Abstract
We attempt to describe geometry in terms of informational quantities for the universe considered as a finite ensemble of correlated quantum particles. As the main dynamical principle, we use the conservation of the sum of all kinds of entropies: thermodynamic, quantum and informational. The fundamental constant of speed is interpreted as the information velocity for the world ensemble and also connected with the gravitational potential of the universe on a particle. The two postulates, which are enough to derive the whole theory of Special Relativity, are re-formulated as the principles of information entropy universality and finiteness of information density.
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References
Carroll, R.: On the Emergence Theme of Physics. World Scientific, Singapore (2010)
Ashtekar, A., Rovelli, C., Smolin, L.: Weaving a classical geometry with quantum threads. Phys. Rev. Lett. 69, 237 (1992). https://doi.org/10.1103/PhysRevLett.69.237
Connes, A.: Von Neumann algebra automorphisms and time thermodynamics relation in general covariant quantum theories. Class. Quant. Grav. 11, 2899 (1994). https://doi.org/10.1088/0264-9381/11/12/007
Jacobson, T.: Thermodynamics of space-time: the Einstein equation of state. Phys. Rev. Lett. 75, 1260 (1995). https://doi.org/10.1103/PhysRevLett.75.1260
Lashkari, N., McDermott, M.B., Van Raamsdonk, M.: Gravitational dynamics from entanglement thermodynamics. JHEP 04, 195 (2014). https://doi.org/10.1007/JHEP04(2014)195
Cao, C., Carroll, S.M., Michalakis, S.: Space from Hilbert space: recovering geometry from bulk entanglement. Phys. Rev. D 95, 024031 (2017). https://doi.org/10.1103/PhysRevD.95.024031
Verlinde, E.P.: On the origin of gravity and the laws of newton. JHEP 04, 029 (2011). https://doi.org/10.1007/JHEP04(2011)029
Padmanabhan, T.: Thermodynamical aspects of gravity: new insights. Rep. Prog. Phys. 73, 046901 (2010). https://doi.org/10.1088/0034-4885/73/4/046901
Padmanabhan, T.: Distribution function of the atoms of spacetime and the nature of gravity. Entropy 17, 7420 (2015). https://doi.org/10.3390/e17117420
Padmanabhan, T.: Emergent perspective of gravity and dark energy. Res. Astron. Astrophys. 12, 891 (2012). https://doi.org/10.1088/1674-4527/12/8/003
Amari, Sh.-I.: Differential-Geometrical Methods in Statistics. Lecture Notes in Statistics, vol. 28. Springer-Verlag, Berlin Heidelberg (1985)
Amari, Sh.-I., Nagaoka, H.: Methods of Information Geometry. Translations of Mathematical Monographs, vol. 191 American Math. Soc (2000)
Caticha, A.: Entropic dynamics. Entropy 17, 6110 (2015). https://doi.org/10.3390/e17096110
Ribeiro, M., et al.: The entropy universe. Entropy 23, 222 (2021). https://doi.org/10.3390/e23020222
Wilde, M.M.: Quantum Information Theory. Cambridge University Press, Cambridge (2013)
Gogberashvili, M.: Information-probabilistic description of the universe. Int. J. Theor. Phys. 55, 4185 (2016). https://doi.org/10.1007/s10773-016-3045-4
Gogberashvili, M., Modrekiladze, B.: Probing the information-probabilistic description. Int. J. Theor. Phys. 61, 149 (2022). https://doi.org/10.1007/s10773-022-05129-3
Gogberashvili, M.: Cosmological constant from the entropy balance condition. Adv. High Energy Phys. 2018, 3702498 (2018). https://doi.org/10.1155/2018/3702498
Gogberashvili, M., Chutkerashvili, U.: Cosmological constant in the thermodynamic models of gravity. Theor. Phys. 2, 163 (2017). https://doi.org/10.22606/tp.2017.24002
Gogberashvili, M.: On the dynamics of the ensemble of particles in the thermodynamic model of gravity. J. Mod. Phys. 5, 1945 (2014). https://doi.org/10.4236/jmp.2014.517189
Gogberashvili, M., Kanatchikov, I.: Cosmological parameters from the thermodynamic model of gravity. Int. J. Theor. Phys. 53, 1779 (2014). https://doi.org/10.1007/s10773-013-1976-6
Gogberashvili, M., Kanatchikov, I.: Machian origin of the entropic gravity and cosmic acceleration. Int. J. Theor. Phys 51, 985 (2012). https://doi.org/10.1007/s10773-011-0971-z
Gogberashvili, M.: Thermodynamic gravity and the Schrodinger equation. Int. J. Theor. Phys. 50, 2391 (2011). https://doi.org/10.1007/s10773-011-0727-9
Gogberashvili, M.: ‘Universal’ FitzGerald contractions. Eur. Phys. J. Chem. 63, 317 (2009). https://doi.org/10.1140/epjc/s10052-009-1108-x
Gogberashvili, M.: Machian solution of hierarchy problem. Eur. Phys. J. C 54, 671 (2008). https://doi.org/10.1140/epjc/s10052-008-0559-9
Landauer, R.: Information is physical. Phys. Today 44, 23 (1991). https://doi.org/10.1063/1.881299
Horodecki, M., Oppenheim, J., Winter, A.: Partial quantum information. Nature 436, 673 (2005). https://doi.org/10.1038/nature03909
del Rio, L., Aberg, J., Renner, R., Dahlsten, O., Vedral, V.: The thermodynamic meaning of negative entropy. Nature 474, 61 (2011). https://doi.org/10.1038/nature10123
Cerf, N.J., Adami, C.: Negative entropy and information in quantum mechanics. Phys. Rev. Lett. 79, 5194 (1997). https://doi.org/10.1103/PhysRevLett.79.5194
Gogberashvili, M.: The energy meaning of Boltzmann’s constant. Mod. Phys. Lett. B 33, 2150235 (2021). https://doi.org/10.1142/S0217984921502353
Atkins, P.: Four Laws that Drive the Universe. Oxford University Press, Oxford (2007)
Kalinin, M., Kononogov, S.: Boltzmann’s constant, the energy meaning of temperature and thermodynamic irreversibility. Meas. Techn. 48, 632 (2005). https://doi.org/10.1007/s11018-005-0195-9
Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. 106, 620 (1957). https://doi.org/10.1103/PhysRev.106.620
Herrera, L.: Landauer principle and general relativity. Entropy 22, 340 (2020). https://doi.org/10.3390/e22030340
Ilgin, I., Yang, I.S.: Energy carries information. Int. J. Mod. Phys. A 29, 1450115 (2014). https://doi.org/10.1142/S0217751X14501152
Pavon, D., Radicella, N.: Does the entropy of the universe tend to a maximum? Gen. Rel. Grav. 45, 63 (2013). https://doi.org/10.1007/s10714-012-1457-x
Krishna, P.B., Mathew, T.K.: Holographic equipartition and the maximization of entropy. Phys. Rev. D 96, 063513 (2017). https://doi.org/10.1103/PhysRevD.96.063513
Hameroff, S., Penrose, R.: Consciousness in the universe. A review of the Orch OR theory. Phys. Life Rev. 11, 39 (2014). https://doi.org/10.1016/j.plrev.2013.08.002
Brukner, C., Zeilinger, A.: Conceptual inadequacy of the Shannon information in quantum measurements. Phys. Rev. A 63, 022113 (2001). https://doi.org/10.1103/PhysRevA.63.022113
Hartman, T., Maldacena, J.: Time evolution of entanglement entropy from black hole interiors. JHEP 05, 014 (2013). https://doi.org/10.1007/JHEP05(2013)014
Liu, H., Suh, S.J.: Entanglement tsunami: universal scaling in holographic thermalization. Phys. Rev. Lett. 112, 011601 (2014). https://doi.org/10.1103/PhysRevLett.112.011601
Liu, H., Suh, S.J.: Entanglement growth during thermalization in holographic systems. Phys. Rev. D 89, 066012 (2014). https://doi.org/10.1103/PhysRevD.89.066012
Kuwahara, T.: Strictly linear light cones in long-range interacting systems of arbitrary dimensions. Phys. Rev. X 10, 031010 (2020). https://doi.org/10.1103/PhysRevX.10.031010
Bekenstein, J.D.: Black holes and entropy. Phys. Rev. D 7, 2333 (1973). https://doi.org/10.1103/PhysRevD.7.2333
Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43 (1975) 199 (erratum: Commun. Math. Phys. 46 (1976) 206). https://doi.org/10.1007/BF02345020
Bekenstein, J.D.: A Universal upper bound on the entropy to energy ratio for bounded systems. Phys. Rev. D 23, 287 (1981). https://doi.org/10.1103/PhysRevD.23.287
Dvali, G.: Entropy bound and unitarity of scattering amplitudes. JHEP 03, 126 (2021). https://doi.org/10.1007/JHEP03(2021)126
Dvali, G.: Unitarity entropy bound: solitons and instantons. Fortsch. Phys. 69, 2000091 (2021). https://doi.org/10.1002/prop.202000091
Dvali, G.: Area law saturation of entropy bound from perturbative unitarity in renormalizable theories. Fortsch. Phys. 69, 2000090 (2021). https://doi.org/10.1002/prop.202000090
Gomes, H., Gryb, S., Koslowski, T.: Einstein gravity as a 3D conformally invariant theory. Class. Quant. Grav. 28, 045005 (2011). https://doi.org/10.1088/0264-9381/28/4/045005
Feynman, R.: The Character of Physical Law. MIT Press, Cambridge (2017)
Araki, H., Lieb, E.H.: Entropy inequalities. Commun. Math. Phys. 18, 160 (1970). https://doi.org/10.1007/BF01646092
Gogberashvili, M.: Symmetries of the entropy balance condition for the universe. PoS Regio2021 017 (2022). https://doi.org/10.22323/1.412.0017
Del Santo, F., Gisin, N.: The Relativity of indeterminacy. Entropy 23, 1326 (2021). https://doi.org/10.3390/e23101326
Bekenstein, J.D.: Universal upper bound on the entropy-to-energy ratio for bounded systems. Phys. Rev. D 23, 287 (1981). https://doi.org/10.1103/PhysRevD.23.287
Brown, H.R.: Physical Relativity. Clarendon Press, Oxford (2005)
Morin, D.: Introduction to Classical Mechanics. Cambridge University Press, Cambridge (2008)
Penrose, R.: Difficulties with inflationary cosmology. Ann. N.Y. Acad. Sci. 571, 249 (1989). https://doi.org/10.1111/j.1749-6632.1989.tb50513.x
Bolejko, K.: Gravitational entropy and the cosmological no-hair conjecture. Phys. Rev. D 97, 083515 (2018). https://doi.org/10.1103/PhysRevD.97.083515
Clifton, T., Ellis, G.F.R., Tavakol, R.: A gravitational entropy proposal. Class Quant. Grav. 30, 125009 (2013). https://doi.org/10.1088/0264-9381/30/12/125009
Rothman, T.: A Phase space approach to gravitational entropy. Gen. Rel. Grav 32, 1185 (2000). https://doi.org/10.1023/A:1001938114706
Schmidt-May, A., von Strauss, M.: Recent developments in bimetric theory. J. Phys. A 49, 183001 (2016). https://doi.org/10.1088/1751-8113/49/18/183001
Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Modified gravity and cosmology. Phys. Rep. 513, 1 (2012). https://doi.org/10.1016/j.physrep.2012.01.001
Acknowledgements
This work was supported by Shota Rustaveli National Science Foundation of Georgia (SRNSFG) through the Grant DI-18-335.
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Gogberashvili, M. Towards an Information Description of Space-Time. Found Phys 52, 74 (2022). https://doi.org/10.1007/s10701-022-00594-6
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DOI: https://doi.org/10.1007/s10701-022-00594-6