An experiment to test the discreteness of time
1Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
2Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
3Dipartimento di Fisica, La Sapienza Università di Roma, Piazzale Aldo Moro 5, Roma, Italy
4Aix-Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
5Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
6Basic Research Community for Physics e.V., Mariannenstraße 89, Leipzig, Germany
Published: | 2022-10-06, volume 6, page 826 |
Eprint: | arXiv:2007.08431v7 |
Doi: | https://doi.org/10.22331/q-2022-10-06-826 |
Citation: | Quantum 6, 826 (2022). |
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Abstract
Time at the Planck scale ($\sim 10^{-44} \mathrm{s}$) is an unexplored physical regime. It is widely believed that probing Planck time will remain for long an impossible task. Yet, we propose an experiment to test the discreteness of time at the Planck scale and estimate that it is not far removed from current technological capabilities.

Featured image: Spacetime view of the proposed experiment. A small mass $m$ undergoes a spin-dependent path superposition in the gravitational field of another mass $M$. The two branches accumulate a difference in phase $\delta\phi$ due to the gravitational interaction. In general relativistic terms, the difference in phase is due to a difference $\delta\tau$ in proper times along the two trajectories: $\delta\phi=\frac{m}{m_P}\frac{\delta\tau}{t_P},$ where $m_P$ and $t_P$ are the Planck mass and Planck time, respectively. If $\delta\tau$ can only take a finite set of values, then so does $\delta\phi$. We show that, under some assumptions, there exists a range of experimental parameters that allow to detect a hypothetical granularity of time.
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