Gravitational time dilation in extended quantum systems

The case of light clocks in Schwarzschild spacetime

verfasst von: 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.
Externe Organisation(en): Universität Wien
Humboldt-Universität zu Berlin
Universität Bremen
University of Southampton
Typ: Artikel
Journal: AVS Quantum Science
Band: 5
Publikationsdatum: 03.2023
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Elektronische, optische und magnetische Materialien, Atom- und Molekularphysik sowie Optik, Physik der kondensierten Materie, Computernetzwerke und -kommunikation, Physikalische und Theoretische Chemie, Theoretische Informatik und Mathematik, Elektrotechnik und Elektronik
Elektronische Version(en): https://doi.org/10.1116/5.0123228 (Zugang: Unbekannt)

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",
}