Emergence of Gravitational Potential and Time Dilation from Non-interacting Systems Coupled to a Global Quantum Clock
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909850813857792 |
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| author | Singh, Ashmeet Friedrich, Oliver |
| author_facet | Singh, Ashmeet Friedrich, Oliver |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01263 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Emergence of Gravitational Potential and Time Dilation from Non-interacting Systems Coupled to a Global Quantum Clock Singh, Ashmeet Friedrich, Oliver General Relativity and Quantum Cosmology Quantum Physics 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. |
| title | Emergence of Gravitational Potential and Time Dilation from Non-interacting Systems Coupled to a Global Quantum Clock |
| topic | General Relativity and Quantum Cosmology Quantum Physics |
| url | https://arxiv.org/abs/2304.01263 |