An experiment to test the discreteness of time

Marios Christodoulou; Andrea Di Biagio; Pierre Martin-Dussaud

doi:10.22331/q-2022-10-06-826

An experiment to test the discreteness of time

Marios Christodoulou^1,2, Andrea Di Biagio^1,3,4, and Pierre Martin-Dussaud^4,5,6

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).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

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.

► BibTeX data

@article{Christodoulou2022experimenttotest,
  doi = {10.22331/q-2022-10-06-826},
  url = {https://doi.org/10.22331/q-2022-10-06-826},
  title = {An experiment to test the discreteness of time},
  author = {Christodoulou, Marios and Biagio, Andrea Di and Martin-Dussaud, Pierre},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {826},
  month = oct,
  year = {2022}
}

► References

[1] G. Edward Marti, Ross B. Hutson, Akihisa Goban, Sara L. Campbell, Nicola Poli, and Jun Ye. ``Imaging optical frequencies with 100 $\mu$Hz precision and 1.1 $\mu$m resolution''. Physical Review Letters 120, 103201 (2018). arXiv:1711.08540.
https://doi.org/10.1103/physrevlett.120.103201
arXiv:1711.08540

[2] Garrett Wendel, Luis Martinez, and Martin Bojowald. ``Physical implications of a fundamental period of time''. Physical Review Letters 124, 241301 (2020). arXiv:2005.11572.
https://doi.org/10.1103/physrevlett.124.241301
arXiv:2005.11572

[3] Sougato Bose, Anupam Mazumdar, Gavin W. Morley, Hendrik Ulbricht, Marko Toroš, Mauro Paternostro, Andrew Geraci, Peter Barker, M. S. Kim, and Gerard Milburn. ``A Spin Entanglement Witness for Quantum Gravity''. Physical Review Letters 119, 240401 (2017). arXiv:1707.06050.
https://doi.org/10.1103/physrevlett.119.240401
arXiv:1707.06050

[4] Chiara Marletto and Vlatko Vedral. ``Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity''. Physical Review Letters 119, 240402 (2017). arXiv:1707.06036.
https://doi.org/10.1103/physrevlett.119.240402
arXiv:1707.06036

[5] Ryan J. Marshman, Anupam Mazumdar, and Sougato Bose. ``Locality and Entanglement in Table-Top Testing of the Quantum Nature of Linearized Gravity''. Physical Review A 101, 052110 (2020). arXiv:1907.01568.
https://doi.org/10.1103/physreva.101.052110
arXiv:1907.01568

[6] Tanjung Krisnanda, Guo Yao Tham, Mauro Paternostro, and Tomasz Paterek. ``Observable quantum entanglement due to gravity''. npj Quantum Information 6, 12 (2020). arXiv:1906.08808.
https://doi.org/10.1038/s41534-020-0243-y
arXiv:1906.08808

[7] Sougato Bose. ``Table-top Testing of the Quantum Nature of Gravity: Assumptions, Implications and Practicalities of a Proposal'' (2020).

[8] Richard Howl, Vlatko Vedral, Devang Naik, Marios Christodoulou, Carlo Rovelli, and Aditya Iyer. ``Non-Gaussianity as a signature of a quantum theory of gravity''. PRX Quantum 2, 010325 (2021). arXiv:2004.01189.
https://doi.org/10.1103/prxquantum.2.010325
arXiv:2004.01189

[9] Markus Arndt and Klaus Hornberger. ``Testing the limits of quantum mechanical superpositions''. Nature Physics 10, 271–277 (2014). arXiv:1410.0270.
https://doi.org/10.1038/nphys2863
arXiv:1410.0270

[10] Oriol Romero-Isart, Mathieu L. Juan, Romain Quidant, and J. Ignacio Cirac. ``Toward Quantum Superposition of Living Organisms''. New Journal of Physics 12, 033015 (2010). arXiv:0909.1469.
https://doi.org/10.1088/1367-2630/12/3/033015
arXiv:0909.1469

[11] Sandra Eibenberger, Stefan Gerlich, Markus Arndt, Marcel Mayor, and Jens Tüxen. ``Matter-wave interference with particles selected from a molecular library with masses exceeding 10000 amu''. Physical Chemistry Chemical Physics 15, 14696 (2013). arXiv:1310.8343.
https://doi.org/10.1039/c3cp51500a
arXiv:1310.8343

[12] Marios Christodoulou and Carlo Rovelli. ``On the possibility of laboratory evidence for quantum superposition of geometries''. Physics Letters B 792, 64–68 (2019). arXiv:1808.05842.
https://doi.org/10.1016/j.physletb.2019.03.015
arXiv:1808.05842

[13] Marios Christodoulou and Carlo Rovelli. ``On the possibility of experimental detection of the discreteness of time''. Frontiers in Physics 8, 207 (2020). arXiv:1812.01542.
https://doi.org/10.3389/fphy.2020.00207
arXiv:1812.01542

[14] Sougato Bose and Gavin W. Morley. ``Matter and spin superposition in vacuum experiment (MASSIVE)'' (2018). arXiv:1810.07045.
arXiv:1810.07045

[15] Hadrien Chevalier, A. J. Paige, and M. S. Kim. ``Witnessing the non-classical nature of gravity in the presence of unknown interactions''. Physical Review A 102, 022428 (2020). arXiv:2005.13922.
https://doi.org/10.1103/physreva.102.022428
arXiv:2005.13922

[16] R. Colella, A. W. Overhauser, and S. A. Werner. ``Observation of Gravitationally Induced Quantum Interference''. Physical Review Letters 34, 1472–1474 (1975).
https://doi.org/10.1103/physrevlett.34.1472

[17] Hartmut Abele and Helmut Leeb. ``Gravitation and quantum interference experiments with neutrons''. New Journal of Physics 14, 055010 (2012). arXiv:1207.2953.
https://doi.org/10.1088/1367-2630/14/5/055010
arXiv:1207.2953

[18] Julen S. Pedernales, Gavin W. Morley, and Martin B. Plenio. ``Motional Dynamical Decoupling for Matter-Wave Interferometry''. Physical Review Letters 125, 023602 (2020). arXiv:1906.00835.
https://doi.org/10.1103/physrevlett.125.023602
arXiv:1906.00835

[19] Thomas W. van de Kamp, Ryan J. Marshman, Sougato Bose, and Anupam Mazumdar. ``Quantum Gravity Witness via Entanglement of Masses: Casimir Screening''. Physical Review A 102, 062807 (2020). arXiv:2006.06931.
https://doi.org/10.1103/physreva.102.062807
arXiv:2006.06931

[20] H. Pino, J. Prat-Camps, K. Sinha, B. P. Venkatesh, and O. Romero-Isart. ``On-chip quantum interference of a superconducting microsphere''. Quantum Science and Technology 3, 025001 (2018). arXiv:1603.01553.
https://doi.org/10.1088/2058-9565/aa9d15
arXiv:1603.01553

[21] National High Magnetic Field Laboratory. ``Selected Scientific Publications Generated from Research Conducted in the 100 Tesla Multi-Shot Magnet''. Technical report. National High Magnetic Field Laboratory (2020). url: nationalmaglab.org/user-facilities/pulsed-field-facility/instruments-pff/100-tesla-multi-shot-magnet.
https://nationalmaglab.org/user-facilities/pulsed-field-facility/instruments-pff/100-tesla-multi-shot-magnet

[22] J. D. Carrillo-Sánchez, J. M. C. Plane, W. Feng, D. Nesvorný, and D. Janches. ``On the size and velocity distribution of cosmic dust particles entering the atmosphere''. Geophysical Research Letters 42, 6518–6525 (2015).
https://doi.org/10.1002/2015gl065149

[23] Matthew Dean Schwartz. ``Quantum field theory and the standard model''. Cambridge University Press. New York (2014).
https://doi.org/10.1017/9781139540940

[24] Andrea Di Biagio (2022). code: AndreaDiBiagio/TimeDiscretenessExperimentPlots.
https://github.com/AndreaDiBiagio/TimeDiscretenessExperimentPlots

[25] Oriol Romero-Isart. ``Quantum superposition of massive objects and collapse models''. Physical Review A 84, 052121 (2011). arXiv:1110.4495.
https://doi.org/10.1103/physreva.84.052121
arXiv:1110.4495

[26] Igor Pikovski, Magdalena Zych, Fabio Costa, and Caslav Brukner. ``Universal decoherence due to gravitational time dilation''. Nature Physics 11, 668–672 (2015). arXiv:1311.1095.
https://doi.org/10.1038/nphys3366
arXiv:1311.1095

[27] S. Bhagavantam and D. A. A. S. Narayana Rao. ``Dielectric Constant of Diamond''. Nature 161, 729–729 (1948).
https://doi.org/10.1038/161729a0

[28] F. Nicastro, J. Kaastra, Y. Krongold, S. Borgani, E. Branchini, R. Cen, M. Dadina, C. W. Danforth, M. Elvis, F. Fiore, A. Gupta, S. Mathur, D. Mayya, F. Paerels, L. Piro, D. Rosa-Gonzales, J. Schaye, J. M. Shull, J. Torres-Zafra, N. Wijers, and L. Zappacosta. ``Observations of the Missing Baryons in the warm-hot intergalactic medium''. Nature 558, 406–409 (2018). arXiv:1806.08395.
https://doi.org/10.1038/s41586-018-0204-1
arXiv:1806.08395

[29] Katia M. Ferrière. ``The interstellar environment of our galaxy''. Reviews of Modern Physics 73, 1031–1066 (2001).
https://doi.org/10.1103/revmodphys.73.1031

[30] G. Gabrielse, X. Fei, L. Orozco, R. Tjoelker, J. Haas, H. Kalinowsky, T. Trainor, and W. Kells. ``Thousandfold improvement in the measured antiproton mass''. Physical Review Letters 65, 1317–1320 (1990).
https://doi.org/10.1103/physrevlett.65.1317

[31] G. Gabrielse. ``Comparing the antiproton and proton, and opening the way to cold antihydrogen''. In Advances In Atomic, Molecular, and Optical Physics. Volume 45, pages 1–39. Elsevier (2001).
https://doi.org/10.1016/S1049-250X(01)80037-9

[32] Konrad Zuse. ``Rechnender Raum (Calculating Space)''. Schriften Zur Dataverarbeitung 1 (1969). url: philpapers.org/rec/ZUSRR.
https://philpapers.org/rec/ZUSRR

[33] Ted Jacobson, Stefano Liberati, and David Mattingly. ``Lorentz violation at high energy: Concepts, phenomena and astrophysical constraints''. Annals of Physics 321, 150–196 (2006). arXiv:astro-ph/0505267.
https://doi.org/10.1016/j.aop.2005.06.004
arXiv:astro-ph/0505267

[34] A. A. Abdo, M. Ackermann, M. Ajello, K. Asano, W. B. Atwood, M. Axelsson, L. Baldini, J. Ballet, G. Barbiellini, M. G. Baring, and others. ``A limit on the variation of the speed of light arising from quantum gravity effects''. Nature 462, 331–334 (2009).
https://doi.org/10.1038/nature08574

[35] Giovanni Amelino-Camelia. ``Burst of support for relativity''. Nature 462, 291–292 (2009).
https://doi.org/10.1038/462291a

[36] Robert J. Nemiroff, Ryan Connolly, Justin Holmes, and Alexander B. Kostinski. ``Bounds on Spectral Dispersion from Fermi-Detected Gamma Ray Bursts''. Physical Review Letters 108, 231103 (2012).
https://doi.org/10.1103/physrevlett.108.231103

[37] D. P. Rideout and R. D. Sorkin. ``A Classical Sequential Growth Dynamics for Causal Sets''. Physical Review D 61, 024002 (1999). arXiv:gr-qc/9904062.
https://doi.org/10.1103/physrevd.61.024002
arXiv:gr-qc/9904062

[38] Fay Dowker. ``Causal sets and the deep structure of spacetime''. In Abhay Ashtekar, editor, 100 Years of Relativity. Pages 445–464. World Scientific (2005). arXiv:gr-qc/0508109.
https://doi.org/10.1142/9789812700988_0016
arXiv:gr-qc/0508109

[39] Rafael D. Sorkin. ``Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)'' (2003). arXiv:gr-qc/0309009.
arXiv:gr-qc/0309009

[40] W. Pauli. ``Die allgemeinen Prinzipien der Wellenmechanik''. In H. Bethe, F. Hund, N. F. Mott, W. Pauli, A. Rubinowicz, G. Wentzel, and A. Smekal, editors, Quantentheorie. Pages 83–272. Springer Berlin Heidelberg, Berlin, Heidelberg (1933).
https://doi.org/10.1007/978-3-642-52619-0_2

[41] Eric A. Galapon. ``Pauli's Theorem and Quantum Canonical Pairs: The Consistency Of a Bounded, Self-Adjoint Time Operator Canonically Conjugate to a Hamiltonian with Non-empty Point Spectrum''. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 458, 451–472 (2002). arXiv:quant-ph/9908033.
https://doi.org/10.1098/rspa.2001.0874
arXiv:quant-ph/9908033

[42] Carlo Rovelli and Lee Smolin. ``Discreteness of area and volume in quantum gravity''. Nuclear Physics B 442, 593–619 (1995). arXiv:gr-qc/9411005.
https://doi.org/10.1016/0550-3213(95)00150-q
arXiv:gr-qc/9411005

[43] Bianca Dittrich and Thomas Thiemann. ``Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?''. Journal of Mathematical Physics 50, 012503 (2009). arXiv:0708.1721.
https://doi.org/10.1063/1.3054277
arXiv:0708.1721

[44] Carlo Rovelli. ``Comment on ``Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?'' by B. Dittrich and T. Thiemann'' (2007). arXiv:0708.2481.
arXiv:0708.2481

[45] Carlo Rovelli and Francesca Vidotto. ``Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory''. Cambridge University Press. Cambridge (2014).
https://doi.org/10.1017/CBO9781107706910

[46] Eugenio Bianchi. ``The length operator in Loop Quantum Gravity''. Nuclear Physics B 807, 591–624 (2009). arXiv:0806.4710.
https://doi.org/10.1016/j.nuclphysb.2008.08.013
arXiv:0806.4710

[47] Albert Einstein. ``Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen''. Annalen der Physik 322, 549–560 (1905).
https://doi.org/10.1002/andp.19053220806

[48] R.A. Millikan. ``A new modification of the cloud method of determining the elementary electrical charge and the most probable value of that charge''. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 19, 209–228 (1910).
https://doi.org/10.1080/14786440208636795

[49] R. A. Millikan. ``On the Elementary Electrical Charge and the Avogadro Constant''. Physical Review 2, 109–143 (1913).
https://doi.org/10.1103/physrev.2.109

Cited by

[1] Marios Christodoulou, Andrea Di Biagio, Richard Howl, and Carlo Rovelli, "Gravity entanglement, quantum reference systems, degrees of freedom", Classical and Quantum Gravity 40 4, 047001 (2023).

[2] Marios Christodoulou, Andrea Di Biagio, Markus Aspelmeyer, Časlav Brukner, Carlo Rovelli, and Richard Howl, "Locally Mediated Entanglement in Linearized Quantum Gravity", Physical Review Letters 130 10, 100202 (2023).

[3] Anne-Catherine de la Hamette, Viktoria Kabel, Esteban Castro-Ruiz, and Časlav Brukner, "Falling through masses in superposition: quantum reference frames for indefinite metrics", arXiv:2112.11473, (2021).

[4] Simone Rijavec, Matteo Carlesso, Angelo Bassi, Vlatko Vedral, and Chiara Marletto, "Decoherence effects in non-classicality tests of gravity", New Journal of Physics 23 4, 043040 (2021).

[5] Carlo Rovelli, "Considerations on Quantum Gravity Phenomenology", Universe 7 11, 439 (2021).

[6] Emily Adlam, "Tabletop Experiments for Quantum Gravity Are Also Tests of the Interpretation of Quantum Mechanics", Foundations of Physics 52 5, 115 (2022).

[7] John Ashmead, "Time dispersion in quantum electrodynamics", arXiv:2211.00202, (2022).

The above citations are from Crossref's cited-by service (last updated successfully 2023-03-31 03:21:00) and SAO/NASA ADS (last updated successfully 2023-03-31 03:21:01). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.