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A postquantum theory of classical gravity? (1811.03116v3)

Published 7 Nov 2018 in hep-th and quant-ph

Abstract: The effort to discover a quantum theory of gravity is motivated by the need to reconcile the incompatibility between quantum theory and general relativity. Here, we present an alternative approach by constructing a consistent theory of classical gravity coupled to quantum field theory. The dynamics is linear in the density matrix, completely positive and trace preserving, and reduces to Einstein's theory of general relativity in the classical limit. Consequently, the dynamics doesn't suffer from the pathologies of the semiclassical theory based on expectation values. The assumption that general relativity is classical necessarily modifies the dynamical laws of quantum mechanics -- the theory must be fundamentally stochastic in both the metric degrees of freedom and in the quantum matter fields. This allows it to evade several no-go theorems purporting to forbid classical-quantum interactions. The measurement postulate of quantum mechanics is not needed -- the interaction of the quantum degrees of freedom with classical space-time necessarily causes decoherence in the quantum system. We first derive the general form of classical-quantum dynamics and consider realisations which have as its limit deterministic classical Hamiltonian evolution. The formalism is then applied to quantum field theory interacting with the classical space-time metric. One can view the classical-quantum theory as fundamental or as an effective theory useful for computing the back-reaction of quantum fields on geometry. We discuss a number of open questions from the perspective of both viewpoints.

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References (176)
  1. Gabriele Veneziano, “Construction of a crossing-simmetric, regge-behaved amplitude for linearly rising trajectories,” Il Nuovo Cimento A (1965-1970) 57, 190–197 (1968).
  2. Amitabha Sen, “Gravity as a spin system,” Phys. Lett., B 119, 89–91 (1982).
  3. Abhay Ashtekar, “New variables for classical and quantum gravity,” Physical Review Letters 57, 2244 (1986).
  4. Carlo Rovelli and Lee Smolin, “Knot theory and quantum gravity,” Physical Review Letters 61, 1155 (1988).
  5. Edward Witten, “On background-independent open-string field theory,” Phys. Rev. D 46, 5467–5473 (1992).
  6. Lucien Hardy, “Probability theories with dynamic causal structure: a new framework for quantum gravity,” arXiv preprint gr-qc/0509120  (2005).
  7. Ognyan Oreshkov, Fabio Costa,  and Časlav Brukner, “Quantum correlations with no causal order,” Nature communications 3, 1–8 (2012).
  8. Lee Smolin, “The thermodynamics of gravitational radiation,” General relativity and gravitation 16, 205–210 (1984).
  9. Stephen W Hawking and Don N Page, “Thermodynamics of black holes in anti-de sitter space,” Communications in Mathematical Physics 87, 577–588 (1983).
  10. Petar Simidzija, Achim Kempf,  and Eduardo Martin-Martinez, “Gravitational wave emission from the cmb and other thermal fields,” Physics Letters B 816, 136208 (2021).
  11. Bryce S DeWitt, “Definition of commutators via the uncertainty principle,” Journal of Mathematical Physics 3, 619–624 (1962).
  12. Kenneth Eppley and Eric Hannah, “The necessity of quantizing the gravitational field,” Foundations of Physics 7, 51–68 (1977).
  13. J Caro and L.L. Salcedo, “Impediments to mixing classical and quantum dynamics,” Physical Review A 60, 842 (1999).
  14. L.L. Salcedo, “Absence of classical and quantum mixing,” Physical Review A 54, 3657 (1996).
  15. Debendranath Sahoo, “Mixing quantum and classical mechanics and uniqueness of planck’s constant,” Journal of Physics A: Mathematical and General 37, 997 (2004).
  16. Daniel R Terno, “Inconsistency of quantum—classical dynamics, and what it implies,” Foundations of Physics 36, 102–111 (2006).
  17. LL Salcedo, “Statistical consistency of quantum-classical hybrids,” Physical Review A 85, 022127 (2012).
  18. Carlos Barceló, Raúl Carballo-Rubio, Luis J Garay,  and Ricardo Gómez-Escalante, “Hybrid classical-quantum formulations ask for hybrid notions,” Physical Review A 86, 042120 (2012).
  19. Chiara Marletto and Vlatko Vedral, “Why we need to quantise everything, including gravity,” NPJ Quantum Information 3, 29 (2017a).
  20. Jonathan Oppenheim, “Is it time to rethink quantum gravity?” International Journal of Modern Physics D  (2023), 10.1142/S0218271823420245.
  21. Iwao Sato, “An attempt to unite the quantum theory of wave field with the theory of general relativity,” Science reports of the Tohoku University 1st ser. Physics, chemistry, astronomy 33, 30–37 (1950).
  22. Christian Møller, ‘‘The energy-momentum complex in general relativity and related problems,” Les Théories Relativistes de la Gravitation, Colloques Internationaux CNRS 91, 2 (1962).
  23. Leon Rosenfeld, “On quantization of fields,” Nuclear Physics 40, 353–356 (1963).
  24. Don N Page and CD Geilker, “Indirect evidence for quantum gravity,” Physical Review Letters 47, 979 (1981).
  25. Isaac Layton, Jonathan Oppenheim,  and Zachary Weller-Davies, “A healthier semi-classical dynamics,” arXiv preprint arXiv:2208.11722  (2022).
  26. Jonathan Oppenheim, Barbara Soda, Carlo Sparaciari,  and Zachary Weller-Davies, “A coherence limit on superpositions constrained by classical gravity,”  (2022a), manuscript in preparation.
  27. Bryce DeWitt, “New directions for research in the theory of gravitation,” Winning paper submitted to Gravity Research Foundation’s essay contest in  (1953).
  28. Michael J Duff, Inconsistency of quantum field theory in curved spacetime, Tech. Rep. (1980) proceedings of Quantum Gravity 2, 81-105.
  29. WG Unruh, “Steps towards a quantum theory of gravity,” in Quantum theory of gravity. Essays in honor of the 60th birthday of Bryce S. DeWitt (1984).
  30. Steve Carlip, “Is quantum gravity necessary?” Classical and Quantum Gravity 25, 154010 (2008).
  31. Yakir Aharonov and Daniel Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed (Wiley-VCH, 2003) pp212-213.
  32. Andrea Mari, Giacomo De Palma,  and Vittorio Giovannetti, “Experiments testing macroscopic quantum superpositions must be slow,” Sci. Rep. 6, 22777 (2016), arXiv:1509.02408 [quant-ph] .
  33. Gordon Baym and Tomoki Ozawa, “Two-slit diffraction with highly charged particles: Niels bohr’s consistency argument that the electromagnetic field must be quantized,” Proceedings of the National Academy of Sciences 106, 3035–3040 (2009), http://www.pnas.org/content/106/9/3035.full.pdf .
  34. Alessio Belenchia, Robert M Wald, Flaminia Giacomini, Esteban Castro-Ruiz, Časlav Brukner,  and Markus Aspelmeyer, “Quantum superposition of massive objects and the quantization of gravity,” Physical Review D 98, 126009 (2018).
  35. The argument in Eppley and Hannah (1977) additionally contain a claim concerning superluminal signalling which is addressed in Albers et al. (2008); Kent (2018).
  36. A similar refutation was independently reached by David Poulin (private communication) and is implicit in Blanchard and Jadczyk (1995); Diosi (1995).
  37. James Mattingly, “Why Eppley and Hannah’s thought experiment fails,” Physical Review D 73, 064025 (2006).
  38. This has since been proven rigorously in Oppenheim et al. (2022c) under the assumptions that the dynamics is Markovian and is a completely positive and trace preserving map..
  39. S. W. Hawking, “Breakdown of predictability in gravitational collapse,” Phys. Rev. D 14, 2460–2473 (1976).
  40. S. W. Hawking, “The unpredictability of quantum gravity,” Communications in Mathematical Physics 87, 395–415 (1982).
  41. Ahmed Almheiri, Donald Marolf, Joseph Polchinski,  and James Sully, “Black holes: complementarity or firewalls?” Journal of High Energy Physics 2013, 1–20 (2013).
  42. Samuel L Braunstein, “Entangled black holes as ciphers of hidden information,” arXiv preprint arXiv:0907.1190v1  (2009).
  43. For a strong case for non-unitarity, see for exampleUnruh (2013); Unruh and Wald (2017).
  44. John Ellis, John S Hagelin, Dimitri V Nanopoulos,  and M Srednicki, “Search for violations of quantum mechanics,” Nuclear Physics B 241, 381–405 (1984).
  45. T. Banks, M. E. Peskin,  and L. Susskind, “Difficulties for the evolution of pure states into mixed states,” Nuclear Physics B 244, 125–134 (1984).
  46. David J Gross, “Is quantum gravity unpredictable?” Nuclear Physics B 236, 349–367 (1984).
  47. Sidney Coleman, ‘‘Black holes as red herrings: topological fluctuations and the loss of quantum coherence,” Nuclear Physics B 307, 867–882 (1988).
  48. William G. Unruh and Robert M. Wald, “Evolution laws taking pure states to mixed states in quantum field theory,” Phys. Rev. D 52, 2176–2182 (1995).
  49. J. Oppenheim and B. Reznik, “Fundamental destruction of information and conservation laws,” Arxiv preprint arXiv:0902.2361  (2009), the manuscript was never submitted to a journal, but an updated version is available upon request.
  50. David Poulin and John Preskill, “Information loss in quantum field theories,”  (2017), Frontiers of Quantum Information Physics, KITP.
  51. LE Ballentine, “Failure of some theories of state reduction,” Physical Review A 43, 9 (1991).
  52. Michael R Gallis and Gordon N Fleming, “Comparison of quantum open-system models with localization,” Physical Review A 43, 5778 (1991).
  53. Abner Shimony, “Desiderata for a modified quantum dynamics,” in PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1990 (Philosophy of Science Association, 1990) pp. 49–59.
  54. Sandro Donadi, Kristian Piscicchia, Catalina Curceanu, Lajos Diósi, Matthias Laubenstein,  and Angelo Bassi, “Underground test of gravity-related wave function collapse,” Nature Physics 17, 74–78 (2021).
  55. Jonathan Oppenheim, Carlo Sparaciari, Barbara Šoda,  and Zachary Weller-Davies, “The two classes of hybrid classical-quantum dynamics,” arXiv preprint arXiv:2203.01332  (2022b).
  56. Wayne Boucher and Jennie Traschen, “Semiclassical physics and quantum fluctuations,” Physical Review D 37, 3522 (1988).
  57. IV Aleksandrov, “The statistical dynamics of a system consisting of a classical and a quantum subsystem,” Zeitschrift für Naturforschung A 36, 902–908 (1981).
  58. Viktor Ivanovych Gerasimenko, “Dynamical equations of quantum-classical systems,” Theoretical and Mathematical Physics 50, 49–55 (1982).
  59. Lajos Diósi, Nicolas Gisin,  and Walter T Strunz, “Quantum approach to coupling classical and quantum dynamics,” Physical Review A 61, 022108 (2000).
  60. Arlen Anderson, “Quantum backreaction on” classical” variables,” Physical review letters 74, 621 (1995).
  61. Raymond Kapral and Giovanni Ciccotti, “Mixed quantum-classical dynamics,” The Journal of chemical physics 110, 8919–8929 (1999).
  62. Raymond Kapral, “Progress in the theory of mixed quantum-classical dynamics,” Annu. Rev. Phys. Chem. 57, 129–157 (2006).
  63. Oleg V Prezhdo and Vladimir V Kisil, “Mixing quantum and classical mechanics,” Physical Review A 56, 162 (1997).
  64. Lajos Diosi, ‘‘A universal master equation for the gravitational violation of quantum mechanics,” Physics letters A 120, 377–381 (1987).
  65. Roger Penrose, “Quantum computation, entanglement and state reduction,” Philosophical transactions-royal society of London series a mathematical physical and engineering sciences , 1927–1937 (1998).
  66. Lev P Pitaevskii, “Vortex lines in an imperfect bose gas,” Sov. Phys. JETP 13, 451–454 (1961).
  67. Eugene P Gross, “Structure of a quantized vortex in boson systems,” Il Nuovo Cimento (1955-1965) 20, 454–477 (1961).
  68. Nicolas Gisin, “Stochastic quantum dynamics and relativity,” Helv. Phys. Acta 62, 363–371 (1989).
  69. Nicolas Gisin, “Weinberg’s non-linear quantum mechanics and supraluminal communications,” Physics Letters A 143, 1–2 (1990).
  70. Joseph Polchinski, “Weinberg’s nonlinear quantum mechanics and the einstein-podolsky-rosen paradox,” Physical Review Letters 66, 397 (1991).
  71. JM Jauch, “The problem of measurement in quantum mechanics,” Helv. Phys. Acta 37, 293–316 (1964).
  72. Lajos Diósi and Jonathan J Halliwell, “Coupling classical and quantum variables using continuous quantum measurement theory,” Physical review letters 81, 2846 (1998).
  73. Asher Peres and Daniel R Terno, “Hybrid classical-quantum dynamics,” Physical Review A 63, 022101 (2001).
  74. D Kafri, JM Taylor,  and GJ Milburn, “A classical channel model for gravitational decoherence,” New Journal of Physics 16, 065020 (2014).
  75. Antoine Tilloy and Lajos Diósi, “Sourcing semiclassical gravity from spontaneously localized quantum matter,” Physical Review D 93, 024026 (2016).
  76. Antoine Tilloy and Lajos Diósi, “Principle of least decoherence for newtonian semiclassical gravity,” Physical Review D 96, 104045 (2017).
  77. Fay Dowker and Yousef Ghazi-Tabatabai, “Dynamical wavefunction collapse models in quantum measure theory,” Journal of Physics A: Mathematical and Theoretical 41, 205306 (2008).
  78. Philip Pearle, “Combining stochastic dynamical state-vector reduction with spontaneous localization,” Phys. Rev. A 39, 2277–2289 (1989).
  79. G. C. Ghirardi, A. Rimini,  and T. Weber, “Unified dynamics for microscopic and macroscopic systems,” Phys. Rev. D 34, 470–491 (1986).
  80. N. Gisin and I. C. Percival, “The quantum-state diffusion model applied to open systems,” Proc. R. Soc. London Ser. A 447, 189N (1992).
  81. Stephen L Adler and Todd A Brun, “Generalized stochastic schrödinger equations for state vector collapse,” Journal of Physics A: Mathematical and General 34, 4797 (2001).
  82. Giancarlo Ghirardi and Angelo Bassi, “Collapse Theories,” in The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta (Metaphysics Research Lab, Stanford University, 2020) Summer 2020 ed.
  83. Frederick Karolyhazy, “Gravitation and quantum mechanics of macroscopic objects,” Il Nuovo Cimento A (1965-1970) 42, 390–402 (1966).
  84. Lajos Diósi, “Models for universal reduction of macroscopic quantum fluctuations,” Physical Review A 40, 1165 (1989).
  85. Roger Penrose, “On gravity’s role in quantum state reduction,” General relativity and gravitation 28, 581–600 (1996).
  86. Michael JW Hall and Marcel Reginatto, “Interacting classical and quantum ensembles,” Physical Review A 72, 062109 (2005).
  87. Jonathan Oppenheim, Carlo Sparaciari, Barbara Šoda,  and Zachary Weller-Davies, “Objective trajectories in hybrid classical-quantum dynamics,” Quantum 7, 891 (2023).
  88. Philippe Blanchard and Arkadiusz Jadczyk, “On the interaction between classical and quantum systems,” Physics Letters A 175, 157–164 (1993).
  89. Ph Blanchard and Arkadiusz Jadczyk, “Event-enhanced quantum theory and piecewise deterministic dynamics,” Annalen der Physik 507, 583–599 (1995), https://arxiv.org/abs/hep-th/9409189.
  90. V. Gorini, A. Kossakowski,  and E. C. G. Sudarshan, “Completely positive dynamical semigroups of N-level systems,” Journal of Mathematical Physics 17, 821–825 (1976).
  91. G. Lindblad, “On the generators of quantum dynamical semigroups,” Comm. Math. Phys. 48, 119–130 (1976).
  92. David Poulin,  (2017), private communication (result announced in Poulin and Preskill (2017)).
  93. Lajos Diosi, “Quantum dynamics with two planck constants and the semiclassical limit,” arXiv preprint quant-ph/9503023  (1995).
  94. Lajos Diósi, “Hybrid quantum-classical master equations,” Physica Scripta 2014, 014004 (2014).
  95. Robert Alicki and Stanisław Kryszewski, “Completely positive bloch-boltzmann equations,” Physical Review A 68, 013809 (2003).
  96. Lajos Diósi, ‘‘The gravity-related decoherence master equation from hybrid dynamics,” in Journal of Physics-Conference Series, Vol. 306 (2011) p. 012006.
  97. Dynamics is time-local if it can be written as σ^˙⁢(t)=𝒦⁢(t)⁢σ^⁢(t)˙^𝜎𝑡𝒦𝑡^𝜎𝑡\dot{\hat{\sigma}}(t)=\mathcal{K}(t)\hat{\sigma}(t)over˙ start_ARG over^ start_ARG italic_σ end_ARG end_ARG ( italic_t ) = caligraphic_K ( italic_t ) over^ start_ARG italic_σ end_ARG ( italic_t ) rather than in convoluted form σ^˙⁢(t)=∫0t𝑑s⁢𝒦⁢(t,s)⁢σ^⁢(s)˙^𝜎𝑡superscriptsubscript0𝑡differential-d𝑠𝒦𝑡𝑠^𝜎𝑠\dot{\hat{\sigma}}(t)=\int_{0}^{t}ds\mathcal{K}(t,s)\hat{\sigma}(s)over˙ start_ARG over^ start_ARG italic_σ end_ARG end_ARG ( italic_t ) = ∫ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_t end_POSTSUPERSCRIPT italic_d italic_s caligraphic_K ( italic_t , italic_s ) over^ start_ARG italic_σ end_ARG ( italic_s ).
  98. Hendrik Anthony Kramers, “Brownian motion in a field of force and the diffusion model of chemical reactions,” Physica 7, 284–304 (1940).
  99. JE Moyal, “Stochastic processes and statistical physics,” Journal of the Royal Statistical Society. Series B (Methodological) 11, 150–210 (1949).
  100. Daniela Frauchiger and Renato Renner, “Single-world interpretations of quantum theory cannot be self-consistent,” arXiv preprint arXiv:1604.07422  (2016).
  101. Richard Arnowitt, Stanley Deser,  and Charles W Misner, “Republication of: The dynamics of general relativity,” General Relativity and Gravitation 40, 1997–2027 (2008).
  102. Jonathan Oppenheim, Carlo Sparaciari, Barbara Šoda,  and Zachary Weller-Davies, “Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity,”  (2022c), arXiv:2203.01982 .
  103. Jonathan Oppenheim, “A post-quantum theory of classical gravity,”  (2018), arXiv:1811.03116 .
  104. As Barbara Šoda noted, one can generalise this formalism to the case where the connection between the Hilbert spaces at points z𝑧{z}italic_z is non-trivial.
  105. K. Kraus, “Complementary observables and uncertainty relations,” Phys. Rev. D 35, 3070–3075 (1987).
  106. Michael M Wolf and J Ignacio Cirac, “Dividing quantum channels,” Communications in Mathematical Physics 279, 147–168 (2008).
  107. Vladimir Buzek, “Reconstruction of liouvillian superoperators,” Physical Review A 58, 1723 (1998).
  108. Heinz-Peter Breuer, Bernd Kappler,  and Francesco Petruccione, “Stochastic wave-function method for non-markovian quantum master equations,” Physical Review A 59, 1633 (1999).
  109. Inken Siemon, Alexander S Holevo,  and Reinhard F Werner, “Unbounded generators of dynamical semigroups,” Open Systems & Information Dynamics 24, 1740015 (2017).
  110. Robert Alicki, “Comment on “reduced dynamics need not be completely positive”,” Physical review letters 75, 3020 (1995).
  111. Peter Stelmachovic and Vladimir Buzek, “Dynamics of open quantum systems initially entangled with environment: Beyond the kraus representation,” Physical Review A 64, 062106 (2001).
  112. RF Pawula, “Rf pawula, phys. rev. 162, 186 (1967).” Phys. Rev. 162, 186 (1967).
  113. R.P Feynman and F.L Vernon, ‘‘The theory of a general quantum system interacting with a linear dissipative system,” Annals of Physics 24, 118–173 (1963).
  114. Andrzej Jamiołkowski, “Linear transformations which preserve trace and positive semidefiniteness of operators,” Reports on Mathematical Physics 3, 275–278 (1972).
  115. Man-Duen Choi, “Completely positive linear maps on complex matrices,” Linear algebra and its applications 10, 285–290 (1975).
  116. Richard Jozsa, ‘‘Fidelity for mixed quantum states,” Journal of Modern Optics 41, 2315–2323 (1994), Lemma 7 introduced this result to the quantum information community.
  117. A helpful suggestion by Carlo Sparaciari has streamlined the presentation of this section.
  118. Mark Srednicki, “Is purity eternal?” Nucl. Phys. B410, 143–154 (1993), arXiv:hep-th/9206056 .
  119. R Alicki, M Fannes,  and A Verbeure, “Unstable particles and the poincare semigroup in quantum field theory,” Journal of Physics A: Mathematical and General 19, 919–927 (1986).
  120. David Beckman, Daniel Gottesman, M.A. Nielsen,  and John Preskill, “Causal and localizable quantum operations,” Physical Review A 64, 052309 (2001).
  121. Avinash Baidya, Chandan Jana, R Loganayagam,  and Arnab Rudra, “Renormalization in open quantum field theory. part i. scalar field theory,” Journal of High Energy Physics 2017, 204 (2017), also, initial work by Poulin and Preskill (unpublished note).
  122. Jonathan Oppenheim and Zachery Weller-Davies, “Lorentz invariant information destruction is not lorentz covariant,”  (2020), unpublished draft.
  123. Jonathan Oppenheim and Zachary Weller-Davies, “Covariant path integrals for quantum fields back-reacting on classical space-time,” arXiv:2302.07283  (2023a).
  124. A Holevo, Journal of Mathematical Physics 37, 1812 (1996).
  125. Bryce S DeWitt, “Quantum theory of gravity. i. the canonical theory,” Physical Review 160, 1113 (1967).
  126. Jonathan Oppenheim, “The constraints of a continuous realisation of hybrid classical-quantum gravity,” Manuscript in preparation.
  127. Jonathan Oppenheim and Zachary Weller-Davies, “The constraints of post-quantum classical gravity,” Journal of High Energy Physics 2022, 1–39 (2022).
  128. Flavio Mercati, “A shape dynamics tutorial,”  (2017), arXiv:1409.0105 [gr-qc] .
  129. E Anderson, J Barbour, B Z Foster, B Kelleher,  and N O Murchadha, “The physical gravitational degrees of freedom,” Classical and Quantum Gravity 22, 1795–1802 (2005).
  130. Henrique Gomes and Tim Koslowski, “The link between general relativity and shape dynamics,” Classical and Quantum Gravity 29, 075009 (2012).
  131. Albert Einstein, “Do gravitational fields play an essential part in the structure of the elementary particles of matter?” The Principle of Relativity. Dover Books on Physics. June 1 , 189–198 (1952).
  132. Jochum J Van der Bij, H Van Dam,  and Yee Jack Ng, “The exchange of massless spin-two particles,” Physica A: Statistical Mechanics and its Applications 116, 307–320 (1982).
  133. Steven Weinberg, “The cosmological constant problem,” Reviews of modern physics 61, 1 (1989).
  134. William G Unruh, “Unimodular theory of canonical quantum gravity,” Physical Review D 40, 1048 (1989).
  135. Enrique Alvarez, “Can one tell einstein’s unimodular theory from einstein’s general relativity?” Journal of High Energy Physics 2005, 002 (2005).
  136. Lee Smolin, “Quantization of unimodular gravity and the cosmological constant problems,” Physical Review D 80, 084003 (2009).
  137. Mikhail Shaposhnikov and Daniel Zenhäusern, “Scale invariance, unimodular gravity and dark energy,” Physics Letters B 671, 187–192 (2009).
  138. This has since been made more precise in Oppenheim et al. (2022c); Oppenheim and Russo (2022).
  139. Vera C Rubin and W Kent Ford Jr, “Rotation of the andromeda nebula from a spectroscopic survey of emission regions,” The Astrophysical Journal 159, 379 (1970).
  140. Jonathan Oppenheim and Zachary Weller-Davies, “Path integrals for classical-quantum dynamics,” arXiv:2301.04677  (2023b).
  141. This purified state is reminiscent of the thermo-field double state, so ubiquitous in discussions around the AdS/CFT correspondence. It suggests that some of the apparent paradoxesMarolf and Wall (2012); Papadodimas and Raju (2014); Jafferis (2017); Oppenheim (2016) found in that context might be resolved by restricting measurements in this manner.
  142. Isaac Layton and Jonathan Oppenheim, “The classical-quantum limit,”  (2023), arXiv:2310.18271 [quant-ph] .
  143. See Holevo (1996); Oppenheim and Reznik (2009); Baez and Fong (2013); Marvian and Spekkens (2014) for extensions of Noether’s theorem to semi-groups.
  144. J David Brown and JW York, “Quasilocal energy in general relativity,” Mathematical aspects of classical field theory (Seattle, WA, 1991) 132, 129–142 (1992).
  145. Jonathan Oppenheim and Andrea Russo, “Gravity in the diffusion regime,”  (2022), manuscript in preparation.
  146. Isaac Layton, Jonathan Oppenheim, Andrea Russo,  and Zachary Weller-Davies, “The weak field limit of quantum matter back-reacting on classical spacetime,” Journal of High Energy Physics 2023, 1–43 (2023).
  147. Nima Arkani-Hamed, Savas Dimopoulos,  and Gia Dvali, “The hierarchy problem and new dimensions at a millimeter,” Physics Letters B 429, 263–272 (1998).
  148. Angelo Bassi, Kinjalk Lochan, Seema Satin, Tejinder P Singh,  and Hendrik Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Reviews of Modern Physics 85, 471 (2013).
  149. Jonas Schmöle, Mathias Dragosits, Hans Hepach,  and Markus Aspelmeyer, “A micromechanical proof-of-principle experiment for measuring the gravitational force of milligram masses,” Classical and Quantum Gravity 33, 125031 (2016).
  150. Daniel Carney, Philip CE Stamp,  and Jacob M Taylor, “Massive non-classical states and the observation of quantum gravity: a user’s manual,” arXiv preprint arXiv:1807.11494  (2018).
  151. Dvir Kafri and J. M. Taylor, “A noise inequality for classical forces,”  (2013), arXiv:1311.4558 .
  152. Sougato Bose, Anupam Mazumdar, Gavin W Morley, Hendrik Ulbricht, Marko Toroš, Mauro Paternostro, Andrew A Geraci, Peter F Barker, MS Kim,  and Gerard Milburn, “Spin entanglement witness for quantum gravity,” Physical review letters 119, 240401 (2017).
  153. Chiara Marletto and Vlatko Vedral, “Gravitationally induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity,” Physical review letters 119, 240402 (2017b).
  154. Mark Albers, Claus Kiefer,  and Marcel Reginatto, “Measurement analysis and quantum gravity,” Physical Review D 78, 064051 (2008).
  155. Adrian Kent, “Simple refutation of the eppley-hannah argument,” arXiv preprint arXiv:1807.08708  (2018).
  156. Bei Lok Hu and Enric Verdaguer, “Stochastic gravity: Theory and applications,” Living Reviews in Relativity 11, 3 (2008).
  157. Bill Unruh, “The view from gr,”  (2013), Black Holes: Complementarity, Fuzz, or Fire?
  158. William G Unruh and Robert M Wald, “Information loss,” Reports on Progress in Physics 80, 092002 (2017).
  159. Romeo Brunetti, Klaus Fredenhagen,  and Rainer Verch, “The generally covariant locality principle–a new paradigm for local quantum field theory,” Communications in Mathematical Physics 237, 31–68 (2003).
  160. Christopher J Fewster and Rainer Verch, “Dynamical locality and covariance: What makes a physical theory the same in all spacetimes?” in Annales Henri Poincaré, Vol. 13 (Springer, 2012) pp. 1613–1674.
  161. Klaus Fredenhagen and Falk Lindner, “Construction of kms states in perturbative qft and renormalized hamiltonian dynamics,” Communications in Mathematical Physics 332, 895–932 (2014).
  162. Klaus Fredenhagen and Kasia Rejzner, “Quantum field theory on curved spacetimes: Axiomatic framework and examples,” Journal of Mathematical Physics 57, 031101 (2016).
  163. Abhay Ashtekar and Anne Magnon, “Quantum fields in curved space-times,” Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 346, 375–394 (1975).
  164. M Asorey, Jose F Carinena,  and M Paramio, “Quantum evolution as a parallel transport,” Journal of Mathematical Physics 23, 1451–1458 (1982).
  165. Charles G Torre and Madhavan Varadarajan, “Functional evolution of free quantum fields,” Classical and quantum gravity 16, 2651 (1999).
  166. Ivan Agullo and Abhay Ashtekar, “Unitarity and ultraviolet regularity in cosmology,” Physical Review D 91, 124010 (2015).
  167. Donald Marolf and Aron C Wall, “Eternal black holes and superselection in ads/cft,” Classical and Quantum Gravity 30, 025001 (2012).
  168. Kyriakos Papadodimas and Suvrat Raju, ‘‘State-dependent bulk-boundary maps and black hole complementarity,” Physical Review D 89, 086010 (2014).
  169. Daniel Louis Jafferis, “Bulk reconstruction and the hartle-hawking wavefunction,” arXiv preprint arXiv:1703.01519  (2017).
  170. Jonathan Oppenheim, “Does Ads/CFT have an ensemble ambiguity problem?”  (2016), unpublished note, partially presented at the It from Qubit Annual Meeting, Simons Foundation headquarters, New York, December 8, 2016.
  171. John C Baez and Brendan Fong, ‘‘A noether theorem for markov processes,” Journal of Mathematical Physics 54, 013301 (2013).
  172. Iman Marvian and Robert W Spekkens, “Extending noether’s theorem by quantifying the asymmetry of quantum states,” Nature communications 5, 3821 (2014).
  173. John Preskill, “Lecture notes for physics 229: Quantum information and computation,” California Institute of Technology 16, 1–8 (1998).
  174. Michael A Nielsen and Isaac L Chuang, Quantum computation and quantum information (Cambridge university press, 2010).
  175. Reinhard F Werner, “Quantum states with einstein-podolsky-rosen correlations admitting a hidden-variable model,” Physical Review A 40, 4277 (1989).
  176. A Kossakowski, “On necessary and sufficient conditions for a generator of a quantum dynamical semi-group,” Bull. Acad. Polon. Sci. Math. 20, 1021 (1972).
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Summary

  • The paper presents a framework for classical-quantum systems via a completely positive, trace-preserving master equation that reconciles classical gravity with quantum matter.
  • The methodology leverages inherent stochastic interactions to bypass no-go theorems and naturally incorporate classical diffusion processes in the gravitational context.
  • The study reveals that quantum back-reaction induces decoherence in quantum matter, approximating Einstein’s equations and offering insights into black-hole evaporation phenomena.

Insights into "A Postquantum Theory of Classical Gravity?"

Jonathan Oppenheim's paper explores an alternative approach to gravity that diverges from the long-standing quest for a quantum theory of gravity. By attempting to construct a theory in which classical gravity interacts with quantum fields, this work addresses the perennial conflict between general relativity (GR) and quantum mechanics. In lieu of quantizing gravity, Oppenheim proposes a framework where gravity remains classical, yet interacts with quantum matter in a consistent, positive, trace-preserving manner. This approach opens fruitful avenues for understanding back-reaction effects and phenomena such as black-hole evaporation, while posing interesting challenges and implications for future theoretical developments.

Key Contributions and Claims

  1. Classical-Quantum Dynamics: The paper presents a general framework for classical-quantum (CQ) systems, offering a completely positive (CP), trace-preserving master equation. This hybrid evolution, expressed via an operator-based approach, aligns with linear quantum mechanics while admitting a classical interpretation for gravity. Notably, the dynamics avoid pathologies inherent in semiclassical models that combine classical and quantum elements.
  2. Stochastic Interaction: A notable aspect is the inherent stochasticity of the CQ interaction, which sidesteps no-go theorems against classical-quantum couplings. This stochastic nature mirrors the classical diffusion processes while facilitating a statistically consistent interface between quantum fields and classical spacetime, effectively incorporating concepts from spontaneous collapse models without ad hoc postulates.
  3. Decoherence and Collapse: The theory postulates that classical spacetime causes decoherence in quantum matter, leading to 'collapse' without requiring a measurement problem resolution. Decoherence aligns with observable phenomena without necessitating changes in the fundamental quantum structure or interpretation.
  4. Back-Reaction and Einstein's Equations: In a limiting case, quantum back-reaction on the classical field adheres to a form akin to Einstein's equations. This approximation provides a bridge to classical general relativity, supporting the assertion that classical gravity may not necessitate quantization under all circumstances.

Implications and Theoretical Speculations

  • Black-Hole Information: The model challenges the necessity for preserving quantum information in gravitational scenarios, possibly providing a natural outlet for information loss, as posited in black-hole evaporation debates. It contrasts with prevailing consensus and dispels concerns of anomalous heating through consistency in energy densities influenced by classical diffusion.
  • Experimental Tests: The stochastic and decoherent nature of spacetime in this framework suggests potential empirical tests through gravitational decoherence effects. These effects could manifest in laboratory conditions or through astrophysical observations like galaxy formation, with the absence or presence of gravitational diffusion serving as experimental constraints.

Future Directions in AI and Quantum Theories

Oppenheim's approach opens new dialogues about the overlap of quantum mechanics and classical phenomena, with direct implications for artificial intelligence models that must consider varying interpretations and predictions about fundamental forces. Future speculative work might involve:

  • Expanding the framework to unifying theories, recognizing unique experimental signatures of CQ gravity.
  • Developing AI models that incorporate fundamental uncertainty principles in classical interpretations, aiding simulations and predictions of quantum phenomena.
  • Investigating AI's role in visualizing and interpreting vast data from experiments designed to test quantum-gravity interactions.

In summary, Oppenheim's theoretical exploration into a consistent CQ interaction model provides a novel perspective where classical gravity's nuances remain palpable, challenging traditional avenues and encouraging re-evaluation of deeply held notions in physics.

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Authors (1)

  1. Jonathan Oppenheim
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