Entropic Information & Black Hole: Black Hole Information Entropy The Missing Link
Physical Science International Journal,
Page 20-34
DOI:
10.9734/psij/2022/v26i130304
Abstract
Understanding the ‘Area Law,’ in regards to the black hole entropy, based on an underlying fundamental theory has been one of the goals pursued by all models of quantum gravity. In black hole thermodynamics, black hole entropy is a measure of uncertainty or lack of information about the actual internal configuration of the system. The Bekenstein bound corresponds to the interpretation in terms of bits of information of a given physical system down to the quantum level. However, at present, it is not known which microstates are counted by the entropy of black holes. Here, i show that the new formulation of entropic information approach, based on the bit of information gives an explanation of information processes involved in calculating entropy on missing information from black holes as well as down to the quantum level. Moreover, this formulation of entropic information constitutes a new coherent global mathematical framework candidate to be the Grand Unification Theory; with information as the ultimate building block of universe.
Keywords:
- Information
- entropy
- entropic information
- black hole
- quantum gravity
- Bekenstein bound
- bits
- grand unification theory
How to Cite
Denis, O. (2022). Entropic Information & Black Hole: Black Hole Information Entropy The Missing Link. Physical Science International Journal, 26(1), 20-34. https://doi.org/10.9734/psij/2022/v26i130304
References
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Bekenstein JD. Nonexistence of baryon number for static black holes Physical Review D. 1972;5:1239-1246. DOI: 10.1103/Physrevd.5.1239
Bekenstein JD. Black holes and the second law Lettere Al Nuovo Cimento Series . 1972;4:737-740. DOI: 10.1007/Bf02757029
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
Hawking SW, Ellis GFR. large scale structure of space time. Cambridge University Press; 1973. ISBN 978-0-521-09906-6.
Bekenstein JD. The quantum mass spectrum of the Kerr black hole Lettere Al Nuovo Cimento Series. 1974;2(11):467-470. DOI: 10.1007/Bf02762768
Hawking SW. Black hole explosions?. Nature. 248 (5443): 30–31. Bibcode:1974Natur. 1974;248...30H. DOI: 10.1038/248030a0. S2CID 4290107
Bekenstein Jacob D. How does the Entropy/Information Bound Work?. Foundations of Physics. 2005;35(11):1805–1823. arXiv:quant-ph/0404042. Bibcode: 2005FoPh...35.1805B. DOI:10.1007/s10701-005-7350-7. S2CID 118942877.
Bekenstein, Jacob (2008). "Bekenstein bound". Scholarpedia. 3 (10): 7374. Bibcode:2008SchpJ...3.7374B. doi:10.4249/scholarpedia.7374.
Bousso Raphael. 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.
Bousso Raphael. 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.
Bousso, Raphael. The holographic principle for general backgrounds. Classical and Quantum Gravity. 2000;17(5):997–1005. arXiv:hep-th/9911002. Bibcode:2000CQGra..17..997B. DOI: 10.1088/0264-9381/17/5/309. S2CID 14741276.
Bekenstein Jacob D. Holographic bound from second law of thermodynamics. Physics Letters B. 2000;481(2–4):339–345. arXiv:hep-th/0003058. Bibcode:2000PhLB..481..339B. DOI: 10.1016/S0370-2693(00)00450-0. S2CID 119427264.
Bousso Raphael. "The holographic principle" (PDF). Reviews of Modern Physics. 2002;74(3):825–874. arXiv:hep-th/0203101. Bibcode:2002RvMP...74..825B. DOI: 10.1103/RevModPhys.74.825. S2CID 55096624. Archived from the original (PDF) on 2010-05-23. Retrieved 2010-05-23.
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. 2003;289(2):58-65. Mirror link.
Bousso, Raphael, Flanagan Éanna É, Marolf Donald. Simple sufficient conditions for the generalized covariant entropy bound. Physical Review D. 2003;68(6):064001. arXiv:hep-th/0305149. Bibcode:2003PhRvD..68f4001B. DOI: 10.1103/PhysRevD.68.064001. S2CID 119049155.
Bekenstein Jacob D. Black holes and information theory. Contemporary Physics. 2004;45(1):31–43. arXiv:quant-ph/0311049. Bibcode:2004ConPh..45...31B. DOI: 10.1080/00107510310001632523. S2CID 118970250.
Tipler FJ. The structure of the world from pure numbers (PDF). Reports on Progress in Physics. 2005;68(4):897–964. arXiv:0704.3276. Bibcode:2005RPPh...68..897T.
DOI:10.1088/0034-4885/68/4/R04.. 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.
Casini Horacio. Relative entropy and the Bekenstein bound. Classical and Quantum Gravity. 2008;25(20):205021. arXiv:0804.2182. Bibcode:2008CQGra..25t5021C. DOI: 10.1088/0264-9381/25/20/205021. S2CID 14456556.
Jacob D Bekenstein. Black holes and entropy, Phys. Rev. D 7, 2333 – Published 15 April 1973An article within the collection: 2015 - General Relativity’s Centennial and the Physical Review D 50th Anniversary Milestones, DOI: https://doi.org/10.1103/PhysRevD.7.2333
Shannon Claude E. A mathematical theory of communication. Bell System Technical Journal. 1948;27(4):623–656. DOI: 10.1002/j.1538-7305.1948.tb00917.x. hdl:11858/00-001M-0000-002C-4317-B. (PDF, archived from here)
Denis O. Entropic information theory: Formulae and quantum gravity bits from bit. Physical Science International Journal. 2021;25(9):23-30. Available:https://doi.org/10.9734/psij/2021/v25i930281
Tipler FJ. The structure of the world from pure numbers (PDF). Reports on Progress in Physics. 2005;68(4):897–964. arXiv:0704.3276. Bibcode:2005RPPh...68..897T. DOI:10.1088/0034-4885/68/4/R04.
Hawking SW. Particle creation by black holes. Communications in Mathematical Physics. 1975;43(3):199–220. Bibcode:1975CMaPh..43..199H. DOI: 10.1007/BF02345020. S2CID 55539246.
Pickett SD, Sternberg MJ. Empirical scale of side-chain conformational entropy in protein folding. J Mol Biol. 1993;231(3):825-39
Richard Feynman. The feynman lectures on physics Vol I. Addison Wesley Longman; 1970. ISBN 978-0-201-02115-8.
Macrostates and Microstates Archived 2012-03-05 at the Wayback Machine.
Reif Frederick. Fundamentals of statistical and thermal physics. McGraw-Hill. 1965;66–70. ISBN 978-0-07-051800-1.
Pathria RK. statistical mechanics. Butterworth-Heinemann. 1965;10. ISBN 0-7506-2469-8 Available:https://en.wikipedia.org/wiki/GW170817 Available:https://fr.wikipedia.org/wiki/Cygnus_X-1 Available:https://en.wikipedia.org/wiki/List_of_most_massive_black_holes
Hawking SW, Penrose R. The singularities of gravitational collapse and cosmology. Proceedings of the Royal Society A. 1970;314(1519):529–548. Bibcode:1970RSPSA.314..529H. DOI: 10.1098/rspa.1970.0021. JSTOR 2416467
Hawking SW. Gravitational radiation from colliding black holes. Physical Review Letters. 1971;26(21):1344–1346. Bibcode:1971PhRvL..26.1344H. DOI: 10.1103/PhysRevLett.26.1344
Bekenstein JD. Nonexistence of baryon number for static black holes Physical Review D. 1972;5:1239-1246. DOI: 10.1103/Physrevd.5.1239
Bekenstein JD. Black holes and the second law Lettere Al Nuovo Cimento Series . 1972;4:737-740. DOI: 10.1007/Bf02757029
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
Hawking SW, Ellis GFR. large scale structure of space time. Cambridge University Press; 1973. ISBN 978-0-521-09906-6.
Bekenstein JD. The quantum mass spectrum of the Kerr black hole Lettere Al Nuovo Cimento Series. 1974;2(11):467-470. DOI: 10.1007/Bf02762768
Hawking SW. Black hole explosions?. Nature. 248 (5443): 30–31. Bibcode:1974Natur. 1974;248...30H. DOI: 10.1038/248030a0. S2CID 4290107
Bekenstein Jacob D. How does the Entropy/Information Bound Work?. Foundations of Physics. 2005;35(11):1805–1823. arXiv:quant-ph/0404042. Bibcode: 2005FoPh...35.1805B. DOI:10.1007/s10701-005-7350-7. S2CID 118942877.
Bekenstein, Jacob (2008). "Bekenstein bound". Scholarpedia. 3 (10): 7374. Bibcode:2008SchpJ...3.7374B. doi:10.4249/scholarpedia.7374.
Bousso Raphael. 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.
Bousso Raphael. 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.
Bousso, Raphael. The holographic principle for general backgrounds. Classical and Quantum Gravity. 2000;17(5):997–1005. arXiv:hep-th/9911002. Bibcode:2000CQGra..17..997B. DOI: 10.1088/0264-9381/17/5/309. S2CID 14741276.
Bekenstein Jacob D. Holographic bound from second law of thermodynamics. Physics Letters B. 2000;481(2–4):339–345. arXiv:hep-th/0003058. Bibcode:2000PhLB..481..339B. DOI: 10.1016/S0370-2693(00)00450-0. S2CID 119427264.
Bousso Raphael. "The holographic principle" (PDF). Reviews of Modern Physics. 2002;74(3):825–874. arXiv:hep-th/0203101. Bibcode:2002RvMP...74..825B. DOI: 10.1103/RevModPhys.74.825. S2CID 55096624. Archived from the original (PDF) on 2010-05-23. Retrieved 2010-05-23.
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. 2003;289(2):58-65. Mirror link.
Bousso, Raphael, Flanagan Éanna É, Marolf Donald. Simple sufficient conditions for the generalized covariant entropy bound. Physical Review D. 2003;68(6):064001. arXiv:hep-th/0305149. Bibcode:2003PhRvD..68f4001B. DOI: 10.1103/PhysRevD.68.064001. S2CID 119049155.
Bekenstein Jacob D. Black holes and information theory. Contemporary Physics. 2004;45(1):31–43. arXiv:quant-ph/0311049. Bibcode:2004ConPh..45...31B. DOI: 10.1080/00107510310001632523. S2CID 118970250.
Tipler FJ. The structure of the world from pure numbers (PDF). Reports on Progress in Physics. 2005;68(4):897–964. arXiv:0704.3276. Bibcode:2005RPPh...68..897T.
DOI:10.1088/0034-4885/68/4/R04.. 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.
Casini Horacio. Relative entropy and the Bekenstein bound. Classical and Quantum Gravity. 2008;25(20):205021. arXiv:0804.2182. Bibcode:2008CQGra..25t5021C. DOI: 10.1088/0264-9381/25/20/205021. S2CID 14456556.
Jacob D Bekenstein. Black holes and entropy, Phys. Rev. D 7, 2333 – Published 15 April 1973An article within the collection: 2015 - General Relativity’s Centennial and the Physical Review D 50th Anniversary Milestones, DOI: https://doi.org/10.1103/PhysRevD.7.2333
Shannon Claude E. A mathematical theory of communication. Bell System Technical Journal. 1948;27(4):623–656. DOI: 10.1002/j.1538-7305.1948.tb00917.x. hdl:11858/00-001M-0000-002C-4317-B. (PDF, archived from here)
Denis O. Entropic information theory: Formulae and quantum gravity bits from bit. Physical Science International Journal. 2021;25(9):23-30. Available:https://doi.org/10.9734/psij/2021/v25i930281
Tipler FJ. The structure of the world from pure numbers (PDF). Reports on Progress in Physics. 2005;68(4):897–964. arXiv:0704.3276. Bibcode:2005RPPh...68..897T. DOI:10.1088/0034-4885/68/4/R04.
Hawking SW. Particle creation by black holes. Communications in Mathematical Physics. 1975;43(3):199–220. Bibcode:1975CMaPh..43..199H. DOI: 10.1007/BF02345020. S2CID 55539246.
Pickett SD, Sternberg MJ. Empirical scale of side-chain conformational entropy in protein folding. J Mol Biol. 1993;231(3):825-39
Richard Feynman. The feynman lectures on physics Vol I. Addison Wesley Longman; 1970. ISBN 978-0-201-02115-8.
Macrostates and Microstates Archived 2012-03-05 at the Wayback Machine.
Reif Frederick. Fundamentals of statistical and thermal physics. McGraw-Hill. 1965;66–70. ISBN 978-0-07-051800-1.
Pathria RK. statistical mechanics. Butterworth-Heinemann. 1965;10. ISBN 0-7506-2469-8 Available:https://en.wikipedia.org/wiki/GW170817 Available:https://fr.wikipedia.org/wiki/Cygnus_X-1 Available:https://en.wikipedia.org/wiki/List_of_most_massive_black_holes
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