Measuring spacetime quantities at the interplay between quantum theory and general relativity raises several interesting questions. In particular, how do we characterise quantum time evolution in the absence of an external time parameter, as demanded by general relativity? What are the limits to our ability to define time evolution, by means of physical clocks, at the overlap between quantum mechanics and general relativity?
In [2] we find fundamental limitations to our ability to operationally define time intervals at different spatial locations due to a gravity-mediated entangling effect between quantum clocks.
In [3] we compare two well-known frameworks to describe consecutive measurements on a quantum system in the absence of an external background time. We find that, if measurements are modelled dynamically and clocks do not have infinite resources, there are modifications to our well-known notions of time evolution and definite temporal order.
References:
[2] Castro Ruiz, Esteban, Flaminia Giacomini, and Časlav Brukner. "Entanglement of quantum clocks through gravity." Proceedings of the National Academy of Sciences 114.12: E2303-E2309. (2017).
[3] Hausmann, L., Schmidhuber, A., & Castro-Ruiz, E. Measurement events relative to temporal quantum reference frames. arXiv preprint arXiv:2308.10967. (2023).
Recommended reading:
- Giovannetti, V., Lloyd, S., & Maccone, L. Quantum time. Physical Review D, 92(4), 045033. (2015).
- Höhn, P. A., Smith, A. R., & Lock, M. P. Trinity of relational quantum dynamics. Physical Review D, 104(6), 066001. (2021).