The entropy of the entangled Hawking radiation
DOI:
https://doi.org/10.59973/ipil.9Keywords:
Information paradox, Quantum gravity, Mass-energy-information principle, Entropy, Black hole, Black hole thermodynamics, Quantum InformationAbstract
Entropic information theory, as a unified informational theory, presents a new informational theoretical framework capable of fully describing the evaporation of the black holes phenomenon while resolving the information paradox, reconciling quantum formalism and relativistic formalism in a single approach. With a set of five new equivalent equations expressing entropy, and by introducing the Hawking temperature into one of them, it is possible to solve the black holes information paradox by being able to calculate the entropy of entangled Hawking radiation, entangled with the fields inside black holes, allowing us to extract information from inside black holes. The proposed model solves the information paradox of black holes by calculating a new entropy formula for the entropy of black holes as equal to the entropy of the pure state of entangled Hawking radiation, itself equal to the fine-grained entropy or von Neumann entropy, itself according to the work of Casini and Bousso equal to the Bekenstein bound which is itself equal, being saturated by Bekenstein-Hawking entropy, at this same entropy. Moreover, since the law of the entropy horizon of black holes turns out to be a special case of the Ryu-Takayanagi conjecture, this general formula for the fine-grained entropy of quantum systems coupled to gravity, equalizes the entropy of entangled Hawking radiation with the gravitational fine-grained entropy of black holes, and makes it possible to relate this resolution of the information paradox of black holes based on the concept of mass of the information bit to quantum gravity explaining the emergence of the quantum gravity process through the fundamentality of entangled quantum information.
References
Vopson M.M., The mass-energy-information equivalence principle. AIP Adv. 2019;9(9):095206. DOI:https://doi.org/10.1063/1.5123794, DOI: https://doi.org/10.1063/1.5123794
Denis , O. (2023). The Emergent Entangled Informational Universe. Physical Science International Journal, 27(1), 54–81. https://doi.org/10.9734/psij/2023/v27i1777. DOI: https://doi.org/10.9734/psij/2023/v27i1777
Hawking SW. (1974-03-01). Black hole explosions?". Nature. 1974;248(5443):30–31. DOI:10.1038/248030a0. ISSN1476-4687. S2CID4290107. DOI: https://doi.org/10.1038/248030a0
Casini H. Relative entropy and the Bekenstein bound. Class Quantum Grav. 2008;25(20):205021. DOI: 10.1088/0264-9381/25/20/205021. arXiv:0804.2182 DOI: https://doi.org/10.1088/0264-9381/25/20/205021
Bousso, Raphael (1999). "Holography in general space-times". Journal of High Energy Physics. 1999 (6): 028. arXiv:hep-th/9906022. Bibcode:1999JHEP...06..028B. doi:10.1088/1126-6708/1999/06/028. S2CID 119518763. DOI: https://doi.org/10.1088/1126-6708/1999/06/028
Bousso, Raphael (1999). "A covariant entropy conjecture". Journal of High Energy Physics. 1999 (7): 004. arXiv:hep-th/9905177. Bibcode:1999JHEP...07..004B. doi:10.1088/1126-6708/1999/07/004. S2CID 9545752. DOI: https://doi.org/10.1088/1126-6708/1999/07/004
Bousso, Raphael (2000). "The holographic principle for general backgrounds". Classical and Quantum Gravity. 17 (5): 997–1005. arXiv:hep-th/9911002. doi:10.1088/0264-9381/17/5/309. S2CID 14741276. DOI: https://doi.org/10.1088/0264-9381/17/5/309
Bekenstein, Jacob D. (2000). "Holographic bound from second law of thermodynamics". Physics Letters B. 481 (2–4): 339–345. arXiv:hep-th/0003058. doi:10.1016/S0370-2693(00)00450-0. S2CID 119427264. DOI: https://doi.org/10.1016/S0370-2693(00)00450-0
Bousso, Raphael (2002). "The holographic principle" (PDF). Reviews of Modern Physics. 74 (3): 825–874. arXiv:hep-th/0203101. doi:10.1103/RevModPhys.74.825. S2CID 55096624. Archived from the original (PDF) on 2011-08-12. Retrieved 2010-05-23. DOI: https://doi.org/10.1103/RevModPhys.74.825
Jacob D. Bekenstein, "Information in the Holographic Universe: Theoretical results about black holes suggest that the universe could be like a gigantic hologram", Scientific American, Vol. 289, No. 2 (August 2003), pp. 58-65. Mirror link. DOI: https://doi.org/10.1038/scientificamerican0803-58
Bousso, Raphael; Flanagan, Éanna É.; Marolf, Donald (2003). "Simple sufficient conditions for the generalized covariant entropy bound". Physical Review D. 68 (6): 064001. arXiv:hep-th/0305149. doi:10.1103/PhysRevD.68.064001. S2CID 119049155. DOI: https://doi.org/10.1103/PhysRevD.68.064001
Bekenstein, Jacob D. (2004). "Black holes and information theory". Contemporary Physics. 45 (1): 31–43. arXiv:quant-ph/0311049. doi:10.1080/00107510310001632523. S2CID 118970250. DOI: https://doi.org/10.1080/00107510310001632523
Tipler, F. J. (2005). "The structure of the world from pure numbers" (PDF). Reports on Progress in Physics. 68 (4): 897–964. arXiv:0704.3276. doi:10.1088/0034-4885/68/4/R04. S2CID 119620977.. Tipler gives a number of arguments for maintaining that Bekenstein's original formulation of the bound is the correct form. See in particular the paragraph beginning with "A few points ..." on p. 903 of the Rep. Prog. Phys. paper (or p. 9 of the arXiv version), and the discussions on the Bekenstein bound that follow throughout the paper.Barrau et Grain 2016] Aurélien Barrau et Julien Grain, Relativité générale : cours et exercices corrigés, Paris, Éditions Dunod, coll. « Sciences Sup / Physique », 17 août 2016, 2e éd. (1re éd. 24 août 2011), 1 vol., VIII-231, 17 × 24 cm (ISBN 978-2-10-074737-5, EAN 9782100747375, OCLC 958388884, BNF 45101424, SUDOC 195038134, présentation en ligne [archive], lire en ligne [archive]).E. Sawaguchi, Journal of the Physical Society of Japan, vol. 8, No. 5, pp. 615-629 (1953).
Almheiri A, Hartman T, Maldacena J, Shaghoulian E, Tajdini A. The entropy of Hawking radiation. Available:https://arxiv.org/abs/2006.06872v1.
Bousso, Penington Entanglement Wedge For Gravitating Regions; Sept 2022.Available: https://arxiv.org/abs/2208.04993
Ryu S, Takayanagi T. Aspects of holographic entanglement entropy. J High Energy Phys.2006-08-21;2006(8). Available:arXiv:hep-th/0605073:045-. DOI: 10.1088/1126-6708/2006/08/045. DOI: 10.1088/1126-6708/2006/08/045. ISSN 1029-8479. S2CID 14858887. DOI: https://doi.org/10.1088/1126-6708/2006/08/045
Stanford Institute for Theoretical Physics. Gravity and entanglement, [retrieved 2017-5-7]; 2015-10-15.
Aurélien Barrau et Julien Grain, Relativité générale : cours et exercices corrigés, Paris, Éditions Dunod, coll. « Sciences Sup / Physique », 17 août 2016, 2e éd. (1re éd. 24 août 2011), 1 vol., VIII-231, 17 × 24 cm (ISBN 978-2-10-074737-5, EAN 9782100747375, OCLC 958388884, BNF 45101424, SUDOC 195038134, présentation en ligne [archive], lire en ligne [archive]).
[Luminet 2011] Jean-Pierre Luminet, Illuminations : cosmos et esthétique, Paris, Éditions Odile Jacob, coll. « Sciences », 22 septembre 2011, 1re éd., 1 vol., 487-[16], 15,5 × 24 cm (ISBN 978-2-7381-2562-0 et 2-7381-2562-X, EAN 9782738125620, OCLC 780211696, BNF 42279998, SUDOC 155577441, présentation en ligne [archive], lire en ligne [archive]).
[Penrose 2007] Roger Penrose (trad. de l'anglais par de l'anglais par Céline Laroche), À la découverte des lois de l'univers : la prodigieuse histoire des mathématiques et de la physique [« The road to reality : a complete guide to the laws of the universe »], Paris, Éditions Odile Jacob, coll. « Sciences », 30 août 2007 (réimpr. 2008 et 2010), 1re éd., 1 vol., XXII-1061, 15,5 × 24 cm (ISBN 978-2-7381-1840-0, EAN 9782738118400, OCLC 209307388, BNF 41131526, SUDOC 118177311, présentation en ligne [archive], lire en ligne [archive])
"Top Cited Articles of All Time (2014 edition)". INSPIRE-HEP. Retrieved 26 December 2015.
physics.aps.org Available:https://physics.aps.org/articles/v9/49(accessed on 02 02 2023).
Denis, O. (2022). The Dark Side of the Entangled Informational Universe. Physical Science International Journal, 26(6), 39–58. https://doi.org/10.9734/psij/2022/v26i6750 DOI: https://doi.org/10.9734/psij/2022/v26i6750
Vopson M.M., Experimental protocol for testing the mass–energy–information equivalence principle. AIP Advances. 2022;12:035311. DOI:https://doi.org/10.1063/5.0087175 DOI: https://doi.org/10.1063/5.0087175
Daffertshofer A, Plastino AR. Landauer’s, principle and the conservation of information. Phys Lett A. 2005;342(3):213-6, DOI: 10.1016/j.physleta.2005.05.058. DOI: https://doi.org/10.1016/j.physleta.2005.05.058
Plenio MB, Vitelli V. The physics of forgetting: Landauer’s erasure principle and information theory. Contemp Phys. 2001;42(1):25-60. DOI: 10.1080/00107510010018916. DOI: https://doi.org/10.1080/00107510010018916
Ladyman J, Presnell S, Short AJ, Groisman B. The connection between logical and thermodynamic irreversibility. Stud Hist Philos Mod Phys. 2007;38(1): 58-79. DOI: 10.1016/j.shpsb.2006.03.007. DOI: https://doi.org/10.1016/j.shpsb.2006.03.007
Barbara Piechocinska, Information erasure, Phys. Rev. A 61, 062314 – Published 17 May 2000, DOI: https://doi.org/10.1103/PhysRevA.61.062314. DOI: https://doi.org/10.1103/PhysRevA.61.062314
Braunstein SL, Pati AK. Quantum information cannot be completely hidden in correlations: Implications for the black-hole information paradox. Phys Rev Lett. 2007;98(8):080502. Available: gr-qc/0603046 DOI:10.1103/PhysRevLett.98.080502, PMID 17359079 DOI: https://doi.org/10.1103/PhysRevLett.98.080502
Lee J-W, Lee J, Kim HC. Quantum informational dark energy: Dark energy from forgetting. arXiv E-Print, 2008;8. [arXiv/0709.0047]
Bérut A, Arakelyan A, Petrosyan A, Ciliberto S, Dillenschneider R, Lutz E. Experimental verification of Landauer’s principle linking information and thermodynamics. Journal Nature on March 8. Nature. 2012;483(7388):187-9. DOI:10.1038/nature10872, PMID 22398556 DOI: https://doi.org/10.1038/nature10872
Jacob D Bekenstein. Black holes and entropy, Phys. Rev. D 7, 2333 – Published 15 April 1973 An article within the collection: 2015 - General Relativity’s Centennial and the Physical Review D 50th Anniversary Milestones; 2019 DOI: https://doi.org/10.1103/PhysRevD.7.2333
Bekenstein JD. How does the Entropy / Information Bound Work? Found Phys. 2005;35(11):1805-23. Available:arXiv:quant-ph/0404042. DOI: 10.1007/s10701-005-7350-7. Bibcode. 2005FoPh... 35.1805B. DOI: 10.1007/s10701-005-7350-7.S2CID. 118942877. DOI: https://doi.org/10.1007/s10701-005-7350-7
Available online at Jacob B. Bekenstein bound. Scholarpedia. 2008;3(10):7374 (accessed: 12-06-2023) DOI: https://doi.org/10.4249/scholarpedia.7374
Wikipedia Available online: https://en.wikipedia.org/wiki/Bekenstein_bound.(accessed on 02 02 2023).
Anna Karlsson, Replica wormhole and island incompatibility with monogamy of entanglement, https://arxiv.org/abs/2007.10523
Ryu S, Takayanagi T. Holographic derivation of entanglement entropy from AdS/CFT. Phys Rev Lett. 2006, Available:arXiv:hep-th/0603001;96(18):181602. DOI: 10.1103/PhysRevLett.96.181602, PMID 1671235 DOI: https://doi.org/10.1103/PhysRevLett.96.181602
Penington G. Entanglement wedge reconstruction and the information paradox. J High Energ Phys; 2020. Available:arXiv:1905.08255 [hep-th];2020(9). DOI: 10.1007/JHEP09(2020)002. DOI: https://doi.org/10.1007/JHEP09(2020)002
Almheiri A, Engelhardt N, Marolf D, Maxfield H. The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole. J High Energ Phys; 2019.Available: arXiv:1905.08762[hep-th] ;2019(12). DOI: 10.1007/JHEP12(2019)063. DOI: https://doi.org/10.1007/JHEP12(2019)063
Hubeny VE, Rangamani M, Takayanagi T. A Covariant holographic entanglement entropy proposal. J Hepatol; 2007.Available:arXiv:0705.0016[hep-th];07:062 DOI: https://doi.org/10.1088/1126-6708/2007/07/062
Lewkowycz A, Maldacena J. Generalized gravitational entropy. J Hepatol; 2013. Available:arXiv:1304.4926[hep-th];08:090. DOI: https://doi.org/10.1007/JHEP08(2013)090
Barrella T, Dong X, Hartnoll SA, Martin VL. Holographic entanglement beyond classical gravity. J Hepatol; 2013. Available:arXiv:1306.4682 [hep-th];09:109. DOI: https://doi.org/10.1007/JHEP09(2013)109
Faulkner T, Lewkowycz A, Maldacena J. Quantum corrections to holographic entanglement entropy. J Hepatol; 2013. Available:arXiv:1307.2892 [hep-th];11:074. DOI: https://doi.org/10.1007/JHEP11(2013)074
Engelhardt N, Wall AC. Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime. J Hepatol. 2015, Available:arXiv:1408.3203 [hep-th];01:073 DOI: https://doi.org/10.1007/JHEP01(2015)073
Almheiri A, Mahajan R, Maldacena J, Zhao Y. The page curve of hawking radiation from semiclassical geometry. J High Energ Phys; 2020. Available:arXiv:1908.10996 [hep-th]. 2020;(3). DOI: 10.1007/JHEP03(2020)149. DOI: https://doi.org/10.1007/JHEP03(2020)149
Van Raamsdonk M. Lectures on gravity and entanglement. New Front Fields Strings. ISBN 978-981-314-943-4. S2CID 119273886. August 31 2016:297-351. Available: arXiv:1609.00026. DOI: 10.1142/9789813149441_0005. DOI: https://doi.org/10.1142/9789813149441_0005
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