O problema do tempo na gravitação e cosmologia quânticas

Autores

DOI:

https://doi.org/10.47456/Cad.Astro.v6n2.49554

Palavras-chave:

gravitação quântica, cosmologia quântica, problema do tempo

Resumo

Neste artigo de divulgação, faz-se uma revisão de conceitos fundamentais da teoria quântica e de sua aplicação à construção de uma teoria quântica da gravitação e da cosmologia. Destaca-se o problema do tempo: como entender a evolução de um Universo quântico se não há uma variável clássica que represente um tempo absoluto?

Biografia do Autor

  • Leonardo Chataignier, Centro Brasileiro de Pesquisas Físicas

    Leonardo Chataignier é Pesquisador Adjunto do Centro Brasileiro de Pesquisas Físicas e Doutor em Física (2021) pela Universität zu Köln. Sua pesquisa atual foca em abordagens canônicas à gravitação quântica e sua aplicação à cosmologia.

Referências

[1] C. Kiefer, Quantum Gravity , International Series of Monographs on Physics (Oxford University Press, 2025), 4a ed.

[2] D. Oriti, Approaches to quantum gravity: Toward a new understanding of space, time and matter (Cambridge University Press, 2009).

[3] C. Rovelli, Quantum gravity , Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2004).

[4] C. Rovelli e F. Vidotto, Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory , Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2014).

[5] S. Bose et al., Spin Entanglement Witness for Quantum Gravity , Phys.Rev.Lett. 119, 240401 (2017).

[6] D. Carney, P. C. E. Stamp e J. M. Taylor, Tabletop experiments for quantum gravity: a user’s manual , Class. Quant. Grav. 36, 034001 (2019).

[7] G. Calcagni, Observational effects from quantum cosmology , Annalen Phys. 525, 323 (2013), [Erratum: Annalen Phys. 525, A165 (2013)].

[8] A. Addazi et al., Quantum gravity phenomenology at the dawn of the multimessenger era—A review , Prog. Part. Nucl. Phys. 125, 103948 (2022).

[9] L. Chataignier, C. Kiefer e P. Moniz, Observations in quantum cosmology , Class. Quant. Grav. 40, 223001 (2023).

[10] P. C. M. Delgado, Introdução à Cosmologia Quântica , Cadernos de Astronomia 4, 99 (2023).

[11] C. Kiefer e B. Sandhoefer, Quantum cosmology, Z. Naturforsch. A 77, 543 (2022).

[12] M. Bojowald, Loop quantum cosmology , Living Rev. Rel. 11, 4 (2008).

[13] M. Bojowald, Quantum Cosmology , vol. 835 deLecture Notes in Physics (Springer, 2011).

[14] I. Agullo e P. Singh, Loop quantum cosmology., inLoop Quantum Gravity: The First 30 Years, editado por A. Ashtekar e J. Pullin (World Scientific, 2017), 183–240.

[15] M. Bojowald, Cosmic Tangle: Loop Quantum Cosmology and CMB Anomalies , Universe 7, 186 (2021).

[16] C. J. Isham, Canonical quantum gravity and the problem of time , NATO Sci. Ser. C409, 157 (1993).

[17] K. V. Kuchar, Time and interpretations of quantum gravity , Int. J. Mod. Phys. D 20, 3 (2011).

[18] E. Anderson, The Problem of Time. Quantum Mechanics Versus General Relativity , vol. 190 de Fundamental Theories of Physics(Springer, 2017).

[19] L. D. Landau e E. M. Lifschits, Mechanics,vol.1de Course of Theoretical Physics (Butterworth-Heinemann, Oxford, 1976), 3a ed.

[20] L. D. Landau e E. M. Lifschits, The Classical Theory of Fields , vol. 2 de Course of Theoretical Physics (ButterworthHeinemann, Oxford, 1975), 4a ed.

[21] J. V. José e E. J. Saletan, Classical Dynamics: A Contemporary Approach (Cambridge University Press, 1998).

[22] J. D. Norton, The Dome: An Unexpectedly Simple Failure of Determinism , Philosophy of Science 75, 786–798 (2008).

[23] L. D. Landau e E. M. Lifshitz, Statistical Physics, Part 1 , vol. 5 de Course of Theoretical Physics (Butterworth-Heinemann, Oxford, 1980), 3a ed.

[24] S. H. Strogatz, Nonlinear Dynamics and Chaos(CRC Press, 2015), 2a ed.

[25] W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik , Zeitschrift für Physik 43, 172–198 (1927).

[26] P. A. M. Dirac, The Principles of Quantum Mechanics (OxfordUniversityPress, 1930), 1a ed.

[27] Cohen-Tannoudji, C. e Diu, B. e Laloë, F., Quantum Mechanics , vol. 1 (Wiley-VCH, 2020), 2a ed.

[28] A. Peres, Quantum Theory: Concepts and Methods, Fundamental Theories of Physics (Kluwer Academic Publishers, 2002).

[29] R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill Higher Education, 2000), 3a ed.

[30] L. de Broglie, Recherches sur la théorie des quanta, Annales de Physique (10e série) 3, 22 (1925).

[31] E. Schrödinger, Quantisierung als Eigenwertproblem. Erste Mitteilung , Annalen der Physik 384, 361 (1926).

[32] E. Schrödinger, Quantisierung als Eigenwertproblem. Zweite Mitteilung , Annalen der Physik 384, 489 (1926).

[33] R. P. Feynman, R. B. Leighton e M. Sands, The Feynman Lectures on Physics, Volume III: Quantum Mechanics (Addison-Wesley, Reading, Massachusetts, 1965).

[34] H.-D. Zeh, On the Interpretation of Measurement in Quantum Theory , Foundationsof Physics 1, 69 (1970).

[35] W. H. Zurek, Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse? , Physical Review D 24, 1516 (1981).

[36] W. H. Zurek, Environment-Induced Superselection Rules , Physical Review D 26, 1862 (1982).

[37] W. H. Zurek, Decoherence, einselection, and the quantum origins of the classical , Rev. Mod. Phys. 75, 715 (2003).

[38] M. A. Schlosshauer, Decoherence and the Quantum-To-Classical Transition (Springer, 2007).

[39] E. Joos et al., Decoherence and the Appearance of a Classical World in Quantum Theory(Springer, 2003), 2a ed.

[40] N. Pinto-Neto, Teorias e Interpretações da Mecânica Quântica (EditoraLivrariadaFísica, 2010).

[41] J. M. Bernardo e A. F. M. Smith, Bayesian Theory , Wiley Series in Probability and Statistics (Wiley, 2000).

[42] E. Jaynes, Probability Theory: The Logic of Science (Cambridge University Press, 2003).

[43] C. A. Fuchs, N. D. Mermin e R. Schack, An Introduction to QBism with an Application to the Locality of Quantum Mechanics , Am. J. Phys. 82, 749 (2014).

[44] A. Einstein, Relativity – The Special & The General Theory (Princeton University Press, 2019), Especial de 100 Anos ed.

[45] C. Misner, K. S. Thorne e J. A. Wheeler, Gravitation (Princeton University Press, 1973).

[46] R. M. Wald, General Relativity (University of Chicago Press, 1984).

[47] R. L. Arnowitt, S. Deser e C. W. Misner, The Dynamics of general relativity , Gen. Rel. Grav. 40, 1997 (2008).

[48] E. Gourgoulhon, 3+1 formalism and bases of numerical relativity (2007). ArXiv:gr -qc/0703035 .

[49] A. Anderson e J. W. York, Jr., Fixing Einstein’s equations , Phys. Rev. Lett. 82, 4384 (1999).

[50] J. W. York, Jr., Conformal ‘thin sandwich’ data for the initial-value problem , Phys. Rev. Lett. 82, 1350 (1999).

[51] P. A. M. Dirac, Generalized Hamiltonian dynamics , Can. J. Math. 2, 129 (1950).

[52] C. W. Misner, Feynman quantization of general relativity , Rev. Mod. Phys. 29, 497 (1957).

[53] P. A. M. Dirac, Generalized Hamiltonian dynamics , Proc. Roy. Soc. Lond. A 246, 326 (1958).

[54] P. A. M. Dirac, The Theory of gravitation in Hamiltonian form , Proc.Roy.Soc.Lond. A246, 333 (1958).

[55] P. A. M. Dirac, Lectures on Quantum Mechanics(Dover Publications, 2001).

[56] S. A. Hojman, K. Kuchař e C. Teitelboim, Geometrodynamics Regained , Annals Phys. 96, 88 (1976).

[57] M. Bojowald, E. I. Duque e A. Shah, Hypersurface deformations: Off-shell properties on phase space , Phys. Rev. D 111(12), 124048 (2025).

[58] J. M. Pons, D. C. Salisbury e L. C. Shepley,Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories , Phys. Rev. D 55, 658 (1997).

[59] M. Henneaux e C. Teitelboim, Quantization of gauge systems (PrincetonUniversity Press, 1992).

[60] A. Komar, Construction of a Complete Set of Independent Observables in the General Theory of Relativity , Phys. Rev. 111, 1182 (1958).

[61] P. G. Bergmann, Observables in General Relativity , Rev. Mod. Phys. 33, 510 (1961).

[62] P. G. Bergmann, ’Gauge-Invariant’ Variables in General Relativity , Phys. Rev. 124, 274 (1961).

[63] B. DeWitt, The quantization of geometry , inGravitation: An Introduction to Current Research , editado por L. Witten (Wiley, New York, 1962), 227–265.

[64] L. Lusanna, The objectivity of spacetime: Dirac observables and gauge variables for the gravitational field , AIPConf.Proc. 841, 330 (2006).

[65] B. Dittrich, Partial and complete observables for canonical general relativity , Class. Quant. Grav. 23, 6155 (2006).

[66] B. Dittrich, Partial and complete observables for Hamiltonian constrained systems , Gen. Rel. Grav. 39, 1891 (2007).

[67] J. Tambornino, Relational Observables in Gravity: a Review , SIGMA 8, 017 (2012).

[68] L.Lusanna, Non-Inertial Frames and Dirac Observables in Relativity (Cambridge University Press, 2019).

[69] L. Chataignier, Timeless Quantum Mechanics and the Early Universe , Springer Theses (Springer, 2022).

[70] C. Goeller, P. A. Hoehn e J. Kirklin, Diffeomorphism-invariant observables and dynamical frames in gravity: reconciling bulk locality with general covariance (2022). ArXiv:2206.01193 .

[71] C. Rovelli, Quantum evolving constants: Reply to comment on ‘Time in quantum gravity: An Hypothesis.’ , Phys. Rev. D 44, 1339 (1991).

[72] B. S. DeWitt, Quantum Theory of Gravity. 1. The Canonical Theory , Phys. Rev. 160, 1113 (1967).

[73] B. F. Schutz, Perfect Fluids in General Relativity: Velocity Potentials and a Variational Principle , Phys. Rev. D 2, 2762 (1970).

[74] B. F. Schutz, Hamiltonian Theory of a Relativistic Perfect Fluid , Phys. Rev. D 4, 3559 (1971).

[75] F. G. Alvarenga et al., Troubles with quantum anisotropic cosmological models: Loss of unitarity , Gen. Rel. Grav. 35, 1659 (2003).

[76] P. A. P. Molinari et al., Radiationdominated bouncing model with slow contraction and inflation , Phys. Rev. D 109(4), 043531 (2024).

[77] A. Einstein, Spielen Gravitationsfelder im Aufbau der materiellen Elementarteilchen eine wesentliche Rolle? , Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1919, 349 (1919).

[78] M. Henneaux e C. Teitelboim, The Cosmological Constant as a Canonical Variable , Phys. Lett. B 143, 415 (1984).

[79] W. G. Unruh, A Unimodular Theory of Canonical Quantum Gravity , Phys.Rev.D 40, 1048 (1989).

[80] A. O. Barvinsky e A. Y. Kamenshchik, Darkness without dark matter and energy – generalized unimodular gravity , Phys. Lett. B774, 59 (2017).

[81] A. O. Barvinsky et al., Dynamics of the generalized unimodular gravity theory , Phys. Rev. D 100, 023542 (2019).

[82] J. Magueijo, Cosmological time and the constants of nature , Phys. Lett. B 820, 136487 (2021).

[83] S. Gryb e K. P. Y. Thébault, Time Regained: Symmetry and Evolution in Classical Mechanics (OxfordUniversityPress, 2024).

[84] R. Casadio et al., Relaxation of first-class constraints and the quantization of gauge theories: From “matter without matter” to the reappearance of time in quantum gravity, Annals Phys. 470, 169783 (2024).

[85] M.S.KlingereR.G.Leigh, The Problem of Time and its Quantum Resolution (2025). ArXiv:2504.00152 .

[86] D. Marolf, Quantum observables and recollapsing dynamics , Class. Quant. Grav. 12, 1199 (1995).

[87] D. Marolf, Observables and a Hilbert space for Bianchi IX , Class. Quant. Grav. 12, 1441 (1995).

[88] S. B. Giddings, D. Marolf e J. B. Hartle, Observables in effective gravity , Phys. Rev. D74, 064018 (2006).

[89] D. Marolf, Solving the Problem of Time in Mini-superspace: Measurement of Dirac Observables , Phys. Rev. D 79, 084016 (2009).

[90] L. Chataignier, Construction of quantum Dirac observables and the emergence of WKB time , Phys. Rev. D 101, 086001 (2020).

[91] P. A. Hoehn, A. R. H. Smith e M. P. E. Lock,Trinity of relational quantum dynamics, Phys. Rev. D 104(6), 066001 (2021).

[92] L.Chataignier, Relational observables, reference frames, and conditional probabilities , Phys. Rev. D 103, 026013 (2021).

[93] P. A. Hoehn, A. R. H. Smith e M. P. E. Lock,Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings, Front. in Phys. 9, 181 (2021).

[94] A. Baldazzi, K. Falls e R. Ferrero, Relational observables in asymptotically safe gravity, Annals Phys. 440, 168822 (2022).

[95] L. Chataignier et al., Relational Dynamics with Periodic Clocks (2024). ArXiv:2409 .06479.

[96] D. N. Page e W. K. Wootters, Evolution without Evolution: Dynamics Described by Stationary Observables , Phys. Rev. D 27, 2885 (1983).

[97] W. K. Wootters, “Time” replaced by quantum correlations , Int. J. Theor. Phys. 23, 701 (1984).

[98] C.E.Dolby, The Conditional probability interpretation of the Hamiltonian constraint (2004). ArXiv:gr-qc/0406034 .

[99] R. P. Woodard, Enforcing the Wheelerde Witt Constraint the Easy Way , Class. Quant. Grav. 10, 483 (1993).

[100] U. H. Gerlach, Derivation of the ten einstein field equations from the semiclassical approximation to quantum geometrodynamics, Phys. Rev. 177, 1929 (1969).

[101] H. D. Zeh, Emergence of Classical Time From a Universal Wave Function , Phys. Lett. A 116, 9 (1986).

[102] H. D. Zeh, Time in Quantum Gravity , Phys. Lett. A 126, 311 (1988).

[103] C. Kiefer, Continuous Measurement of Minisuperspace Variables by Higher Multipoles, Class. Quant. Grav. 4, 1369 (1987).

[104] A. Strominger, Third quantization , Phil. Trans. R. Soc. A 329, 395 (1989).

[105] M. McGuigan, Third Quantization and the Wheeler-dewitt Equation , Phys. Rev. D 38, 3031 (1988).

[106] C. Kiefer e H. D. Zeh, Arrow of time in a recollapsing quantum universe , Phys. Rev. D51, 4145 (1995).

[107] E. Joos, Why do we observe a classical space-time? , Phys. Lett. A 116, 6 (1986).

[108] C. Kiefer, L. Chataignier e M. Tyagi, Time and its arrow from quantum geometrodynamics? , J. Phys. Conf. Ser. 2883, 012008 (2024).

[109] L. Chataignier, C. Kiefer e M. Tyagi, Origin of time and probability in quantum cosmology , J. Phys. Conf. Ser. 3017, 012007 (2025).

[110] D. Z. Albert, Time and Chance (Harvard University Press, 2000).

[111] C. Kiefer, N. Kwidzinski e D. Piontek, Singularity avoidance in Bianchi I quantum cosmology , Eur. Phys. J. C 79, 686 (2019).

[112] R. Haag, Local Quantum Physics –Fields, Particles, Algebras (Springer, 1992).

[113] A. Connes e C. Rovelli, Von Neumann algebra automorphisms and time thermodynamics relation in general covariant quantum theories , Class. Quant. Grav. 11, 2899 (1994).

[114] M. Takesaki, Theory of Operator Algebras II, vol. 125 de Encyclopaedia of Mathematical Sciences (Springer, 2003).

[115] T. Regge e C. Teitelboim, Role of Surface Integrals in the Hamiltonian Formulation of General Relativity , AnnalsPhys. 88, 286 (1974).

[116] A. P. Balachandran, L. Chandar e E. Ercolessi,Edge states in gauge theories: Theory, interpretations and predictions , Int. J. Mod. Phys. A 10, 1969 (1995).

[117] D. Marolf, Mass superselection, canonical gauge transformations, and asymptotically flat variational principles , Class. Quant. Grav. 13, 1871 (1996).

[118] T. Andrade e D. Marolf, Asymptotic Symmetries from finite boxes , Class. Quant. Grav. 33(1), 015013 (2016).

[119] M. Henneaux e C. Troessaert, The Asymptotic Structure of Gravity at Spatial Infinity in Four Spacetime Dimensions , Proc. Steklov Inst. Math. 309(1), 127 (2020).

[120] O. Fuentealba, M. Henneaux e C. Troessaert,Asymptotic Symmetry Algebra of Einstein Gravity and Lorentz Generators , Phys. Rev. Lett. 131(11), 111402 (2023).

[121] D. Marolf, Unitarity and Holography in Gravitational Physics , Phys. Rev. D 79, 044010 (2009).

[122] T. Jacobson, Boundary unitarity and the black hole information paradox ,Int.J.Mod. Phys. D 22, 1342002 (2013).

[123] D. Marolf, Holography without strings? , Class. Quant. Grav. 31, 015008 (2014).

[124] T. Jacobson e P. Nguyen, Diffeomorphism invariance and the black hole information paradox , Phys. Rev. D 100(4), 046002 (2019).

[125] G. ’t Hooft, The Holographic principle: Opening lecture , Subnucl. Ser. 37, 72 (2001).

[126] R. Bousso, The Holographic principle , Rev. Mod. Phys. 74, 825 (2002).

[127] A. C. Wall, A Survey of Black Hole Thermodynamics (2018). ArXiv:1804.10610 .

[128] J. M. Maldacena, The Large Nlimit of superconformal field theories and supergravity , Adv. Theor. Math. Phys. 2, 231 (1998).

[129] O. Aharony et al., Large N field theories, string theory and gravity , Phys. Rept. 323, 183 (2000).

[130] H. Năstase, Introduction to the AdS/CFT Correspondence (Cambridge University Press, 2015).

[131] L. Freidel, Reconstructing AdS/CFT (2008). ArXiv:0804.0632 .

[132] M. A. Demis¯ e, T T and Holography / , Tese de Doutorado, Chicago U., Chicago U. (2021). ArXiv:2112.02596 .

[133] G. Araujo-Regado, R. Khan e A. C. Wall, Cauchy slice holography: a new AdS/CFT dictionary , JHEP 03, 026 (2023).

[134] M. J. Blacker et al., Radial canonical AdS 3 gravity and TT, JHEP 01, 092 (2025).

[135] H. Everett, The Theory of the Universal Wave Function , Tese de Doutorado, Princeton University (1956).

[136] H. Everett, Relative state formulation of quantum mechanics , Rev. Mod. Phys. 29, 454 (1957).

[137] S. Saunders et al. (eds.), Many worlds? Everett, quantum theory, and reality (Oxford University Press, 2012).

[138] D. Wallace, The emergent multiverse: quantum theory according to the Everett Interpretation (Oxford University Press, Oxford, 2012).

[139] N. Pinto-Neto, The de Broglie–Bohm Quantum Theory and Its Application to Quantum Cosmology , Universe 7(5), 134 (2021).

[140] D. Dürr, S. Goldstein e N. Zanghì, Bohmian mechanics and the meaning of the wave function , inFoundations of Quantum Mechanics: A Symposium in Honor of Abner Shimony (1995).

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Publicado

29-10-2025

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[1]
L. Chataignier, “O problema do tempo na gravitação e cosmologia quânticas”, Cad. Astro., vol. 6, nº 2, p. 87–109, out. 2025, doi: 10.47456/Cad.Astro.v6n2.49554.