Lorentzian Holographic Gravity and the Time-Energy Uncertainty Principle

Document Type : Regular article

Author

Graduate School of Human and Environmental Studies, Kyoto University

Abstract

In this article, we present a heuristic derivation of the on-shell equation of the Lorentzian classicalized holographic tensor network in the presence of a non-zero mass in the bulk spacetime. This derivation of the on-shell equation is based on two physical assumptions. First, the Lorentzian bulk theory is in the ground state. Second, the law of Lorentzian holographic gravity is identified with the time--energy uncertainty principle. The arguments in this derivation could lead to a novel picture of Lorentzian gravity as a quantum mechanical time uncertainty based on the holographic principle and classicalization.

Keywords

Main Subjects

[1] G. ’t Hooft, arXiv:gr-qc/9310026. DOI: 10.48550/arXiv.gr-qc/9310026
[2] L. Susskind, “The world as a hologram”, J. Math. Phys. 36, 6377 (1995). DOI:10.1063/1.531249
[3] R. Bousso, “The holographic principle”, Rev. Mod. Phys. 74, 825 (2002). DOI:10.1103/RevModPhys.74.825
[4] J. M. Maldacena, “The large-N limit of superconformal field theories and supergravity”, Adv. Theor. Math. Phys. 2, 231 (1998). DOI: 10.1023/A:1026654312961
[5] 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). DOI: 10.1016/S03701573(99)00083-6
[6]B. Swingle, “Entanglement renormalization and holography”, Phys. Rev. D 86, 065007 (2012). DOI:10.1103/PhysRevD.86.065007
[7] H. Matsueda, M. Ishibashi and Y. Hashizume, “Tensor network and a black hole”, Phys. Rev. D 87, 066002 (2013). DOI: 10.1103/PhysRevD.87.066002
[8] 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). DOI: 10.1103/PhysRevD.91.125036
[9] A. Jahn and J. Eisert, “Holographic tensor network models and quantum error correction: a topical review”, Quantum Sci. Technol. 6, 033002 (2021). DOI: 10.1088/20589565/ac0293
[10]B. Chen, B. Czech and Z. Wang, “Quantum information in holographic duality”, Rep. Prog. Phys. 85, 046001 (2022). DOI: 10.1088/1361-6633/ac51b5
[11] E. Konishi, “Holographic interpretation of Shannon entropy of coherence of quantum pure states”, EPL 129, 11006 (2020). DOI: 10.1209/0295-5075/129/11006
[12] E. Konishi, “Addendum: Holographic interpretation of Shannon entropy of coherence of quantum pure states”, EPL 132, 59901 (2020). DOI: 10.1209/0295-5075/132/59901
[13] G. Vidal, “Entanglement renormalization”, Phys. Rev. Lett. 99, 220405 (2007). DOI:10.1103/PhysRevLett.99.220405
[14] G. Vidal, “Class of quantum many-body states that can be efficiently simulated”, Phys. Rev. Lett. 101, 110501 (2008). DOI: 10.1103/PhysRevLett.101.110501
[15] 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). DOI: 10.1103/PhysRevLett.96.181602
[16] M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy. Lect. Notes Phys., Vol. 931 Springer (2017). DOI: 10.1007/978-3-319-52573-0
[17] E. Konishi, “Imaginary-time path-integral in bulk space from the holographic principle”, JHAP 1, (1) 47-56 (2021). DOI: 10.22128/jhap.2021.432.1001
[18] G. C. Wick, A. S. Wightman and E. P. Wigner, “The intrinsic parity of elementary particles”, Phys. Rev. 88, 101 (1952). DOI: 10.1103/PhysRev.88.101
[19] J. M. Jauch, “Systems of observables in quantum mechanics”, Helv. Phys. Acta. 33, 711 (1960).
[20] E. Konishi, “Euclidean and Lorentzian actions of the classicalized holographic tensor network”, JHAP 2, (4) 1-10 (2022). DOI: 10.22128/jhap.2022.621.1036
[21] G. L. Sewell, “Quantum fields on manifolds: PCT and gravitationally induced thermal states”, Ann. Phys. 141, 201 (1982). DOI: 10.1016/0003-4916(82)90285-8
[22] D. Harlow, “Jerusalem lectures on black holes and quantum information”, Rev. Mod. Phys. 88, 015002 (2016). DOI: 10.1103/RevModPhys.88.015002
[23] E. Konishi, “On-shell equation of the Lorentzian classicalized holographic tensor network”, JHAP 3, (3) 37-44 (2023). DOI: 10.22128/jhap.2023.679.1052
[24] W. Heisenberg, “Uber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik”, Zeitschrift f¨ur Physik 43, 172 (1927). DOI: 10.1007/BF01397280
[25] L. Landau and R. Peierls, “Erweiterung des Unbestimmtheitsprinzips f¨ur die relativistische Quantentheorie”, Zeitschrift f¨ur Physik 69, 56 (1931). DOI: 10.1007/BF01391513
[26] L. Mandelstam and Ig. Tamm, “The uncertainty relation between energy and time in non-relativistic quantum mechanics”, J. Phys. USSR 9, 249 (1945).
[27] A. Messiah, Quantum Mechanics. Vol 1. North-Holland, Amsterdam (1972).
[28] M. Jammer, The Philosophy of Quantum Mechanics. Wiley, New York (1974).
[29] E. Konishi, “Quantum measuring systems: considerations from the holographic principle”, JHAP 3, (1) 31-38 (2023). DOI: 10.22128/jhap.2023.652.1039
Volume 4, Issue 1
March 2024
Pages 65-70
  • Receive Date: 18 January 2024
  • Revise Date: 28 January 2024
  • Accept Date: 18 February 2024