Gravitational time dilation in extended quantum systems

The case of light clocks in Schwarzschild spacetime

authored by: Tupac Bravo, Dennis Rätzel, Ivette Fuentes
Abstract: The precision of optical atomic clocks is approaching a regime where they resolve gravitational time dilation on smaller scales than their own extensions. Hence, an accurate description of quantum clocks has to take their spatial extension into account. In this article, as a first step toward a fully relativistic description of extended quantum clocks, we investigate a quantized version of Einstein's light clock fixed at a constant distance from a large massive object like the Earth. The model consists of a quantum light field in a one-dimensional cavity in Schwarzschild spacetime, where the distance between the mirrors is fixed by a rigid rod. By comparing a vertical and a horizontal clock, we propose an operational way to define the clock time when the clock resolves gravitational time dilation on scales smaller than its extension. In particular, we show that the time measured by the vertical light clock is equivalent to the proper time defined at its center. We also derive fundamental bounds on the precision of these clocks for measurements of proper time and the Schwarzschild radius.
External Organisation(s): University of Vienna
Humboldt-Universität zu Berlin
University of Bremen
University of Southampton
Type: Article
Journal: AVS Quantum Science
Volume: 5
Publication date: 03.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Electronic, Optical and Magnetic Materials, Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Computer Networks and Communications, Physical and Theoretical Chemistry, Computational Theory and Mathematics, Electrical and Electronic Engineering
Electronic version(s): https://doi.org/10.1116/5.0123228 (Access: Unknown)

BibTeX

@article{737646c38db9408f933996f798a5cde7,
title = "Gravitational time dilation in extended quantum systems: The case of light clocks in Schwarzschild spacetime",
abstract = "The precision of optical atomic clocks is approaching a regime where they resolve gravitational time dilation on smaller scales than their own extensions. Hence, an accurate description of quantum clocks has to take their spatial extension into account. In this article, as a first step toward a fully relativistic description of extended quantum clocks, we investigate a quantized version of Einstein's light clock fixed at a constant distance from a large massive object like the Earth. The model consists of a quantum light field in a one-dimensional cavity in Schwarzschild spacetime, where the distance between the mirrors is fixed by a rigid rod. By comparing a vertical and a horizontal clock, we propose an operational way to define the clock time when the clock resolves gravitational time dilation on scales smaller than its extension. In particular, we show that the time measured by the vertical light clock is equivalent to the proper time defined at its center. We also derive fundamental bounds on the precision of these clocks for measurements of proper time and the Schwarzschild radius.",
author = "Tupac Bravo and Dennis R{\"a}tzel and Ivette Fuentes",
note = "Publisher Copyright: {\textcopyright} 2023 Author(s).",
year = "2023",
month = mar,
doi = "10.1116/5.0123228",
language = "English",
volume = "5",
journal = "AVS Quantum Science",
issn = "2639-0213",
publisher = "American Institute of Physics",
number = "1",
}