-Wootters formulation of quantum mechanics by treating time as a quantum degree of freedom.<n>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.
• Score: 0.02864713389096699
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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