Quantum area fluctuations from gravitational phase space
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1.
Perimeter Institute
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2.
California Institute of Technology
Abstract
We study the gravitational phase space associated to a stretched horizon within a finite-sized causal diamond in (d + 2)-dimensional spacetimes. By imposing the Raychaudhuri equation, we obtain its constrained symplectic form using the covariant phase space formalism and derive the relevant quantum commutators by inverting the symplectic form and quantizing. Finally, we compute the area fluctuations of the causal diamond by taking a Carrollian limit of the stretched horizon in pure Minkowski spacetime, and derive the relationship〈(ΔA)² 〉≥ 2πG/d〈A〉, showing that the variance of the area fluctuations is proportional to the area itself.
Copyright and License
© The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3.
Acknowledgement
We thank Mathew Bub for collaborating in the early stages of this work. We would also like to thank Kwinten Fransen, Laurent Freidel, and Prahar Mitra for useful conversations.
Funding
Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. L.C. is grateful to K.Z. and T.H. for generously hosting him twice at Caltech, where this project was initiated and brought to completion. T.H. and K.Z. are supported by the Heising-Simons Foundation “Observational Signatures of Quantum Gravity” collaboration grant 2021-2817, the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and the Walter Burke Institute for Theoretical Physics. K.Z. is also supported by a Simons Investigator award.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2504.12282 (arXiv)
Funding
- Innovation, Science and Economic Development Canada
- Ministry of Colleges and Universities
- Heising-Simons Foundation
- 2021-2817
- United States Department of Energy
- DE-SC0011632
- SCOAP3
Dates
- Accepted
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2025-07-13
- Available
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2025-08-25Published