Relating approaches to interacting quantum clocks and systems
Abstract
The problem of describing the dynamics of quantum systems relative to quantum clocks with which they interact is relevant to the physics of quantum reference frames and quantum gravity alike. There have been different approaches that derive a relational time-dependent Schrödinger equation for the system relative to the clock from a time-independent Hamiltonian constraint. We show that some of these approaches, due to Smith and Ahmadi, Gemsheim and Rost, as well as the so-called Born-Oppenheimer approach, can be unified in a single framework for describing conditional quantum states. In particular, the Born-Oppenheimer approach to quantum cosmology is seen to correspond to a type of interacting Page-Wootters formalism. We discuss the issue of unitarity and linearity, or lack thereof, in the relational dynamics, and we conclude with a brief outlook to further developments.
Related
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BibTeX
@misc{semiao2026relating,
title = {{Relating approaches to interacting quantum clocks and systems}},
author = {Artur Semião and Leonardo Chataignier},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40791},
eprint = {2610.40791},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40791},
}
RIS
TY - UNPB
TI - Relating approaches to interacting quantum clocks and systems
AU - Artur Semião
AU - Leonardo Chataignier
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40791
UR - https://arxiv.org/abs/2610.40791
AB - The problem of describing the dynamics of quantum systems relative to quantum clocks with which they interact is relevant to the physics of quantum reference frames and quantum gravity alike. There have been different approaches that derive a relational time-dependent Schrödinger equation for the system relative to the clock from a time-independent Hamiltonian constraint. We show that some of these approaches, due to Smith and Ahmadi, Gemsheim and Rost, as well as the so-called Born-Oppenheimer approach, can be unified in a single framework for describing conditional quantum states. In particular, the Born-Oppenheimer approach to quantum cosmology is seen to correspond to a type of interacting Page-Wootters formalism. We discuss the issue of unitarity and linearity, or lack thereof, in the relational dynamics, and we conclude with a brief outlook to further developments.
ER -