Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Renormalisation of postquantum-classical gravity (2402.17844v3)

Published 27 Feb 2024 in hep-th and gr-qc

Abstract: One of the obstacles to reconciling quantum theory with general relativity, is constructing a theory which is both consistent with observation, and and gives finite answers at high energy, so that the theory holds at arbitrarily short distances. Quantum field theory achieves this through the process of renormalisation, but famously, perturbative quantum gravity fails to be renormalisable, even without coupling to matter. Recently, an alternative to quantum gravity has been proposed, in which the geometry of spacetime is taken to be classical rather than quantum, while still being coupled to quantum matter fields [1, 2]. This can be done consistently, provided the dynamics is fundamentally stochastic. Here, we find that the pure gravity theory is formally renormalisable. We do so via the path integral formulation by relating the classical-quantum action to that of quadratic gravity which is renormalisable. Because the action induces stochastic dynamics of space-time, rather than deterministic evolution of a quantum field, the classical-quantum theory is free of tachyons and negative norm ghosts. The key remaining question is whether the renormalisation prescription retains completely positive (CP) dynamics. This consideration appears to single out the scale invariant and asymptotically free theory. We give further evidence that the theory is CP, by showing that the two-point function of the scalar mode is positive. To support the use of precision accelerometers in testing the quantum nature of spacetime, we also compute the power spectral density of the acceleration. The results presented here have a number of implications for inflation, CMB data, and experiments to test the quantum nature of spacetime. They may also provide a way to compute probabilities in the regime of quantum gravity where spacetime can be treated as effectively classical.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (96)
  1. Jonathan Oppenheim, “A postquantum theory of classical gravity?” Physical Review X 13, 041040 (2023a), arXiv:1811.03116.
  2. Jonathan Oppenheim and Zachary Weller-Davies, “Covariant path integrals for quantum fields back-reacting on classical space-time,” arXiv:2302.07283  (2023a).
  3. Amitabha Sen, “Gravity as a spin system,” Phys. Lett., B 119, 89–91 (1982).
  4. Abhay Ashtekar, “New variables for classical and quantum gravity,” Physical Review Letters 57, 2244 (1986).
  5. Carlo Rovelli and Lee Smolin, “Knot theory and quantum gravity,” Physical Review Letters 61, 1155 (1988).
  6. Carlo Rovelli, Quantum gravity (Cambridge university press, 2004).
  7. Gabriele Veneziano, “Construction of a crossing-simmetric, regge-behaved amplitude for linearly rising trajectories,” Il Nuovo Cimento A (1965-1970) 57, 190–197 (1968).
  8. Joseph Polchinski, String theory (2005).
  9. Steven Weinberg, “Ultraviolet divergences in quantum theories of gravitation,” in General relativity (1979).
  10. 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).
  11. Christian Møller et al., “Les théories relativistes de la gravitation,” Colloques Internationaux CNRS 91 (1962).
  12. Leon Rosenfeld, “On quantization of fields,” Nuclear Physics 40, 353–356 (1963).
  13. Nicolas Gisin, “Stochastic quantum dynamics and relativity,” Helv. Phys. Acta 62, 363–371 (1989).
  14. Nicolas Gisin, “Weinberg’s non-linear quantum mechanics and supraluminal communications,” Physics Letters A 143, 1–2 (1990).
  15. Joseph Polchinski, “Weinberg’s nonlinear quantum mechanics and the einstein-podolsky-rosen paradox,” Physical Review Letters 66, 397 (1991).
  16. Don N Page and C.D. Geilker, “Indirect evidence for quantum gravity,” Physical Review Letters 47, 979 (1981).
  17. Bryce DeWitt, “New directions for research in the theory of gravitation,” Winning paper submitted to Gravity Research Foundation’s essay contest in  (1953).
  18. Michael J Duff, Inconsistency of quantum field theory in curved spacetime, Tech. Rep. (1980) proceedings of Quantum Gravity 2, 81-105.
  19. 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).
  20. Steve Carlip, “Is quantum gravity necessary?” Classical and Quantum Gravity 25, 154010 (2008).
  21. Philippe Blanchard and Arkadiusz Jadczyk, “On the interaction between classical and quantum systems,” Physics Letters A 175, 157–164 (1993).
  22. 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.
  23. Lajos Diosi, “Quantum dynamics with two planck constants and the semiclassical limit,” arXiv preprint quant-ph/9503023  (1995).
  24. David Poulin and John Preskill, “Information loss in quantum field theories,”  (2017), Frontiers of Quantum Information Physics, KITP.
  25. Jonathan Oppenheim, Carlo Sparaciari, Barbara Šoda,  and Zachary Weller-Davies, “The two classes of hybrid classical-quantum dynamics,”   (2022), arXiv:2203.01332 [quant-ph] .
  26. D Kafri, JM Taylor,  and GJ Milburn, “A classical channel model for gravitational decoherence,” New Journal of Physics 16, 065020 (2014).
  27. Antoine Tilloy and Lajos Diósi, ‘‘Sourcing semiclassical gravity from spontaneously localized quantum matter,” Physical Review D 93, 024026 (2016).
  28. Antoine Tilloy and Lajos Diósi, “Principle of least decoherence for newtonian semiclassical gravity,” Physical Review D 96, 104045 (2017).
  29. Jonathan Oppenheim, “The constraints of a continuous realisation of hybrid classical-quantum gravity,” Manuscript in preparation.
  30. Jonathan Oppenheim and Zachary Weller-Davies, “Path integrals for classical-quantum dynamics,” arXiv:2301.04677  (2023b).
  31. Kellogg S Stelle, “Renormalization of higher-derivative quantum gravity,” Physical Review D 16, 953 (1977).
  32. KS Stelle, “Classical gravity with higher derivatives,” General Relativity and Gravitation 9, 353–371 (1978).
  33. Alberto Salvio, ‘‘Quadratic gravity,” Frontiers in Physics  (2018).
  34. John F Donoghue and Gabriel Menezes, “On quadratic gravity,” arXiv preprint arXiv:2112.01974  (2021).
  35. RP Woodard, “Don’t throw the baby out with the bath water,” arXiv preprint arXiv:2306.09596  (2023).
  36. Philip D Mannheim, “Ghost problems from pauli–villars to fourth-order quantum gravity and their resolution,” International Journal of Modern Physics D 29, 2043009 (2020).
  37. Bob Holdom and Jing Ren, “Quadratic gravity: from weak to strong,” International Journal of Modern Physics D 25, 1643004 (2016).
  38. Damiano Anselmi, “On the quantum field theory of the gravitational interactions,” Journal of High Energy Physics 2017, 1–20 (2017).
  39. Alberto Salvio, Alessandro Strumia,  and Hardi Veermäe, “New infra-red enhancements in 4-derivative gravity,” The European Physical Journal C 78, 1–12 (2018).
  40. Alberto Salvio, “Bicep/keck data and quadratic gravity,” Journal of Cosmology and Astroparticle Physics 2022, 027 (2022).
  41. Alberto Salvio, “Metastability in quadratic gravity,” Physical Review D 99 (2019), 10.1103/physrevd.99.103507.
  42. Isaac Layton, Jonathan Oppenheim,  and Zachary Weller-Davies, “A healthier semi-classical dynamics,” arXiv preprint arXiv:2208.11722  (2022).
  43. 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).
  44. L. Onsager and S. Machlup, ‘‘Fluctuations and irreversible processes,” Phys. Rev. 91, 1505–1512 (1953).
  45. Isaac Layton, Jonathan Oppenheim,  and Emanuele Panella, “Normalisation and interpretations of generalised stochastic path integrals,”  (2023a), manuscript in preparation.
  46. Paul Cecil Martin, ED Siggia,  and HA Rose, “Statistical dynamics of classical systems,” Physical Review A 8, 423 (1973).
  47. Jonathan Oppenheim, Carlo Sparaciari, Barbara Šoda,  and Zachary Weller-Davies, “Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity,” Nature Communications 14, 7910 (2023), arXiv:2203.01982.
  48. Jonathan Oppenheim, Andrea Russo,  and Zachary Weller-Davies, “Diffeomorphism invariant classical-quantum path integrals for nordstrom gravity,”   (2024), arXiv:2401.05514 [gr-qc] .
  49. 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 (2023b).
  50. Michael Ostrogradsky, Mémoire sur les équations différentielles relatives an probléme des isopérimétres (Mem.Acad.St.Petersbourg 6, 1850) pp. 385–517.
  51. Hannes Risken and Hannes Risken, Fokker-planck equation (Springer, 1996).
  52. Richard P Woodard, “The theorem of ostrogradsky,” arXiv preprint arXiv:1506.02210  (2015).
  53. Alexander Ganz and Karim Noui, “Reconsidering the ostrogradsky theorem: higher-derivatives lagrangians, ghosts and degeneracy,” Classical and Quantum Gravity 38, 075005 (2021).
  54. Detlef Dürr and Alexander Bach, “The onsager-machlup function as lagrangian for the most probable path of a diffusion process,” Communications in Mathematical Physics 60, 153–170 (1978).
  55. Ying Chao and Jinqiao Duan, ‘‘The onsager–machlup function as lagrangian for the most probable path of a jump-diffusion process,” Nonlinearity 32, 3715 (2019).
  56. Richard P Feynman and Albert R Hibbs, Quantum mechanics and path integrals (McGraw-Hill, New York., 1965) section 12.6 on Brownian motion.
  57. Kunio Yasue, “A simple derivation of the onsager–machlup formula for one-dimensional nonlinear diffusion process,” Journal of Mathematical Physics 19, 1671–1673 (1978).
  58. Iosif L Buchbinder and Ilya Shapiro, Introduction to quantum field theory with applications to quantum gravity (Oxford University Press, USA, 2021).
  59. Richard Arnowitt, Stanley Deser,  and Charles W Misner, “Republication of: The dynamics of general relativity,” General Relativity and Gravitation 40, 1997–2027 (2008).
  60. RJ Rivers, “Lagrangian theory for neutral massive spin-2 fields,” Il Nuovo Cimento (1955-1965) 34, 386–403 (1964).
  61. Peter Van Nieuwenhuizen, “On ghost-free tensor lagrangians and linearized gravitation,” Nuclear Physics B 60, 478–492 (1973).
  62. Salomon Bochner, “Monotone funktionen, stieltjessche integrale und harmonische analyse,” Mathematische Annalen 108, 378–410 (1933).
  63. Luis Alvarez-Gaume, Alex Kehagias, Costas Kounnas, Dieter Lüst,  and Antonio Riotto, “Aspects of quadratic gravity,” Fortschritte der Physik 64, 176–189 (2016).
  64. Juan Maldacena, “Einstein gravity from conformal gravity,” arXiv preprint arXiv:1105.5632  (2011).
  65. Alberto Salvio and Alessandro Strumia, “Agravity,” Journal of High Energy Physics 2014, 1–26 (2014).
  66. J Julve and M Tonin, “Quantum gravity with higher derivative terms,” Nuovo Cim., B 46, 137–152 (1978).
  67. ES Fradkin and Arkady A Tseytlin, “Renormalizable asymptotically free quantum theory of gravity,” Nuclear Physics B 201, 469–491 (1982).
  68. David G Boulware, Gary T Horowitz,  and Andrew Strominger, “Zero-energy theorem for scale-invariant gravity,” Physical Review Letters 50, 1726 (1983).
  69. Francois David and Andrew Strominger, “On the calculability of newton’s constant and the renormalizability of scale invariant quantum gravity,” Physics Letters B 143, 125–129 (1984).
  70. Hans-Christoph Grunau and Frédéric Robert, “Positivity and almost positivity of biharmonic green’s functions under dirichlet boundary conditions,” Archive for rational mechanics and analysis 195, 865–898 (2010).
  71. Jonathan Oppenheim and Andrea Russo, “Gravity in the diffusion regime,”  (2022), manuscript in preparation.
  72. Alessia Platania, “Black holes in asymptotically safe gravity,” arXiv preprint arXiv:2302.04272  (2023).
  73. 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).
  74. 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 (2017).
  75. Ludovico Lami, Julen S Pedernales,  and Martin B Plenio, “Testing the quantumness of gravity without entanglement,” arXiv preprint arXiv:2302.03075  (2023).
  76. Serhii Kryhin and Vivishek Sudhir, “Distinguishable consequence of classical gravity on quantum matter,” arXiv preprint arXiv:2309.09105  (2023).
  77. 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).
  78. LE Ballentine, “Failure of some theories of state reduction,” Physical Review A 43, 9 (1991).
  79. Michael R Gallis and Gordon N Fleming, “Comparison of quantum open-system models with localization,” Physical Review A 43, 5778 (1991).
  80. 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.
  81. Bassam Helou, BJJ Slagmolen, David E McClelland,  and Yanbei Chen, “Lisa pathfinder appreciably constrains collapse models,” Physical Review D 95, 084054 (2017).
  82. 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).
  83. Alexei A Starobinsky, “A new type of isotropic cosmological models without singularity,” Physics Letters B 91, 99–102 (1980).
  84. Alexander Vilenkin, “Classical and quantum cosmology of the starobinsky inflationary model,” Physical Review D 32, 2511 (1985).
  85. Lei-Hua Liu, Tomislav Prokopec,  and Alexei A Starobinsky, “Inflation in an effective gravitational model and asymptotic safety,” Physical Review D 98, 043505 (2018).
  86. Stephen L Adler, “Einstein gravity as a symmetry-breaking effect in quantum field theory,” Reviews of Modern Physics 54, 729 (1982).
  87. 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).
  88. Jonathan Oppenheim, “Is it time to rethink quantum gravity?” International Journal of Modern Physics D  (2023b).
  89. Arkady A Tseytlin, “R4 terms in 11 dimensions and conformal anomaly of (2, 0) theory,” Nuclear Physics B 584, 233–250 (2000).
  90. Elias Kiritsis and Boris Pioline, “On r4 threshold corrections in type iib string theory and (p, q)-string instantons,” Nuclear Physics B 508, 509–534 (1997).
  91. David J Gross and Edward Witten, “Superstring modifications of einstein’s equations,” Nuclear Physics B 277, 1–10 (1986).
  92. John F Donoghue, “General relativity as an effective field theory: The leading quantum corrections,” Physical Review D 50, 3874 (1994).
  93. Mark Iosifovich Freidlin and Alexander D Wentzell, “Random perturbations,” in Random perturbations of dynamical systems (Springer, 1998) pp. 15–43.
  94. Markus F Weber and Erwin Frey, “Master equations and the theory of stochastic path integrals,” Reports on Progress in Physics 80, 046601 (2017).
  95. Goran Lindblad, “On the Generators of Quantum Dynamical Semigroups,” Commun. Math. Phys. 48, 119 (1976).
  96. Vittorio Gorini, Andrzej Kossakowski,  and E. C. G. Sudarshan, “Completely positive dynamical semigroups of n‐level systems,” Journal of Mathematical Physics 17, 821–825 (1976), https://aip.scitation.org/doi/pdf/10.1063/1.522979 .
Citations (1)
View on Semantic Scholar

Summary

  • The paper demonstrates that a pure gravity theory in a classical-quantum coupling framework is formally renormalisable using path integrals.
  • The methodology employs stochastic dynamics to naturally circumvent ghost instabilities typical of quadratic gravity.
  • The approach predicts measurable signatures through acceleration fluctuation power spectra, potentially enabling tabletop-scale empirical tests.

Renormalisation of Postquantum-Classical Gravity

In the intricate landscape of theoretical physics, the reconciliation of quantum theory with general relativity remains a formidable challenge. The paper under discussion, "Renormalisation of Postquantum-Classical Gravity," authored by Grudka et al., addresses this challenge by proposing a novel approach where the geometry of spacetime is treated classically, even when coupled with quantum matter fields. This approach hinges on fundamentally stochastic dynamics, providing an alternative route to quantum gravity that skirts the historical issue of non-renormalisability in perturbative quantum gravity.

Core Contributions

The primary contribution of the paper is the demonstration that a pure gravity theory, when cast in the framework of classical-quantum coupling, can be formally renormalisable. This is achieved via the path integral formulation, aligning the classical-quantum action with that of quadratic gravity. Quadratic gravity is well-regarded for being renormalisable, albeit with the caveat of harboring tachyons and ghosts due to higher-order derivatives in the action. However, the classical-quantum formulation posited here is purportedly free of these issues, thanks to its stochastic interpretation, which naturally circumvents the ghost-related instabilities seen in quadratic gravity.

The paper further explores the dynamics induced by this classical-quantum coupling, posing that it importantly retains the property of completely positive (CP) dynamics—a criterion that is a touchstone for ensuring consistent evolution of probabilities. Theoretical evidence suggests that the CP condition singles out theories that are both scale-invariant and asymptotically free.

Implications and Future Directions

The implications of this research stretch across both practical and theoretical realms. Practically, the classical treatment of the gravitational field may permit experimental tests through precision measurements. The authors compute the power spectral density of acceleration fluctuations, which is governed by a dimensionless coupling constant that can be empirically constrained. Such empirical tests, potentially realizable on a tabletop scale, could offer insights into the long-standing question of spacetime's classical or quantum nature.

Theoretically, this approach prompts a reevaluation of the necessary conditions for a consistent theory of gravity. By spotlighting the role of stochastic dynamics and renormalisation simultaneously, this paper provides a fresh perspective that may enrich the ongoing discourse on quantum gravity. Moreover, the theory's alignment with concepts such as asymptotic safety and scale invariance could yield intersecting lines of inquiry with other high-energy physics frameworks.

Conclusion

The work presents rigorous theoretical groundwork suggesting that treating spacetime as classical in a hybrid classical-quantum framework is a viable path to reconciling gravity with quantum mechanics. This path avoids the pitfalls of non-renormalisability and ghost instabilities, offering a theoretically and empirically testable quantum theory that retains classical spacetime geometry. Future research will need to solidify this framework, addressing open questions such as renormalisation of the matter sector and further empirical constraints, ultimately aiming to integrate these ideas into a coherent description of spacetime.

File Document Download Save Streamline Icon: https://streamlinehq.com PDF File Document Download Save Streamline Icon: https://streamlinehq.com Markdown