Quantum reference frames for an indefinite metric

Author(s)
Anne Catherine de la Hamette, Viktoria Kabel, Esteban Castro-Ruiz, Časlav Brukner
Abstract

The current theories of quantum physics and general relativity on their own do not allow us to study situations in which the gravitational source is quantum. Here, we propose a strategy to determine the dynamics of objects in the presence of mass configurations in superposition, and hence an indefinite spacetime metric, using quantum reference frame (QRF) transformations. Specifically, we show that, as long as the mass configurations in the different branches are related via relative-distance-preserving transformations, one can use an extension of the current framework of QRFs to change to a frame in which the mass configuration becomes definite. Assuming covariance of dynamical laws under quantum coordinate transformations, this allows to use known physics to determine the dynamics. We apply this procedure to find the motion of a probe particle and the behavior of clocks near the mass configuration, and thus find the time dilation caused by a gravitating object in superposition. Comparison with other models shows that semi-classical gravity and gravitational collapse models do not obey the covariance of dynamical laws under quantum coordinate transformations.

Organisation(s)
Quantum Optics, Quantum Nanophysics and Quantum Information
External organisation(s)
Österreichische Akademie der Wissenschaften (ÖAW), Eidgenössische Technische Hochschule Zürich, Université Paris-Saclay
Journal
Communications Physics
Volume
6
No. of pages
15
ISSN
2399-3650
DOI
https://doi.org/10.1038/s42005-023-01344-4
Publication date
08-2023
Peer reviewed
Yes
Austrian Fields of Science 2012
103025 Quantum mechanics, 103028 Theory of relativity
ASJC Scopus subject areas
Physics and Astronomy(all)
Portal url
https://ucrisportal.univie.ac.at/en/publications/quantum-reference-frames-for-an-indefinite-metric(36cf45cf-605c-4816-b18f-0285c628a648).html