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Moving mirrors

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Moving mirrors, in physics, are simplified (1+1)-dimensional versions of the dynamical Casimir effect..[1] Moving mirrors are used as toy models for black hole evaporation since particular accelerated boundaries create energy, particles, and entropy, without the complications of higher dimensions or spacetime curvature.[2][3][4] Moving mirrors have an exact mathematical identity to the ordinary electron: classical radiation from an accelerating electron in (3+1)D is dual to quantum radiation from an accelerating mirror in (1+1)D.[5][6]

More information

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One of the first studies investigating particle radiation resulting from the moving mirrors was conducted by Moore.[7] The development of the moving mirror and its relation to the black hole evaporation process started in 1970s when Stephen Hawking proposed that black holes can emit particles and energy when quantum mechanical effects are taken into account.[8] However, due to unresolved questions associated with the Hawking radiation, along with the need for experimental verification, analog models were used to address issues without losing the essential physical properties of the black hole radiation process. One of these analog models is called the moving mirror model, set in (1+1)-dimensions where accelerated boundaries emit energy, particles, and entropy similiar to black hole radiance.

There have been a number of studies in recent years investigating the relationship between certain black hole models and their analog moving mirrors, including Schwarzschild[9] [10], Reissner-Nordström[11], Kerr[12], their extremal limits[13][14], Taub-NUT[15], CGHS[16]. A moving mirror is also used to represent de Sitter[17] and Schwarzschild-de-Sitter[18] cosmologies. Moreover, there have been introduced some new types of moving mirrors with interesting features. These new models include Schwarzschild-Planck[19][20], Inertial Horizon[21], Dual-Temperature[22], and Light-Airy[23] mirrors. A special attention attracts the anti-de Sitter (AdS) spacetime analog mirror model, AdS moving mirror[24], which is unique in several respects:

  • The trajectory moves in the opposite direction with respect to the de Sitter[17] mirror trajectory with horizons in retarded time, becoming asymptotically uniformly accelerated as it approaches the horizons.
  • The flux radiation is thermal and negative over all times, resulting in finite but negative total energy.
  • The particle energy suffers from an infrared divergence, yet the stress-energy is perfectly finite.
  • The entropy is always negative, diverging at the horizons, which signals information loss.

How can the particles carry the total negative energy if particle energy is always positive? This and other curious issues related to the AdS dynamical Casimir effect are still open questions that need further discussion and investigations[25][26]

It has been discovered recently that it is possible to map classical electron radiation in (3+1)-dimensions onto (1+1)-dimensional moving mirror models. The example of this equivalence has been verified mathematically for some existing moving mirror models already[5][6]. They investigated the radiation from a classical point charge moving along particular moving mirror trajectories and found some similar physical properties in their radiation process.

Summary of significance of moving mirrors (MM):

  • MM is a lower-dimensional model: it is (1+1)D, not (3+1)D as black hole models; therefore, there is no spacetime curvature, i.e. the geometry is simpler.
  • Some MM models can solve issues such as infinite energy and infinite particle production during the black hole evaporation process.
  • MMs are simplified versions of the dynamical Casimir effect (DCE) that, in turn, has been measured in the laboratory within the framework of MMs. Thus, MMs have the potential to simulate the black hole evaporation process experimentally in the laboratory.
  • MMs have an exact mathematical identity to the ordinary electron: classical electron radiation in (3+1)D has duality to (1+1)D MMs.

References

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  1. ^ Casimir, H.B.G. "On the attraction between two perfectly conducting plates}". Indag.Math. 10 (4): 261–263.
  2. ^ DeWitt, Bryce S. (1975-08-01). "Quantum field theory in curved spacetime". Physics Reports. 19 (6): 295–357. Bibcode:1975PhR....19..295D. doi:10.1016/0370-1573(75)90051-4. ISSN 0370-1573.
  3. ^ Fulling, S. A.; Davies, P. C. W. (1976). "Radiation from a Moving Mirror in Two Dimensional Space-Time: Conformal Anomaly". Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. 348 (1654): 393–414. Bibcode:1976RSPSA.348..393F. doi:10.1098/rspa.1976.0045. ISSN 0080-4630. JSTOR 79130.
  4. ^ Davies, P. C. W.; Fulling, S. A. (1977). "Radiation from Moving Mirrors and from Black Holes". Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. 356 (1685): 237–257. Bibcode:1977RSPSA.356..237D. doi:10.1098/rspa.1977.0130. ISSN 0080-4630. JSTOR 79378.
  5. ^ a b Lynch, Morgan H; Ievlev, Evgenii; Good, Michael R R (2024-02-01). "Accelerated electron thermometer: observation of 1D Planck radiation". Progress of Theoretical and Experimental Physics. 2024 (2): 023D01. doi:10.1093/ptep/ptad157. ISSN 2050-3911.
  6. ^ a b Ievlev, Evgenii; Good, Michael R. R.; Davies, Paul C. W. (2024-11-15). "Electron-mirror duality and thermality". The European Physical Journal C. 84 (11): 1159. arXiv:2405.06086. Bibcode:2024EPJC...84.1159I. doi:10.1140/epjc/s10052-024-13557-0. ISSN 1434-6052.
  7. ^ Moore, Gerald T. (1970-09-01). "Quantum Theory of the Electromagnetic Field in a Variable-Length One-Dimensional Cavity". Journal of Mathematical Physics. 11 (9): 2679–2691. Bibcode:1970JMP....11.2679M. doi:10.1063/1.1665432. ISSN 0022-2488.
  8. ^ Hawking, S. W. (1975-08-01). "Particle creation by black holes". Communications in Mathematical Physics. 43 (3): 199–220. Bibcode:1975CMaPh..43..199H. doi:10.1007/BF02345020. ISSN 1432-0916.
  9. ^ Good, Michael R. R.; Anderson, Paul R.; Evans, Charles R. (2016-09-12). "Mirror reflections of a black hole". Physical Review D. 94 (6): 065010. arXiv:1605.06635. Bibcode:2016PhRvD..94f5010G. doi:10.1103/PhysRevD.94.065010.
  10. ^ Good, M. R. R.; Ong, Y. C.; Myrzakul, A.; Yelshibekov, K. (2019-07-16). "Information preservation for null shell collapse: a moving mirror model". General Relativity and Gravitation. 51 (7): 92. arXiv:1801.08020. Bibcode:2019GReGr..51...92G. doi:10.1007/s10714-019-2575-5. ISSN 1572-9532.
  11. ^ Good, Michael R. R.; Ong, Yen Chin (2020-12-21). "Particle spectrum of the Reissner–Nordström black hole". The European Physical Journal C. 80 (12): 1169. Bibcode:2020EPJC...80.1169G. doi:10.1140/epjc/s10052-020-08761-7. ISSN 1434-6052.
  12. ^ Good, Michael R R; Foo, Joshua; Linder, Eric V (2021-04-22). "Accelerating boundary analog of a Kerr black hole". Classical and Quantum Gravity. 38 (8): 085011. arXiv:2006.01349. Bibcode:2021CQGra..38h5011G. doi:10.1088/1361-6382/abebb6. ISSN 0264-9381.
  13. ^ Good, Michael R. R. (2020-05-26). "Extremal Hawking radiation". Physical Review D. 101 (10): 104050. arXiv:2003.07016. Bibcode:2020PhRvD.101j4050G. doi:10.1103/PhysRevD.101.104050.
  14. ^ Foo, Joshua; Good, Michael R.R. (2021-01-13). "Hawking radiation particle spectrum of a Kerr-Newman black hole". Journal of Cosmology and Astroparticle Physics. 2021 (1): 019. arXiv:2006.09681. Bibcode:2021JCAP...01..019F. doi:10.1088/1475-7516/2021/01/019. ISSN 1475-7516.
  15. ^ Foo, Joshua; Good, Michael R. R.; Mann, Robert B. (2021-09-20). "Analog Particle Production Model for General Classes of Taub-NUT Black Holes". Universe. 7 (9): 350. arXiv:2012.02348. Bibcode:2021Univ....7..350F. doi:10.3390/universe7090350. ISSN 2218-1997.
  16. ^ Myrzakul, Aizhan; Xiong, Chi; Good, Michael R. R. (2021-12-10). "CGHS Black Hole Analog Moving Mirror and Its Relativistic Quantum Information as Radiation Reaction". Entropy. 23 (12): 1664. Bibcode:2021Entrp..23.1664M. doi:10.3390/e23121664. ISSN 1099-4300. PMC 8700335. PMID 34945970.
  17. ^ a b Good, Michael R. R.; Zhakenuly, Abay; Linder, Eric V. (2020-08-28). "Mirror at the edge of the universe: Reflections on an accelerated boundary correspondence with de Sitter cosmology". Physical Review D. 102 (4): 045020. arXiv:2005.03850. Bibcode:2020PhRvD.102d5020G. doi:10.1103/PhysRevD.102.045020.
  18. ^ Fernández-Silvestre, Diego; Foo, Joshua; Good, Michael R R (2022-03-03). "On the duality of Schwarzschild–de Sitter spacetime and moving mirror". Classical and Quantum Gravity. 39 (5): 055006. arXiv:2109.04147. Bibcode:2022CQGra..39e5006F. doi:10.1088/1361-6382/ac4b03. ISSN 0264-9381.
  19. ^ Good, Michael R. R.; Linder, Eric V.; Wilczek, Frank (2020-01-30). "Moving mirror model for quasithermal radiation fields". Physical Review D. 101 (2): 025012. arXiv:1909.01129. Bibcode:2020PhRvD.101b5012G. doi:10.1103/PhysRevD.101.025012.
  20. ^ Good, Michael R R; Linder, Eric V (2021-04-01). "Modified Schwarzschild metric from a unitary accelerating mirror analog". New Journal of Physics. 23 (4): 043007. Bibcode:2021NJPh...23d3007G. doi:10.1088/1367-2630/abe506. ISSN 1367-2630.
  21. ^ Good, Michael; Abdikamalov, Ernazar (2020-08-20). "Radiation from an Inertial Mirror Horizon". Universe. 6 (9): 131. arXiv:2008.08776. Bibcode:2020Univ....6..131G. doi:10.3390/universe6090131. ISSN 2218-1997.
  22. ^ Good, M. R. R.; Mitra, A.; Zarikas, V. (2021-10-01). "Dual-Temperature Acceleration Radiation". Astronomy Reports. 65 (10): 942–946. arXiv:2102.00158. Bibcode:2021ARep...65..942G. doi:10.1134/S1063772921100115. ISSN 1562-6881.
  23. ^ Good, Michael R. R.; Linder, Eric V. (2021-03-05). "Light and Airy: A Simple Solution for Relativistic Quantum Acceleration Radiation". Universe. 7 (3): 60. arXiv:2101.10576. Bibcode:2021Univ....7...60G. doi:10.3390/universe7030060. ISSN 2218-1997.
  24. ^ Myrzakul, Aizhan; Good, Michael R. R. (2025-04-20). "The CAT and the mirror: Classical acceleration temperature and the Anti-de Sitter dynamical Casimir effect". International Journal of Modern Physics A. 40 (10n11): 2543014–2543021. Bibcode:2025IJMPA..4043014M. doi:10.1142/S0217751X25430146. ISSN 0217-751X.
  25. ^ Myrzakul, Aizhan; Good, Michael R. R. (2025-04-20). "The CAT and the mirror: Classical acceleration temperature and the Anti-de Sitter dynamical Casimir effect". International Journal of Modern Physics A. 40 (10n11): 2543014–2543021. Bibcode:2025IJMPA..4043014M. doi:10.1142/S0217751X25430146. ISSN 0217-751X.
  26. ^ Good, Michael R. R.; Linder, Eric V. (2025-04-10), Through the Looking-Glass, and What AdS Found There: quantum particle production with a Whittaker spectrum, arXiv:2504.07458, retrieved 2025-05-15
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