Quantum Reference Frames For Lorentz Symmetry

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Luca Apadula^1,2, Esteban Castro-Ruiz³, and Časlav Brukner^1,2

¹Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
²Institute for Quantum Optics and Quantum Information (IQOQI-Vienna), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
³Institute for Theoretical Physics, ETH Zurich, Switzerland

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Abstract

Since their first introduction, Quantum Reference Frame (QRF) transformations have been extensively discussed, generalising the covariance of physical laws to the quantum domain. Despite important progress, a formulation of QRF transformations for Lorentz symmetry is still lacking. The present work aims to fill this gap. We first introduce a reformulation of relativistic quantum mechanics independent of any notion of preferred temporal slicing. Based on this, we define transformations that switch between the perspectives of different relativistic QRFs. We introduce a notion of ”quantum Lorentz transformations” and ”superposition of Lorentz boosts”, acting on the external degrees of freedom of a quantum particle. We analyse two effects, superposition of time dilations and superposition of length contractions, that arise only if the reference frames exhibit both relativistic and quantum-mechanical features. Finally, we discuss how the effects could be observed by measuring the wave-packet extensions from relativistic QRFs.

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► BibTeX data

@article{Apadula2024quantumreference, doi = {10.22331/q-2024-08-14-1440}, url = {https://doi.org/10.22331/q-2024-08-14-1440}, title = {Quantum {R}eference {F}rames for {L}orentz {S}ymmetry}, author = {Apadula, Luca and Castro-Ruiz, Esteban and Brukner, {v{C}}aslav}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {8}, pages = {1440}, month = aug, year = {2024} }

► References

[1] Y. Aharonov and T. Kaufherr. Quantum frames of reference. Phys. Rev. D, 30: 368–385, Jul 1984. 10.1103/PhysRevD.30.368. URL https://doi.org/10.1103/PhysRevD.30.368.
https://doi.org/10.1103/PhysRevD.30.368

[2] C Rovelli. Quantum reference systems. Classical and Quantum Gravity, 8 (2): 317–331, feb 1991. 10.1088/0264-9381/8/2/012. URL https://doi.org/10.1088/0264-9381/8/2/012.
https://doi.org/10.1088/0264-9381/8/2/012

[3] Alexei Kitaev, Dominic Mayers, and John Preskill. Superselection rules and quantum protocols. Phys. Rev. A, 69: 052326, May 2004. 10.1103/PhysRevA.69.052326. URL https://doi.org/10.1103/PhysRevA.69.052326.
https://doi.org/10.1103/PhysRevA.69.052326

[4] Stephen D. Bartlett, Terry Rudolph, and Robert W. Spekkens. Reference frames, superselection rules, and quantum information. Rev. Mod. Phys., 79: 555–609, Apr 2007a. 10.1103/RevModPhys.79.555. URL https://doi.org/10.1103/RevModPhys.79.555.
https://doi.org/10.1103/RevModPhys.79.555

[5] Gilad Gour and Robert W Spekkens. The resource theory of quantum reference frames: manipulations and monotones. New Journal of Physics, 10 (3): 033023, 2008. 10.1088/1367-2630/10/3/033023. URL https://dx.doi.org/10.1088/1367-2630/10/3/033023.
https://doi.org/10.1088/1367-2630/10/3/033023

[6] Florian Girelli and David Poulin. Quantum reference frames and deformed symmetries. Phys. Rev. D, 77: 104012, May 2008. 10.1103/PhysRevD.77.104012. URL https://doi.org/10.1103/PhysRevD.77.104012.
https://doi.org/10.1103/PhysRevD.77.104012

[7] Stephen D. Bartlett, Terry Rudolph, and Robert W. Spekkens. Reference frames, superselection rules, and quantum information. Rev. Mod. Phys., 79: 555–609, Apr 2007b. 10.1103/RevModPhys.79.555. URL https://doi.org/10.1103/RevModPhys.79.555.
https://doi.org/10.1103/RevModPhys.79.555

[8] Renato M Angelo, Nicolas Brunner, Sandu Popescu, Anthony J Short, and Paul Skrzypczyk. Physics within a quantum reference frame. Journal of Physics A: Mathematical and Theoretical, 44 (14): 145304, 2011. https://doi.org/10.1088/1751-8113/44/14/145304.
https://doi.org/10.1088/1751-8113/44/14/145304

[9] RM Angelo and AD Ribeiro. Kinematics and dynamics in noninertial quantum frames of reference. Journal of Physics A: Mathematical and Theoretical, 45 (46): 465306, 2012. 10.1088/1751-8113/45/46/465306.
https://doi.org/10.1088/1751-8113/45/46/465306

[10] Matthew C. Palmer, Florian Girelli, and Stephen D. Bartlett. Changing quantum reference frames. Phys. Rev. A, 89: 052121, May 2014. 10.1103/PhysRevA.89.052121. URL https://doi.org/10.1103/PhysRevA.89.052121.
https://doi.org/10.1103/PhysRevA.89.052121

[11] Jacques Pienaar. A relational approach to quantum reference frames for spins. January 2016.

[12] Alexander R. H. Smith, Marco Piani, and Robert B. Mann. Quantum reference frames associated with noncompact groups: The case of translations and boosts and the role of mass. Phys. Rev. A, 94: 012333, Jul 2016. 10.1103/PhysRevA.94.012333. URL https://doi.org/10.1103/PhysRevA.94.012333.
https://doi.org/10.1103/PhysRevA.94.012333

[13] Takayuki Miyadera, Leon Loveridge, and Paul Busch. Approximating relational observables by absolute quantities: a quantum accuracy-size trade-off. Journal of Physics A: Mathematical and Theoretical, 49 (18): 185301, 2016. 10.1088/1751-8113/49/18/185301.
https://doi.org/10.1088/1751-8113/49/18/185301

[14] Leon Loveridge, Paul Busch, and Takayuki Miyadera. Relativity of quantum states and observables. EPL (Europhysics Letters), 117 (4): 40004, 2017. 10.1209/0295-5075/117/40004.
https://doi.org/10.1209/0295-5075/117/40004

[15] Alessio Belenchia, Robert M. Wald, Flaminia Giacomini, Esteban Castro-Ruiz, Časlav Brukner, and Markus Aspelmeyer. Quantum superposition of massive objects and the quantization of gravity. Phys. Rev. D, 98: 126009, Dec 2018. 10.1103/PhysRevD.98.126009. URL https://doi.org/10.1103/PhysRevD.98.126009.
https://doi.org/10.1103/PhysRevD.98.126009

[16] Flaminia Giacomini, Esteban Castro-Ruiz, and Časlav Brukner. Quantum mechanics and the covariance of physical laws in quantum reference frames. Nature Commun., 10 (1): 494, 2019a. 10.1038/s41467-018-08155-0.
https://doi.org/10.1038/s41467-018-08155-0

[17] Flaminia Giacomini, Esteban Castro-Ruiz, and Časlav Brukner. Relativistic quantum reference frames: The operational meaning of spin. Phys. Rev. Lett., 123: 090404, Aug 2019b. 10.1103/PhysRevLett.123.090404. URL https://doi.org/10.1103/PhysRevLett.123.090404.
https://doi.org/10.1103/PhysRevLett.123.090404

[18] Esteban Castro-Ruiz, Flaminia Giacomini, Alessio Belenchia, and Časlav Brukner. Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems. Nature Communications, 11 (1): 2672, 2020a. 10.1038/s41467-020-16013-1. URL https://doi.org/10.1038/s41467-020-16013-1.
https://doi.org/10.1038/s41467-020-16013-1

[19] Augustin Vanrietvelde, Philipp A. Hoehn, Flaminia Giacomini, and Esteban Castro-Ruiz. A change of perspective: switching quantum reference frames via a perspective-neutral framework. Quantum, 4: 225, January 2020. ISSN 2521-327X. 10.22331/q-2020-01-27-225. URL https://doi.org/10.22331/q-2020-01-27-225.
https://doi.org/10.22331/q-2020-01-27-225

[20] Augustin Vanrietvelde, Philipp A. Hoehn, and Flaminia Giacomini. Switching quantum reference frames in the N-body problem and the absence of global relational perspectives. September 2018. 10.22331/q-2023-08-22-1088. URL https://doi.org/10.22331/q-2023-08-22-1088.
https://doi.org/10.22331/q-2023-08-22-1088

[21] Luis C. Barbado, Esteban Castro-Ruiz, Luca Apadula, and Časlav Brukner. Unruh effect for detectors in superposition of accelerations. Phys. Rev. D, 102: 045002, Aug 2020. 10.1103/PhysRevD.102.045002. URL https://doi.org/10.1103/PhysRevD.102.045002.
https://doi.org/10.1103/PhysRevD.102.045002

[22] Esteban Castro-Ruiz, Flaminia Giacomini, Alessio Belenchia, and Časlav Brukner. Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems. Nature communications, 11 (1): 1–12, 2020b. https://doi.org/10.1038/s41467-020-16013-1.
https://doi.org/10.1038/s41467-020-16013-1

[23] Flaminia Giacomini and Časlav Brukner. Einstein’s equivalence principle for superpositions of gravitational fields and quantum reference frames. 2020. URL https://arxiv.org/abs/2012.13754.
arXiv:2012.13754

[24] Anne-Catherine de la Hamette, Viktoria Kabel, Esteban Castro-Ruiz, and Časlav Brukner. Falling through masses in superposition: quantum reference frames for indefinite metrics. 2021a. URL https://doi.org/10.1038/s42005-023-01344-4. 10.1038/s42005-023-01344-4.
https://doi.org/10.1038/s42005-023-01344-4

[25] Carlo Cepollaro and Flaminia Giacomini. Quantum generalisation of einstein’s equivalence principle can be verified with entangled clocks as quantum reference frames. 2021. URL https://arxiv.org/abs/2112.03303.
arXiv:2112.03303

[26] Anne-Catherine de la Hamette, Thomas D. Galley, Philipp A. Hoehn, Leon Loveridge, and Markus P. Mueller. Perspective-neutral approach to quantum frame covariance for general symmetry groups. 2021b. URL https://arxiv.org/abs/2110.13824.
arXiv:2110.13824

[27] Philipp A Höhn, Marius Krumm, and Markus P Müller. Internal quantum reference frames for finite abelian groups. Journal of Mathematical Physics, 63 (11): 112207, 2022. URL https://doi.org/10.1063/5.0088485.
https://doi.org/10.1063/5.0088485

[28] Philipp A Höhn, Alexander RH Smith, and Maximilian PE Lock. Equivalence of approaches to relational quantum dynamics in relativistic settings. Frontiers in Physics, page 181, 2021. 10.3389/fphy.2021.587083.
https://doi.org/10.3389/fphy.2021.587083

[29] Philipp A. Höhn, Alexander R. H. Smith, and Maximilian P. E. Lock. Trinity of relational quantum dynamics. Phys. Rev. D, 104: 066001, Sep 2021. 10.1103/PhysRevD.104.066001. URL https://doi.org/10.1103/PhysRevD.104.066001.
https://doi.org/10.1103/PhysRevD.104.066001

[30] Esteban Castro-Ruiz and Ognyan Oreshkov. Relative subsystems and quantum reference frame transformations. 2021. URL https://arxiv.org/abs/2110.13199.
arXiv:2110.13199

[31] Flaminia Giacomini. Spacetime Quantum Reference Frames and superpositions of proper times. Quantum, 5: 508, July 2021. ISSN 2521-327X. 10.22331/q-2021-07-22-508. URL https://doi.org/10.22331/q-2021-07-22-508.
https://doi.org/10.22331/q-2021-07-22-508

[32] Flaminia Giacomini and Časlav Brukner. Quantum superposition of spacetimes obeys einstein’s equivalence principle. AVS Quantum Science, 4 (1): 015601, mar 2022. 10.1116/5.0070018. URL https://doi.org/10.1116.
https://doi.org/10.1116/5.0070018

[33] Flaminia Giacomini and Achim Kempf. Second-quantized unruh-dewitt detectors and their quantum reference frame transformations. Phys. Rev. D, 105: 125001, Jun 2022. 10.1103/PhysRevD.105.125001. URL https://doi.org/10.1103/PhysRevD.105.125001.
https://doi.org/10.1103/PhysRevD.105.125001

[34] Viktoria Kabel, Anne-Catherine de la Hamette, Esteban Castro-Ruiz, and Časlav Brukner. Quantum conformal symmetries for spacetimes in superposition. 2022. URL https://arxiv.org/abs/2207.00021.
arXiv:2207.00021

[35] Michael Reisenberger and Carlo Rovelli. Spacetime states and covariant quantum theory. Phys. Rev. D, 65: 125016, Jun 2002. 10.1103/PhysRevD.65.125016. URL https://doi.org/10.1103/PhysRevD.65.125016.
https://doi.org/10.1103/PhysRevD.65.125016

[36] Donald Marolf and Carlo Rovelli. Relativistic quantum measurement. Phys. Rev. D, 66: 023510, Jul 2002. 10.1103/PhysRevD.66.023510. URL https://doi.org/10.1103/PhysRevD.66.023510.
https://doi.org/10.1103/PhysRevD.66.023510

[37] Carlo Rovelli. Relational quantum mechanics. International Journal of Theoretical Physics, 35 (8): 1637–1678, aug 1996. 10.1007/bf02302261. URL https://doi.org/10.10072Fbf02302261.
https://doi.org/10.1007/bf02302261

[38] Anne-Catherine de la Hamette and Thomas D. Galley. Quantum reference frames for general symmetry groups. Quantum, 4: 367, November 2020. ISSN 2521-327X. 10.22331/q-2020-11-30-367. URL http://dx.doi.org/10.22331/q-2020-11-30-367.
https://doi.org/10.22331/q-2020-11-30-367

[39] Titouan Carette, Jan Głowacki, and Leon Loveridge. Operational quantum reference frame transformations, 2023.

[40] Alexander R. H. Smith and Mehdi Ahmadi. Quantum clocks observe classical and quantum time dilation. Nature Communications, 11 (1): 5360, 2020. 10.1038/s41467-020-18264-4. URL https://doi.org/10.1038/s41467-020-18264-4.
https://doi.org/10.1038/s41467-020-18264-4

[41] Piotr T. Grochowski, Alexander R. H. Smith, Andrzej Dragan, and Kacper Dębski. Quantum time dilation in atomic spectra. Phys. Rev. Res., 3: 023053, Apr 2021. 10.1103/PhysRevResearch.3.023053. URL https://doi.org/10.1103/PhysRevResearch.3.023053.
https://doi.org/10.1103/PhysRevResearch.3.023053

[42] Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone, 2022. URL https://doi.org/10.1088/1367-2630/acb793.
https://doi.org/10.1088/1367-2630/acb793

[43] Marion Mikusch, Luis C. Barbado, and Časlav Brukner. Transformation of spin in quantum reference frames. Phys. Rev. Res., 3: 043138, Nov 2021. 10.1103/PhysRevResearch.3.043138. URL https://doi.org/10.1103/PhysRevResearch.3.043138.
https://doi.org/10.1103/PhysRevResearch.3.043138

[44] Steven Weinberg. RELATIVISTIC QUANTUM MECHANICS, volume 1, page 49–106. Cambridge University Press, 1995. 10.1017/CBO9781139644167.004.
https://doi.org/10.1017/CBO9781139644167.004

[45] Rafael D Sorkin. Impossible measurements on quantum fields, volume 2, pages 293–305. 1993. URL https://arxiv.org/abs/gr-qc/9302018.
https://arxiv.org/abs/gr-qc/9302018

[46] David B Malament. In defense of dogma: Why there cannot be a relativistic quantum mechanics of (localizable) particles. In Perspectives on quantum reality, pages 1–10. Springer, 1996. 10.1007/978-94-015-8656-6_1. URL https://doi.org/10.1007/978-94-015-8656-6_1.
https://doi.org/10.1007/978-94-015-8656-6_1

[47] Paul Busch. Unsharp localization and causality in relativistic quantum theory. Journal of Physics A: Mathematical and General, 32 (37): 6535–6546, sep 1999. 10.1088/0305-4470/32/37/305. URL https://doi.org/10.1088.
https://doi.org/10.1088/0305-4470/32/37/305

[48] A. S. Wightman. On the localizability of quantum mechanical systems. Rev. Mod. Phys., 34: 845–872, 1962. 10.1103/RevModPhys.34.845.
https://doi.org/10.1103/RevModPhys.34.845

[49] Don N. Page and William K. Wootters. Evolution without evolution: Dynamics described by stationary observables. Phys. Rev. D, 27: 2885–2892, Jun 1983. 10.1103/PhysRevD.27.2885. URL https://doi.org/10.1103/PhysRevD.27.2885.
https://doi.org/10.1103/PhysRevD.27.2885

[50] N. L. Diaz and R. Rossignoli. History state formalism for dirac’s theory. Phys. Rev. D, 99: 045008, Feb 2019. 10.1103/PhysRevD.99.045008. URL https://doi.org/10.1103/PhysRevD.99.045008.
https://doi.org/10.1103/PhysRevD.99.045008

[51] N. L. Diaz, J. M. Matera, and R. Rossignoli. History state formalism for scalar particles. Phys. Rev. D, 100: 125020, Dec 2019. 10.1103/PhysRevD.100.125020. URL https://doi.org/10.1103/PhysRevD.100.125020.
https://doi.org/10.1103/PhysRevD.100.125020

Cited by

[1] Matthew J. Lake and Marek Miller, “Quantum reference frames, revisited”, arXiv:2312.03811, (2023).

[2] Viktoria Kabel, Anne-Catherine de la Hamette, Luca Apadula, Carlo Cepollaro, Henrique Gomes, Jeremy Butterfield, and Časlav Brukner, “Identification is Pointless: Quantum Reference Frames, Localisation of Events, and the Quantum Hole Argument”, arXiv:2402.10267, (2024).

[3] Viktoria Kabel, Časlav Brukner, and Wolfgang Wieland, “Quantum reference frames at the boundary of spacetime”, Physical Review D 108 10, 106022 (2023).

[4] Shadi Ali Ahmad, Wissam Chemissany, Marc S. Klinger, and Robert G. Leigh, “Quantum Reference Frames from Top-Down Crossed Products”, arXiv:2405.13884, (2024).

[5] Carlo Cepollaro, Ali Akil, Paweł Cieśliński, Anne-Catherine de la Hamette, and Časlav Brukner, “The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations”, arXiv:2406.19448, (2024).

The above citations are from SAO/NASA ADS (last updated successfully 2024-08-14 13:54:01). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2024-08-14 13:54:00: Could not fetch cited-by data for 10.22331/q-2024-08-14-1440 from Crossref. This is normal if the DOI was registered recently.

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Time Stamp: August 14, 2024

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Quantum Reference Frames for Lorentz Symmetry

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