Conformal cyclic cosmology, gravitational entropy and quantum information. (English) Zbl 1528.83137
Summary: We inspect the basic ideas underlying Roger Penrose’s Conformal Cyclic Cosmology from the perspective of modern quantum information. We show that the assumed loss of degrees of freedom in black holes is not compatible with the quantum notion of entropy. We propose a unitary version of Conformal Cyclic Cosmology, in which quantum information is globally preserved during the entire evolution of our universe, and across the crossover surface to the subsequent aeon. Our analysis suggests that entanglement with specific quantum gravitational degrees of freedom might be at the origin of the second law of thermodynamics and the quantum-to-classical transition at mesoscopic scales.
MSC:
| 83F05 | Relativistic cosmology |
| 81P17 | Quantum entropies |
| 53C18 | Conformal structures on manifolds |
| 16E40 | (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) |
| 54C70 | Entropy in general topology |
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
| 26E70 | Real analysis on time scales or measure chains |
| 83C57 | Black holes |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
References:
| [1] | Ringström, H., The Cauchy Problem in General Relativity (2009), Zürich: European Mathematical Society, Zürich · Zbl 1169.83003 · doi:10.4171/053 |
| [2] | Misner, CW, The isotropy of the universe, Astrophys. J., 151, 431 (1968) · doi:10.1086/149448 |
| [3] | Liddle, A.R.: In: Masiero, A., Senjanović, G., Smirnov, A. (eds.) An Introduction to Cosmological Inflation, p. 269. doi:10.1142/9789814527538 |
| [4] | Hawking, SW; Ellis, GFR, The Large Scale Structure of Space-time (1973), Cambridge: Cambridge University Press, Cambridge · Zbl 0265.53054 · doi:10.1017/CBO9780511524646 |
| [5] | Wald, RM, General Relativity (1984), Chicago: University of Chicago Press, Chicago · Zbl 0549.53001 · doi:10.7208/chicago/9780226870373.001.0001 |
| [6] | Anguige, K.; Tod, KP, Isotropic cosmological singularities: I. Polytropic perfect fluid spacetimes, Ann. Phys., 276, 2, 257-293 (1999) · Zbl 1003.83027 · doi:10.1006/aphy.1999.5946 |
| [7] | Anguige, K.; Tod, KP, Isotropic cosmological singularities II. The Einstein-Vlasov system, Ann. Phys., 276, 2, 294-320 (1999) · Zbl 1003.83028 · doi:10.1006/aphy.1999.5947 |
| [8] | Anguige, K., Isotropic cosmological singularities III. The Cauchy problem for the inhomogeneous conformal Einstein-Vlasov equations, Ann. Phys., 282, 2, 395-419 (2000) · Zbl 0973.83042 · doi:10.1006/aphy.2000.6037 |
| [9] | Tod, KP, Isotropic cosmological singularities: other matter models, Class. Quant. Gravity, 20, 3, 521-534 (2003) · Zbl 1034.83032 · doi:10.1088/0264-9381/20/3/309 |
| [10] | Tod, P., Isotropic cosmological singularities in spatially homogeneous models with a cosmological constant, Class. Quant. Gravity, 24, 9, 2415-2432 (2007) · Zbl 1115.83023 · doi:10.1088/0264-9381/24/9/017 |
| [11] | Friedrich, H., The asymptotic characteristic initial value problem for Einstein’s vacuum field equations as an initial value problem for a first-order quasilinear symmetric hyperbolic system, Proc. Roy. Soc. Lond. A Math. Phys. Sci., 378, 1774, 401-421 (1981) · Zbl 0481.58026 · doi:10.1098/rspa.1981.0159 |
| [12] | Friedrich, H., On purely radiative space-times, Commun. Math. Phys., 103, 1, 35-65 (1986) · Zbl 0584.53038 · doi:10.1007/BF01464281 |
| [13] | Friedrich, H., Existence and structure of past asymptotically simple solutions of Einstein’s field equations with positive cosmological constant, J. Geom. Phys., 3, 1, 101-117 (1986) · Zbl 0592.53061 · doi:10.1016/0393-0440(86)90004-5 |
| [14] | Friedrich, H., On the existence of \(n\)-geodesically complete or future complete solutions of Einstein’s field equations with smooth asymptotic structure, Commun. Math. Phys., 107, 4, 587-609 (1986) · Zbl 0659.53056 · doi:10.1007/BF01205488 |
| [15] | Friedrich, H., On the global existence and the asymptotic behavior of solutions to the Einstein-Maxwell-Yang-Mills equations, J. Differ. Geom., 34, 2, 275-345 (1991) · Zbl 0737.53070 · doi:10.4310/jdg/1214447211 |
| [16] | Friedrich, H., Gravitational fields near space-like and null infinity, J. Geom. Phys., 24, 2, 83-163 (1998) · Zbl 0896.53053 · doi:10.1016/S0393-0440(97)82168-7 |
| [17] | Friedrich, H., Smooth non-zero rest-mass evolution across time-like infinity, Ann. Henri Poincaré, 16, 10, 2215-2238 (2015) · Zbl 1326.83086 · doi:10.1007/s00023-014-0368-7 |
| [18] | Tod, P., The equations of conformal cyclic cosmology, Gen. Relativ. Gravit., 47, 3, 1-13 (2015) · Zbl 1317.83113 · doi:10.1007/s10714-015-1859-7 |
| [19] | Penrose, R.: Before the Big Bang: an outrageous new perspective and its implications for particle physics. In: Proceedings of EPAC, Edinburgh, pp. 2759-2763 (2006). http://accelconf.web.cern.ch/AccelConf/e06/PAPERS/THESPA01.PDF |
| [20] | Penrose, R., Cycles of Time: An Extraordinary New View of the Universe (2010), London: The Bodley Head, London · Zbl 1222.00011 |
| [21] | Tod, P.: Some questions about conformal cyclic cosmology. Preprint arXiv:2202.10864 (2022) |
| [22] | Gurzadyan, VG; Penrose, R., On CCC-predicted concentric low-variance circles in the CMB sky, Eur. Phys. J. Plus, 128, 2, 1-17 (2013) · doi:10.1140/epjp/i2013-13022-4 |
| [23] | Gurzadyan, VG; Penrose, R., CCC and the Fermi paradox, Eur. Phys. J. Plus, 131, 11 (2016) · doi:10.1140/epjp/i2016-16011-1 |
| [24] | Meissner, KA; Nurowski, P.; Ruszczycki, B., Structures in the microwave background radiation, Proc. Roy. Soc. A Math. Phys. Eng. Sci., 469, 2155, 20130116 (2013) · doi:10.1098/rspa.2013.0116 |
| [25] | An, D.; Meissner, KA; Nurowski, P., Ring-type structures in the Planck map of the CMB, Mon. Not. R. Astron. Soc., 473, 3, 3251-3255 (2017) · doi:10.1093/mnras/stx2299 |
| [26] | An, D.; Meissner, KA; Nurowski, P.; Penrose, R., Apparent evidence for Hawking points in the CMB sky, Mon. Not. R. Astron. Soc., 495, 3, 3403-3408 (2020) · doi:10.1093/mnras/staa1343 |
| [27] | DeAbreu, A.; Contreras, D.; Scott, D., Searching for concentric low variance circles in the cosmic microwave background, J. Cosmol. Astropart. Phys., 2015, 12, 031-031 (2015) · doi:10.1088/1475-7516/2015/12/031 |
| [28] | Jow, DL; Scott, D., Re-evaluating evidence for hawking points in the CMB, J. Cosmol. Astropart. Phys., 2020, 3, 021-021 (2020) · doi:10.1088/1475-7516/2020/03/021 |
| [29] | Lopez, M., Bonizzi, P., Driessens, K., Koekoek, G., de Vries, J., Westra, R.: Searching for ring-like structures in the cosmic microwave background (2021). arXiv preprint arXiv:2105.03990 |
| [30] | Aurell, E.; Eckstein, M.; Horodecki, P., Quantum black holes as solvents, Found. Phys., 51, 2, 1-13 (2021) · Zbl 07422272 · doi:10.1007/s10701-021-00456-7 |
| [31] | Aurell, E.; Eckstein, M.; Horodecki, P., Hawking radiation and the quantum marginal problem, J. Cosmol. Astropart. Phys., 2022, 1, 014 (2022) · Zbl 1486.83090 · doi:10.1088/1475-7516/2022/01/014 |
| [32] | Page, DN, Is black-hole evaporation predictable?, Phys. Rev. Lett., 44, 301-304 (1980) · doi:10.1103/PhysRevLett.44.301 |
| [33] | Popescu, S., Nonlocality beyond quantum mechanics, Nat. Phys., 10, 4, 264 (2014) · doi:10.1038/nphys2916 |
| [34] | Horodecki, P.; Ramanathan, R., The relativistic causality versus no-signaling paradigm for multi-party correlations, Nat. Commun., 10, 1, 1701 (2019) · doi:10.1038/s41467-019-09505-2 |
| [35] | Lübbe, C.: Conformal scalar fields, isotropic singularities and conformal cyclic cosmologies (2013). preprint arXiv:1312.2059 |
| [36] | Tod, P.: Conformal methods in general relativity with application to conformal cyclic cosmology: a minicourse given at the IXth IMLG Warsaw 2018 (2021). preprint arXiv:2102.02701 |
| [37] | Bachelot, A., Propagation of massive scalar fields in pre-big bang cosmologies, Commun. Math. Phys., 380, 2, 973-1001 (2020) · Zbl 1454.81057 · doi:10.1007/s00220-020-03880-4 |
| [38] | Nurowski, P., Poincaré-Einstein approach to Penrose’s conformal cyclic cosmology, Class. Quant. Gravity, 38, 14, 145004 (2021) · Zbl 1482.83140 · doi:10.1088/1361-6382/ac0237 |
| [39] | Nurowski, P.: Conformally flat models in Penrose’s conformal cyclic cosmology (2021). preprint arXiv:2102.11823 · Zbl 1482.83140 |
| [40] | Kopiński, J., Kroon, J.A.V.: The Bach equation and the matching of spacetimes in the conformal cyclic cosmology models. Phys. Rev. D 106, 084034 (2022) doi:10.1103/PhysRevD.106.084034 preprint arXiv:2201.10875 |
| [41] | Penrose, R.; Hawking, SW; Israel, W., Singularity and time-asymmetry, General Relativity: An Einstein Centenary Survey, 581-638 (1979), Cambridge: Cambridge University Press, Cambridge · Zbl 0424.53001 |
| [42] | Clifton, T.; Ellis, GFR; Tavakol, R., A gravitational entropy proposal, Class. Quant. Gravity, 30, 12 (2013) · Zbl 1271.83008 · doi:10.1088/0264-9381/30/12/125009 |
| [43] | Egan, CA; Lineweaver, CH, A larger estimate of the entropy of the universe, Astrophys. J., 710, 2, 1825-1834 (2010) · doi:10.1088/0004-637x/710/2/1825 |
| [44] | Li, N.; Li, X-L; Song, S-P, Kullback-Leibler entropy and Penrose conjecture in the Lemaître-Tolman-Bondi model, Eur. Phys. J. C, 75, 3, 1-9 (2015) · Zbl 1411.83068 · doi:10.1007/s10701-018-0162-3 |
| [45] | Marozzi, G.; Uzan, J-P; Umeh, O.; Clarkson, C., Cosmological evolution of the gravitational entropy of the large-scale structure, Gen. Relativ. Gravit., 47, 10, 1-19 (2015) · Zbl 1327.83282 · doi:10.1007/s10714-015-1955-8 |
| [46] | Belgiorno, F.; Catino, G., A Weyl entropy of pure spacetime regions, Class. Quant. Gravity, 37, 22 (2020) · Zbl 1479.83109 · doi:10.1088/1361-6382/abb958 |
| [47] | Gregoris, D.; Ong, YC; Wang, B., Thermodynamics of shearing massless scalar field spacetimes is inconsistent with the Weyl curvature hypothesis, Phys. Rev. D, 102 (2020) · doi:10.1103/PhysRevD.102.023539 |
| [48] | Gregoris, D.; Ong, YC, Understanding gravitational entropy of black holes: a new proposal via curvature invariants, Phys. Rev. D, 105 (2022) · doi:10.1103/PhysRevD.105.104017 |
| [49] | Penrose, R., On gravity’s role in quantum state reduction, Gen. Relativ. Gravit., 28, 5, 581-600 (1996) · Zbl 0855.53046 · doi:10.1007/BF02105068 |
| [50] | Penrose, R., On the gravitization of quantum mechanics 1: quantum state reduction, Found. Phys., 44, 5, 557-575 (2014) · Zbl 1311.81009 · doi:10.1007/s10701-013-9770-0 |
| [51] | Braunstein, SL; van Loock, P., Quantum information with continuous variables, Rev. Mod. Phys., 77, 513-577 (2005) · Zbl 1205.81010 · doi:10.1103/RevModPhys.77.513 |
| [52] | Cerf, NJ; Adami, C., Negative entropy and information in quantum mechanics, Phys. Rev. Lett., 79, 5194-5197 (1997) · Zbl 0944.81003 · doi:10.1103/PhysRevLett.79.5194 |
| [53] | Zurek, WH, Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys., 75, 715-775 (2003) · Zbl 1205.81031 · doi:10.1103/RevModPhys.75.715 |
| [54] | Weedbrook, C.; Pirandola, S.; García-Patrón, R.; Cerf, NJ; Ralph, TC; Shapiro, JH; Lloyd, S., Gaussian quantum information, Rev. Mod. Phys., 84, 621-669 (2012) · doi:10.1103/RevModPhys.84.621 |
| [55] | Unruh, WG; Wald, RM, Information loss, Rep. Prog. Phys., 80, 9 (2017) · doi:10.1088/1361-6633/aa778e |
| [56] | Hawking, SW, Black hole explosions?, Nature, 248, 5443, 30-31 (1974) · Zbl 1370.83053 · doi:10.1038/248030a0 |
| [57] | Wald, RM, On particle creation by black holes, Commun. Math. Phys., 45, 1, 9-34 (1975) · doi:10.1007/BF01609863 |
| [58] | Heusler, M., Black Hole Uniqueness Theorems (1996), Cambridge: Cambridge University Press, Cambridge · Zbl 0945.83001 · doi:10.1017/CBO9780511661396 |
| [59] | Gisin, N., Stochastic quantum dynamics and relativity, Helv. Phys. Acta, 62, 4, 363-371 (1989) · Zbl 0632.46068 |
| [60] | Simon, C.; Bužek, V.; Gisin, N., No-signaling condition and quantum dynamics, Phys. Rev. Lett., 87 (2001) · doi:10.1103/PhysRevLett.87.170405 |
| [61] | Visser, M., Thermality of the Hawking flux, J. High Energy Phys., 2015, 7, 1-15 (2015) · Zbl 1388.83506 · doi:10.1007/JHEP07(2015)009 |
| [62] | Zurek, WH, Entropy evaporated by a black hole, Phys. Rev. Lett., 49, 1683-1686 (1982) · doi:10.1103/PhysRevLett.49.1683 |
| [63] | Page, DN, Comment on entropy evaporated by a black hole, Phys. Rev. Lett., 50, 1013-1013 (1983) · doi:10.1103/PhysRevLett.50.1013 |
| [64] | Page, DN, Hawking radiation and black hole thermodynamics, New J. Phys., 7, 203-203 (2005) · doi:10.1088/1367-2630/7/1/203 |
| [65] | ’t Hooft, G.: Dimensional reduction in quantum gravity (1993). preprint gr-qc/9310026 |
| [66] | Page, DN, Information in black hole radiation, Phys. Rev. Lett., 71, 3743-3746 (1993) · Zbl 0972.83567 · doi:10.1103/PhysRevLett.71.3743 |
| [67] | Harlow, D., Jerusalem lectures on black holes and quantum information, Rev. Mod. Phys., 88 (2016) · doi:10.1103/RevModPhys.88.015002 |
| [68] | Marolf, D., The black hole information problem: past, present, and future, Rep. Prog. Phys., 80, 9 (2017) · doi:10.1088/1361-6633/aa77cc |
| [69] | Almheiri, A.; Hartman, T.; Maldacena, J.; Shaghoulian, E.; Tajdini, A., The entropy of Hawking radiation, Rev. Mod. Phys., 93 (2021) · doi:10.1103/RevModPhys.93.035002 |
| [70] | Ashtekar, A., Implications of a positive cosmological constant for general relativity, Rep. Prog. Phys., 80, 10 (2017) · doi:10.1088/1361-6633/aa7bb1 |
| [71] | Krenn, G.; Zeilinger, A., Entangled entanglement, Phys. Rev. A, 54, 1793-1797 (1996) · doi:10.1103/PhysRevA.54.1793 |
| [72] | Walther, P.; Resch, KJ; Brukner, V.; Zeilinger, A., Experimental entangled entanglement, Phys. Rev. Lett., 97 (2006) · doi:10.1103/PhysRevLett.97.020501 |
| [73] | Nelson, W.; Wilson-Ewing, E., Pre-big-bang cosmology and circles in the cosmic microwave background, Phys. Rev. D, 84 (2011) · doi:10.1103/PhysRevD.84.043508 |
| [74] | Tod, P., Penrose’s circles in the CMB and a test of inflation, Gen. Relativ. Gravit., 44, 11, 2933-2938 (2012) · Zbl 1255.85035 · doi:10.1007/s10714-012-1431-7 |
| [75] | Balasin, H.; Nachbagauer, H., The energy-momentum tensor of a black hole, or what curves the Schwarzschild geometry?, Class. Quant. Gravity, 10, 11, 2271-2278 (1993) · Zbl 0788.53087 · doi:10.1088/0264-9381/10/11/010 |
| [76] | Arndt, M.; Hornberger, K., Testing the limits of quantum mechanical superpositions, Nat. Phys., 10, 4, 271-277 (2014) · doi:10.1038/nphys2863 |
| [77] | Fein, YY; Geyer, P.; Zwick, P.; Kiałka, F.; Pedalino, S.; Mayor, M.; Gerlich, S.; Arndt, M., Quantum superposition of molecules beyond 25 kDa, Nat. Phys., 15, 12, 1242-1245 (2019) · doi:10.1038/s41567-019-0663-9 |
| [78] | Carlesso, M.; Donadi, S.; Ferialdi, L.; Paternostro, M.; Ulbricht, H.; Bassi, A., Present status and future challenges of non-interferometric tests of collapse models, Nat. Phys., 18, 3, 243-250 (2022) · doi:10.1038/s41567-021-01489-5 |
| [79] | Bassi, A.; Lochan, K.; Satin, S.; Singh, TP; Ulbricht, H., Models of wave-function collapse, underlying theories, and experimental tests, Rev. Mod. Phys., 85, 471-527 (2013) · doi:10.1103/RevModPhys.85.471 |
| [80] | Donadi, S.; Piscicchia, K.; Curceanu, C.; Diósi, L.; Laubenstein, M.; Bassi, A., Underground test of gravity-related wave function collapse, Nat. Phys., 17, 1, 74-78 (2021) · doi:10.1038/s41567-020-1008-4 |
| [81] | Horodecki, R.; Horodecki, P.; Horodecki, M.; Horodecki, K., Quantum entanglement, Rev. Mod. Phys., 81, 865-942 (2009) · Zbl 1205.81012 · doi:10.1103/RevModPhys.81.865 |
| [82] | Grudka, A.; Hall, MJ; Horodecki, M.; Horodecki, R.; Oppenheim, J.; Smolin, JA, Do black holes create polyamory?, J. High Energy Phys., 2018, 11, 1-25 (2018) · Zbl 1404.83075 · doi:10.1007/JHEP11(2018)045 |
| [83] | Haag, R., Local Quantum Physics: Fields, Particles Algebras Theoretical and Mathematical Physics (1996), Berlin: Springer, Berlin · Zbl 0857.46057 · doi:10.1007/978-3-642-61458-3 |
| [84] | Dieks, D., Communication by EPR devices, Phys. Lett. A, 92, 6, 271-272 (1982) · doi:10.1016/0375-9601(82)90084-6 |
| [85] | Wootters, WK; Żurek, WH, A single quantum cannot be cloned, Nature, 299, 5886, 802-803 (1982) · Zbl 1369.81022 · doi:10.1038/299802a0 |
| [86] | Hayden, P.; Preskill, J., Black holes as mirrors: quantum information in random subsystems, J. High Energy Phys., 2007, 9, 120-120 (2007) · doi:10.1088/1126-6708/2007/09/120 |
| [87] | Susskind, L.; Thorlacius, L.; Uglum, J., The stretched horizon and black hole complementarity, Phys. Rev. D, 48, 3743-3761 (1993) · doi:10.1103/PhysRevD.48.3743 |
| [88] | Almheiri, A.; Marolf, D.; Polchinski, J.; Sully, J., Black holes: complementarity or firewalls?, J. High Energy Phys., 2013, 2, 1-20 (2013) · Zbl 1342.83121 · doi:10.1007/JHEP02(2013)062 |
| [89] | Penrose, R., The Road to Reality: A Complete Guide to the Laws of the Universe (2004), London: Jonathan Cape, London · Zbl 1188.00007 |
| [90] | Penrose, R., The Big Bang and its dark-matter content: whence, whither, and wherefore, Found. Phys., 48, 10, 1177-1190 (2018) · Zbl 1411.83068 · doi:10.1007/s10701-018-0162-3 |
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