Journal of Holography Applications in Physics
de Sitter spacetime from holographic flat spacetime with inexact bulk quantum mechanics
Document Type : Regular article
Author
Graduate School of Human and Environmental Studies, Kyoto University
Abstract
We argue that the flat spacetime with inexact quantum mechanics in it is dual to the de Sitter spacetime with exact quantum mechanics in it, and the positive cosmological constant of this de Sitter spacetime is in the second order of the degree of the violation of the bulk quantum mechanics in the flat spacetime.
The flat spacetime is holographic and has a dual time-contracted boundary conformal field theory with two redefined central charges at null infinity.
The vanishing smallness of the observed positive cosmological constant suggests the extraordinary exactness of the bulk quantum mechanics in the flat spacetime.
Keywords
- Holographic Principle
- Quantum Entanglement
- Holographic Tensor Network
- Classicalization
- de Sitter Spacetime
Main Subjects
Article PDF
[1] G. ’t Hooft, arXiv:gr-qc/9310026.
[2] L. Susskind, “The world as a hologram”, J. Math. Phys. 36, 6377 (1995).
[3] R. Bousso, “The holographic principle”, Rev. Mod. Phys. 74, 825 (2002).
[4] J. D. Bekenstein, “Black holes and entropy”, Phys. Rev. D 7, 2333 (1973).
[5] S. W. Hawking, “Particle creation by black holes”, Commun. Math. Phys. 43, 199 (1975).
[6] G. W. Gibbons and S. W. Hawking, “Action integrals and partition functions in quantum gravity”, Phys. Rev. D 15, 2752 (1977).
[7] A. Strominger and C. Vafa, “Microscopic origin of the Bekenstein–Hawking entropy”, Phys. Lett. B 379, 99 (1996).
[8] J. M. Maldacena, “The large-N limit of superconformal field theories and supergravity”, Adv. Theor. Math. Phys. 2, 231 (1998).
[9] S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from non-critical string theory”, Phys. Lett. B 428, 105 (1998).
[10] E. Witten, “Anti de Sitter space and holography”, Adv. Theor. Math. Phys. 2, 253 (1998).
[11] O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, “Large-N field theories, string theory and gravity”, Phys. Rep. 323, 183 (2000).
[12] S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence”, Phys. Rev. Lett. 96, 181602 (2006).
[13] S. Ryu and T. Takayanagi, “Aspects of holographic entanglement entropy”, J. High Energy Phys. 08, 045 (2006).
[14] V. E. Hubeny, M. Rangamani and T. Takayanagi, “A covariant holographic entanglement entropy proposal”, J. High Energy Phys. 07, 062 (2007).
[15] M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy. Lect. Notes Phys., Vol. 931 Springer (2017).
[16] G. Vidal, “Entanglement renormalization”, Phys. Rev. Lett. 99, 220405 (2007).
[17] G. Vidal, “Class of quantum many-body states that can be efficiently simulated”, Phys. Rev. Lett. 101, 110501 (2008).
[18] B. Swingle, “Entanglement renormalization and holography”, Phys. Rev. D 86, 065007 (2012).
[19] B. Swingle, “Spacetime from entanglement”, Annu. Rev. Condens. Matter Phys. 9, 345 (2018).
[20] H. Matsueda, M. Ishibashi and Y. Hashizume, “Tensor network and a black hole”, Phys. Rev. D 87, 066002 (2013).
[21] N. Bao, C. Cao, S. M. Carroll, A. Chatwin-Davies and N. Hunter-Jones, “Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence”, Phys. Rev. D 91, 125036 (2015).
[22] E. Konishi, “Holographic interpretation of Shannon entropy of coherence of quantum pure states”, EPL 129, 11006 (2020).
[23] E. Konishi, “Random walk of bipartite spins in a classicalized holographic tensor net- work”, Results in Physics 19, 103410 (2020).
[24] E. Konishi, “Addendum: Holographic interpretation of Shannon entropy of coherence of quantum pure states”, EPL 132, 59901 (2020).
[25] E. Konishi, “Imaginary-time path-integral in bulk space from the holographic principle”, JHAP 1, 47 (2021).
[26] B. d’Espagnat, Conceptual Foundations of Quantum Mechanics. 2nd edn. W. A. Benjamin, Reading, Massachusetts (1976).
[27] D. Harlow and E. Shaghoulian, “Global symmetry, Euclidean gravity, and the black hole information problem”, J. High Energy Phys. 04, 175 (2021).
[28] D. Harlow and E. Shaghoulian, “Euclidean gravity and holography”, Int. J. Mod. Phys. D 2141005 (2021).
[29] D. Klemm and L. Vanzo, “Aspects of quantum gravity in de Sitter spaces”, J. Cos. Astr. Phys. 11, 006 (2004).
[30] G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, arXiv:1806.08362.
[31] P. Agrawal, G. Obied, P. J. Steinhardt and C. Vafa, “On the cosmological implications of the string Swampland”, Phys. Lett. B 784, 271 (2018).
[32] D. Andriot, “On the de Sitter swampland criterion”, Phys. Lett. B 785, 570 (2018).
[33] S. K. Garg and C. Krishnan, “Bounds on slow roll and the de Sitter Swampland”, J. High Energy Phys. 11, 075 (2019).
[34] H. Ooguri, E. Palti, G. Shiu and C. Vafa, “Distance and de Sitter conjectures on the Swampland”, Phys. Lett. B 788, 180 (2019).
[35] D. L¨ust, E. Palti and C. Vafa, “AdS and the Swampland”, Phys. Lett. B 797, 134867 (2019).
[36] E. Palti, “The Swampland: Introduction and Review”, Fortschr. Phys. 67, 1900037 (2019).
[37] C. P. Slichter, Principles of Magnetic Resonance. 3rd edn. Springer-Verlag, Berlin (1990).
[38] R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals. McGraw-Hill,
New York (1965).
[39] W. Rindler, “Visual horizons in world-models”, Mon. Not. Roy. Astr. Soc. 116, 662 (1956).
[40] J. D. Brown and M. Henneaux, “Central charges in the canonical realization of asymptotic symmetries: an example from three dimensional gravity”, Commun. Math. Phys. 104, 207 (1986).
[41] A. Strominger, “The dS/CFT correspondence”, J. High Energy Phys. 10, 029 (2001).
[42] A. Bagchi and R. Fareghbal, “BMS/GCA redux: towards flatspace holography from non-relativistic symmetries”, J. High Energy Phys. 10, 092 (2012).
[43] N. Margolus and L. B. Levitin, “The maximum speed of dynamical evolution”, Physica D 120, 188 (1998).
[44] S. Lloyd, “Computational capacity of the Universe”, Phys. Rev. Lett. 88, 237901 (2002).
[45] J. D. Barrow and D. J. Shaw, “The value of the cosmological constant”, Gen. Relativ. Gravit. 43, 2555 (2011).
[2] L. Susskind, “The world as a hologram”, J. Math. Phys. 36, 6377 (1995).
[3] R. Bousso, “The holographic principle”, Rev. Mod. Phys. 74, 825 (2002).
[4] J. D. Bekenstein, “Black holes and entropy”, Phys. Rev. D 7, 2333 (1973).
[5] S. W. Hawking, “Particle creation by black holes”, Commun. Math. Phys. 43, 199 (1975).
[6] G. W. Gibbons and S. W. Hawking, “Action integrals and partition functions in quantum gravity”, Phys. Rev. D 15, 2752 (1977).
[7] A. Strominger and C. Vafa, “Microscopic origin of the Bekenstein–Hawking entropy”, Phys. Lett. B 379, 99 (1996).
[8] J. M. Maldacena, “The large-N limit of superconformal field theories and supergravity”, Adv. Theor. Math. Phys. 2, 231 (1998).
[9] S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from non-critical string theory”, Phys. Lett. B 428, 105 (1998).
[10] E. Witten, “Anti de Sitter space and holography”, Adv. Theor. Math. Phys. 2, 253 (1998).
[11] O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, “Large-N field theories, string theory and gravity”, Phys. Rep. 323, 183 (2000).
[12] S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence”, Phys. Rev. Lett. 96, 181602 (2006).
[13] S. Ryu and T. Takayanagi, “Aspects of holographic entanglement entropy”, J. High Energy Phys. 08, 045 (2006).
[14] V. E. Hubeny, M. Rangamani and T. Takayanagi, “A covariant holographic entanglement entropy proposal”, J. High Energy Phys. 07, 062 (2007).
[15] M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy. Lect. Notes Phys., Vol. 931 Springer (2017).
[16] G. Vidal, “Entanglement renormalization”, Phys. Rev. Lett. 99, 220405 (2007).
[17] G. Vidal, “Class of quantum many-body states that can be efficiently simulated”, Phys. Rev. Lett. 101, 110501 (2008).
[18] B. Swingle, “Entanglement renormalization and holography”, Phys. Rev. D 86, 065007 (2012).
[19] B. Swingle, “Spacetime from entanglement”, Annu. Rev. Condens. Matter Phys. 9, 345 (2018).
[20] H. Matsueda, M. Ishibashi and Y. Hashizume, “Tensor network and a black hole”, Phys. Rev. D 87, 066002 (2013).
[21] N. Bao, C. Cao, S. M. Carroll, A. Chatwin-Davies and N. Hunter-Jones, “Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence”, Phys. Rev. D 91, 125036 (2015).
[22] E. Konishi, “Holographic interpretation of Shannon entropy of coherence of quantum pure states”, EPL 129, 11006 (2020).
[23] E. Konishi, “Random walk of bipartite spins in a classicalized holographic tensor net- work”, Results in Physics 19, 103410 (2020).
[24] E. Konishi, “Addendum: Holographic interpretation of Shannon entropy of coherence of quantum pure states”, EPL 132, 59901 (2020).
[25] E. Konishi, “Imaginary-time path-integral in bulk space from the holographic principle”, JHAP 1, 47 (2021).
[26] B. d’Espagnat, Conceptual Foundations of Quantum Mechanics. 2nd edn. W. A. Benjamin, Reading, Massachusetts (1976).
[27] D. Harlow and E. Shaghoulian, “Global symmetry, Euclidean gravity, and the black hole information problem”, J. High Energy Phys. 04, 175 (2021).
[28] D. Harlow and E. Shaghoulian, “Euclidean gravity and holography”, Int. J. Mod. Phys. D 2141005 (2021).
[29] D. Klemm and L. Vanzo, “Aspects of quantum gravity in de Sitter spaces”, J. Cos. Astr. Phys. 11, 006 (2004).
[30] G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, arXiv:1806.08362.
[31] P. Agrawal, G. Obied, P. J. Steinhardt and C. Vafa, “On the cosmological implications of the string Swampland”, Phys. Lett. B 784, 271 (2018).
[32] D. Andriot, “On the de Sitter swampland criterion”, Phys. Lett. B 785, 570 (2018).
[33] S. K. Garg and C. Krishnan, “Bounds on slow roll and the de Sitter Swampland”, J. High Energy Phys. 11, 075 (2019).
[34] H. Ooguri, E. Palti, G. Shiu and C. Vafa, “Distance and de Sitter conjectures on the Swampland”, Phys. Lett. B 788, 180 (2019).
[35] D. L¨ust, E. Palti and C. Vafa, “AdS and the Swampland”, Phys. Lett. B 797, 134867 (2019).
[36] E. Palti, “The Swampland: Introduction and Review”, Fortschr. Phys. 67, 1900037 (2019).
[37] C. P. Slichter, Principles of Magnetic Resonance. 3rd edn. Springer-Verlag, Berlin (1990).
[38] R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals. McGraw-Hill,
New York (1965).
[39] W. Rindler, “Visual horizons in world-models”, Mon. Not. Roy. Astr. Soc. 116, 662 (1956).
[40] J. D. Brown and M. Henneaux, “Central charges in the canonical realization of asymptotic symmetries: an example from three dimensional gravity”, Commun. Math. Phys. 104, 207 (1986).
[41] A. Strominger, “The dS/CFT correspondence”, J. High Energy Phys. 10, 029 (2001).
[42] A. Bagchi and R. Fareghbal, “BMS/GCA redux: towards flatspace holography from non-relativistic symmetries”, J. High Energy Phys. 10, 092 (2012).
[43] N. Margolus and L. B. Levitin, “The maximum speed of dynamical evolution”, Physica D 120, 188 (1998).
[44] S. Lloyd, “Computational capacity of the Universe”, Phys. Rev. Lett. 88, 237901 (2002).
[45] J. D. Barrow and D. J. Shaw, “The value of the cosmological constant”, Gen. Relativ. Gravit. 43, 2555 (2011).
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Volume 2, Issue 3
We would like to dedicate this issue to the memory of Prof. M.R. Setare.August 2022Pages 71-80
- Receive Date: 16 June 2022
- Revise Date: 18 July 2022
- Accept Date: 18 July 2022