Earthquake Quantization

Republished By Plato

Followers: 0

Earthquake Quantization PlatoBlockchain Data Intelligence. Vertical Search. Ai.

Benjamin Koch^1,2 and Enrique Muñoz²

¹Institut für Theoretische Physik and Atominstitut, Technische Universität Wien, Wiedner Hauptstrasse 8–10, A-1040 Vienna, Austria
²Facultad de Física, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago, Chile

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

Abstract

In this homage to Einstein’s 144th birthday we propose a novel quantization prescription, where the paths of a path-integral are not random, but rather solutions of a geodesic equation in a random background. We show that this change of perspective can be made mathematically equivalent to the usual formulations of non-relativistic quantum mechanics. To conclude, we comment on conceptual issues, such as quantum gravity coupled to matter and the quantum equivalence principle.

[embedded content]

Popular summary

Imagine that you are sitting on a balloon and observing the motion of few people walking on a square. Surprisingly, you do not see a smooth flow but rather a random zigzag. When trying to make sense of this crazy motion you might conclude that
the people are
+ actually drunk and are thus moving strangely on their own cause;
+ sober, but they have a hard time trying to move steadily since they are suffering from a massive
earthquake, which you in your safe balloon, can not perceive directly.

The first alternative of this analogy corresponds to intrinsic random motion of the path integral (PI) quantization, while the second alternative corresponds to random motion caused by a random background.

The idea of this short comment is that the paths of the PI could actually not be random
by themselves, instead they are the result of a law of motion which is intimately linked to a random nature of space-time itself.

► BibTeX data

@article{Koch2024earthquake, doi = {10.22331/q-2024-01-02-1216}, url = {https://doi.org/10.22331/q-2024-01-02-1216}, title = {Earthquake {Q}uantization}, author = {Koch, Benjamin and Mu{~{n}}oz, Enrique}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {8}, pages = {1216}, month = jan, year = {2024}<br /> }

► References

[1] R. P. Feynman, Phys. Rev. 80 (1950), 440-457 [doi:10.1103/PhysRev.80.440].
https://doi.org/10.1103/PhysRev.80.440

[2] Note that this name is not meant as trivialization of the devastating effects an earthquake can provoke in inhabited regions. Instead, we encourage everyone to donate to those who are helping in the aftermath of such an event.

[3] W. a Heisenberg, Z. Phys. 43 (1927), 172-198 doi:10.1007/BF01397280.
https://doi.org/10.1007/BF01397280

[4] E. Schrödinger, Annalen Phys. 384 (1926) no.4, 361-376 doi:10.1002/andp.19263840404.
https://doi.org/10.1002/andp.19263840404

[5] R. P. Feynman, Rev. Mod. Phys. 20 (1948), 367-387 doi:10.1103/RevModPhys.20.367.
https://doi.org/10.1103/RevModPhys.20.367

[6] E. Nelson, Phys. Rev. 150 (1966), 1079-1085 doi:10.1103/PhysRev.150.1079.
https://doi.org/10.1103/PhysRev.150.1079

[7] F. Kuipers, Springer, 2023, ISBN 978-3-031-31447-6, 978-3-031-31448-3 doi:10.1007/978-3-031-31448-3 [arXiv:2301.05467 [quant-ph]].
https://doi.org/10.1007/978-3-031-31448-3
arXiv:2301.05467

[8] F. Kuipers, Eur. Phys. J. Plus 138 (2023), 542 doi:10.1140/epjp/s13360-023-04184-x [arXiv:2304.07524 [quant-ph]].
https://doi.org/10.1140/epjp/s13360-023-04184-x
arXiv:2304.07524

[9] D. Bohm, Phys. Rev. 85 (1952), 166-179 doi:10.1103/PhysRev.85.166.
https://doi.org/10.1103/PhysRev.85.166

[10] D. Bohm, Phys. Rev. 85 (1952), 180-193 doi:10.1103/PhysRev.85.180.
https://doi.org/10.1103/PhysRev.85.180

[11] H. Everett, Rev. Mod. Phys. 29 (1957), 454-462 doi:10.1103/RevModPhys.29.454.
https://doi.org/10.1103/RevModPhys.29.454

[12] S. Albeverio, R. Krohn, S. Mazzuchi, Springer: Lecture notes in mathematics, 523 (1976).

[13] S. Deser, Annalen Phys. 9 (2000), 299-307 299::AID-ANDP299>3.0.CO;2-Edoi:10.1002/(SICI)1521-3889 [arXiv:gr-qc/9911073 [gr-qc]].
<a href="https://doi.org/10.1002/(SICI)1521-3889(200005)9:3/5ensuremathhttps://doi.org/10.1002/(SICI)1521-3889(200005)9:3/5ensuremath<
arXiv:gr-qc/9911073

[14] G. ‘t Hooft and M. J. G. Veltman, Ann. Inst. H. Poincare Phys. Theor. A 20 (1974), 69-94.

[15] R. L. Arnowitt, S. Deser and C. W. Misner, Gen. Rel. Grav. 40 (2008), 1997-2027 doi:10.1007/s10714-008-0661-1 [arXiv:gr-qc/0405109 [gr-qc]].
https://doi.org/10.1007/s10714-008-0661-1
arXiv:gr-qc/0405109

[16] J. W. Barrett and L. Glaser, J. Phys. A 49 (2016) no.24, 245001 doi:10.1088/1751-8113/49/24/245001 [arXiv:1510.01377 [gr-qc]].
https://doi.org/10.1088/1751-8113/49/24/245001
arXiv:1510.01377

[17] J. W. Barrett, P. Druce and L. Glaser, J. Phys. A 52 (2019) no.27, 275203 doi:10.1088/1751-8121/ab22f8 [arXiv:1902.03590 [gr-qc]].
https://doi.org/10.1088/1751-8121/ab22f8
arXiv:1902.03590

[18] A. H. Chamseddine, A. Connes and W. D. van Suijlekom, doi.org/10.1140/epjs/s11734-023-00842-4 [arXiv:2207.10901 [hep-th]].
https://doi.org/10.1140/epjs/s11734-023-00842-4
arXiv:2207.10901

[19] M. Reitz, B. Šoda and A. Kempf, [arXiv:2303.01519 [gr-qc]].
arXiv:2303.01519

[20] S. Carlip, Rept. Prog. Phys. 64 (2001), 885 https://doi.org/10.1088/0034-4885/64/8/301 [arXiv:gr-qc/0108040 [gr-qc]].
https://doi.org/10.1088/0034-4885/64/8/301
arXiv:gr-qc/0108040

[21] Feynman, Richard Phillips and Hibbs, Albert Roach, “Quantum mechanics and path integrals” McGraw-Hill, New York, NY (1965).

[22] P. Donà, A. Eichhorn and R. Percacci, Phys. Rev. D 89 (2014) no.8, 084035 doi.org/10.1103/PhysRevD.89.084035 [arXiv:1311.2898 [hep-th]].
https://doi.org/10.1103/PhysRevD.89.084035
arXiv:1311.2898

[23] J. Alfaro, P. Gonzalez and R. Avila, Class. Quant. Grav. 28 (2011), 215020 doi.org/10.1088/0264-9381/28/21/215020 [arXiv:1009.2800 [gr-qc]].
https://doi.org/10.1088/0264-9381/28/21/215020
arXiv:1009.2800

[24] J. Alfaro, Phys. Part. Nucl. 44 (2013), 175-189 doi.org/10.1134/S1063779613020032.
https://doi.org/10.1134/S1063779613020032

[25] B. Koch, AIP Conf. Proc. 1232 (2010) no.1, 313-320 doi.org/10.1063/1.3431507 [arXiv:1004.2879 [hep-th]].
https://doi.org/10.1063/1.3431507
arXiv:1004.2879

[26] Cariñena, J. F. and Clemente-Gallardo, J. and Marmo, G., Theoretical and Mathematical Physics, 152 (2007) no.1, 894. doi.org/10.1007/s11232-007-0075-3.
https://doi.org/10.1007/s11232-007-0075-3

[27] C. W. Misner, K. S. Thorne and J. A. Wheeler, W. H. Freeman, 1973, ISBN 978-0-7167-0344-0, 978-0-691-17779-3.

[28] C. Lammerzahl, Acta Phys. Polon. 29 (1998), 1057 [arXiv:gr-qc/9807072 [gr-qc]].
arXiv:gr-qc/9807072

[29] F. Giacomini and Č. Brukner, [arXiv:2012.13754 [quant-ph]].
arXiv:2012.13754

[30] F. Giacomini and Č. Brukner, AVS Quantum Sci. 4 (2022) no.1, 015601 doi.org/10.1116/5.0070018 [arXiv:2109.01405 [quant-ph]].
https://doi.org/10.1116/5.0070018
arXiv:2109.01405

[31] J. Foo, R. B. Mann and M. Zych, [arXiv:2302.03259 [gr-qc]].
arXiv:2302.03259

[32] B. Koch and E. Muñoz, Eur. Phys. J. C 78 (2018) no.4, 278 doi.org/10.1140/epjc/s10052-018-5753-9 [arXiv:1706.05388 [hep-th]].
https://doi.org/10.1140/epjc/s10052-018-5753-9
arXiv:1706.05388

[33] B. Koch, E. Muñoz and I. Reyes, Phys. Rev. D 96 (2017) no.8, 085011 doi.org/10.1103/PhysRevD.96.085011 [arXiv:1706.05386 [hep-th]].
https://doi.org/10.1103/PhysRevD.96.085011
arXiv:1706.05386

[34] B. Koch and E. Muñoz, Eur. Phys. J. C 79 (2019) no.11, 941 doi.org/10.1140/epjc/s10052-019-7459-z [arXiv:1901.08673 [hep-th]].
https://doi.org/10.1140/epjc/s10052-019-7459-z
arXiv:1901.08673

[35] B. Koch and E. Muñoz, Phys. Rev. D 103 (2021) no.10, 105025 doi.org/10.1103/PhysRevD.103.105025 [arXiv:2012.15242 [hep-th]].
https://doi.org/10.1103/PhysRevD.103.105025
arXiv:2012.15242

Cited by

Could not fetch Crossref cited-by data during last attempt 2024-01-02 12:45:26: Could not fetch cited-by data for 10.22331/q-2024-01-02-1216 from Crossref. This is normal if the DOI was registered recently. On SAO/NASA ADS no data on citing works was found (last attempt 2024-01-02 12:45:27).

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.

SEO Powered Content & PR Distribution. Get Amplified Today.
PlatoData.Network Vertical Generative Ai. Empower Yourself. Access Here.
PlatoAiStream. Web3 Intelligence. Knowledge Amplified. Access Here.
PlatoESG. Carbon, CleanTech, Energy, Environment, Solar, Waste Management. Access Here.
PlatoHealth. Biotech and Clinical Trials Intelligence. Access Here.
Source: https://quantum-journal.org/papers/q-2024-01-02-1216/

Time Stamp: January 2, 2024

Time Stamp: Oct 13, 2022

Earthquake Quantization

Republished By Plato

Abstract

Popular summary

► BibTeX data

► References

Cited by

More from Quantum Journal

Digital quantum simulation of non-perturbative dynamics of open systems with orthogonal polynomials

Depth-efficient proofs of quantumness

Quantum Interior Point Methods for Semidefinite Optimization

Quantum scattering as a work source

Overhead-constrained circuit knitting for variational quantum dynamics

Graph-theoretic approach to Bell experiments with low detection efficiency

Efficient classical algorithms for simulating symmetric quantum systems

Fast quantum circuit cutting with randomized measurements

Parameter Setting in Quantum Approximate Optimization of Weighted Problems

Role of matter coherence in entanglement due to gravity

Contextuality in entanglement-assisted one-shot classical communication

About Us

Vertical Search & Ai

Platform

Stay Connected

Account