Advertisement

Synthese

pp 1–27 | Cite as

The multiple realizability of general relativity in quantum gravity

  • Rasmus JakslandEmail author
S.I.: Spacetime Functionalism
  • 115 Downloads

Abstract

Must a theory of quantum gravity have some truth to it if it can recover general relativity in some limit of the theory? This paper answers this question in the negative by indicating that general relativity is multiply realizable in quantum gravity. The argument is inspired by spacetime functionalism—multiple realizability being a central tenet of functionalism—and proceeds via three case studies: induced gravity, thermodynamic gravity, and entanglement gravity. In these, general relativity in the form of the Einstein field equations can be recovered from elements that are either manifestly multiply realizable or at least of the generic nature that is suggestive of functions. If general relativity, as argued here, can inherit this multiple realizability, then a theory of quantum gravity can recover general relativity while being completely wrong about the posited microstructure. As a consequence, the recovery of general relativity cannot serve as the ultimate arbiter that decides which theory of quantum gravity that is worthy of pursuit, even though it is of course not irrelevant either qua quantum gravity. Thus, the recovery of general relativity in string theory, for instance, does not guarantee that the stringy account of the world is on the right track; despite sentiments to the contrary among string theorists.

Keywords

Quantum gravity General relativity Spacetime functionalism Entanglement Emergent gravity Multiple realizability String theory 

Notes

Acknowledgements

I would like to express my gratitude to Niels Linnemann, Kian Salimkhani, Astrid Rasch, Richard Dawid, Sorin Bangu, and two anonymous reviewers of Synthese for valuable feedback on and helpful discussion of earlier drafts of this paper. I also send my thanks for constructing comments to the participants at the Spacetime Functionalism Workshop (University of Geneva) and 1st Scandinavian Workshop on the Metaphysics of Science (NTNU) where earlier versions of this paper was presented.

References

  1. Alishahiha, M., Allahbakhshi, D., & Naseh, A. (2013). Entanglement thermodynamics. Journal of High Energy Physics, 2013(8), 102.  https://doi.org/10.1007/JHEP08(2013)102. ISSN 1029-8479.CrossRefGoogle Scholar
  2. Antoniadis, I., Kiritsis, E., Rizos, J., & Tomaras, T. N. (2003). D-branes and the standard model. Nuclear Physics B, 660(1), 81–115.  https://doi.org/10.1016/S0550-3213(03)00256-6. ISSN 0550-3213.CrossRefGoogle Scholar
  3. Barceló, C., Liberati, S., & Visser, M. (2011). Analogue gravity. Living Reviews in Relativity, 14(1), 3.  https://doi.org/10.12942/lrr-2011-3. ISSN 1433-8351.CrossRefGoogle Scholar
  4. Baytaş, B., Bianchi, E., & Yokomizo, N. (2018). Gluing polyhedra with entanglement in loop quantum gravity. Physical Review D, 98(2), 026001.CrossRefGoogle Scholar
  5. Bealer, G. (1997). Self-consciousness. The Philosophical Review, 106(1), 69–117.  https://doi.org/10.2307/2998342. (ISSN 00318108, 15581470).CrossRefGoogle Scholar
  6. Becker, K., Becker, M., & Schwarz, J. H. (2007). String theory and M-theory : A modern introduction. Cambridge: Cambridge University Press. ISBN 0-521-86069-5.Google Scholar
  7. Bekenstein, J. D. (1973). Black holes and entropy. Physical Review D, 7(8), 2333–2346.CrossRefGoogle Scholar
  8. Bekenstein, J. D. (1981). Universal upper bound on the entropy-to-energy ratio for bounded systems. Physical Review D, 23(2), 287–298.CrossRefGoogle Scholar
  9. Bianchi, E., & Myers, R. C. (2014). On the architecture of spacetime geometry. Classical and Quantum Gravity, 31(21), 214002.CrossRefGoogle Scholar
  10. Bickle, J. (2016). Multiple realizability. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy (Vol. Spring 2016). https://plato.stanford.edu/archives/spr2017/entries/mind-identity/.
  11. Bousso, R. (2002). The holographic principle. Reviews of Modern Physics, 74(3), 825–874. CrossRefGoogle Scholar
  12. Brown, H. R. (2005). Physical relativity: Space–time structure from a dynamical perspective. Oxford: Oxford University Press. ISBN 978-0-19-927583-0.CrossRefGoogle Scholar
  13. Butterfield, J., de Haro, S., & Mayerson, D. R. (2016). Conceptual aspects of gauge/gravity duality. Foundations of Physics, 46(11), 1381–1425.CrossRefGoogle Scholar
  14. Cabrera, F. (2018). String theory, non-empirical theory assessment, and the context of pursuit. Synthese.  https://doi.org/10.1007/s11229-018-01987-9. ISSN 1573-0964.
  15. Callan, C. G., Friedan, D., Martinec, E. J., & Perry, M. J. (1985). Strings in background fields. Nuclear Physics B, 262(4), 593–609.  https://doi.org/10.1016/0550-3213(85)90506-1. ISSN 0550-3213.CrossRefGoogle Scholar
  16. Callan, C. G., Lovelace, C., Nappi, C. R., & Yost, S. A. (1987). String loop corrections to beta functions. Nuclear Physics B, 288, 525–550.CrossRefGoogle Scholar
  17. Camilleri, K., & Ritson, S. (2015). The role of heuristic appraisal in conflicting assessments of string theory. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 51, 44–56.  https://doi.org/10.1016/j.shpsb.2015.07.003. ISSN 1355-2198.CrossRefGoogle Scholar
  18. Cao, C. J., & Carroll, S. M. (2018). Bulk entanglement gravity without a boundary: Towards finding Einstein’s equation in Hilbert space. Physical Review D, 97(8), 086003.  https://doi.org/10.1103/PhysRevD.97.086003.CrossRefGoogle Scholar
  19. Carlip, S. (2014). Challenges for emergent gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 46(Part B), 200–208.CrossRefGoogle Scholar
  20. Casini, H., Huerta, M., & Myers, R. C. (2011). Towards a derivation of holographic entanglement entropy. Journal of High Energy Physics, 2011(5), 36.CrossRefGoogle Scholar
  21. Chirco, G., Haggard, H. M., Riello, A., & Rovelli, C. (2014). Spacetime thermodynamics without hidden degrees of freedom. Physical Review D, 90(4), 044044.CrossRefGoogle Scholar
  22. Chirco, G., Oriti, D., & Zhang, M. (2018). Group field theory and tensor networks: Towards a Ryu–Takayanagi formula in full quantum gravity. Classical and Quantum Gravity, 35(11), 115011.CrossRefGoogle Scholar
  23. Crowther, K., & Linnemann, N. (2017). Renormalizability, fundamentality, and a final theory: The role of UV-completion in the search for quantum gravity. The British Journal for the Philosophy of Science.  https://doi.org/10.1093/bjps/axx052. ISSN 0007-0882.
  24. Crowther, K., Linnemann, N. S., & Wüthrich, C. (2019). What we cannot learn from analogue experiments. Synthese.  https://doi.org/10.1007/s11229-019-02190-0. ISSN 1573-0964.
  25. Dardashti, R., Dawid, R., & Thébault, K. (Eds.). (2019). Why trust a theory?: Epistemology of fundamental physics. Cambridge: Cambridge University Press.  https://doi.org/10.1017/9781108671224. ISBN 978-1-108-47095-7.CrossRefGoogle Scholar
  26. Dardashti, R., Thébault, K. P. Y., & Winsberg, E. (2015). Confirmation via analogue simulation: What dumb holes could tell us about gravity. The British Journal for the Philosophy of Science, 68(1), 55–89.  https://doi.org/10.1093/bjps/axv010. ISSN 0007-0882.CrossRefGoogle Scholar
  27. Dawid, R. (2006). Underdetermination and theory succession from the perspective of string theory. Philosophy of Science, 73(3), 298–322.  https://doi.org/10.1086/515415. ISSN 00318248, 1539767X.CrossRefGoogle Scholar
  28. Dawid, R. (2009). On the conflicting assessments of the current status of string theory. Philosophy of Science, 76(5), 984–996.  https://doi.org/10.1086/605794. ISSN 00318248, 1539767X.CrossRefGoogle Scholar
  29. Dawid, R. (2013a). String theory and the scientific method. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  30. Dawid, R. (2013b). Theory assessment and final theory claim in string theory. Foundations of Physics, 43(1), 81–100.  https://doi.org/10.1007/s10701-011-9592-x. ISSN 1572-9516.CrossRefGoogle Scholar
  31. de Haro, S. (2017). Dualities and emergent gravity: Gauge/gravity duality. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 59, 109–125.CrossRefGoogle Scholar
  32. Dieks, D., van Dongen, J., & de Haro, S. (2015). Emergence in holographic scenarios for gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 52(Part B), 203–216.CrossRefGoogle Scholar
  33. Dougherty, J., & Callender, C. (2017). Black hole thermodynamics: More than an analogy?. http://philsci-archive.pitt.edu/13195/. Accessed 11 July 2017.
  34. Dowker, F. (2006). Causal sets as discrete spacetime. Contemporary Physics, 47(1), 1–9.CrossRefGoogle Scholar
  35. Eisert, J., Cramer, M., & Plenio, M. B. (2010). Colloquium: Area laws for the entanglement entropy. Reviews of Modern Physics, 82(1), 277–306.  https://doi.org/10.1103/RevModPhys.82.277.CrossRefGoogle Scholar
  36. Faulkner, T., Guica, M., Hartman, T., Myers, R. C., & Van Raamsdonk, M. (2014). Gravitation from entanglement in holographic CFTs. Journal of High Energy Physics, 2014(3), 51.CrossRefGoogle Scholar
  37. Frigg, R. (2008). A field guide to recent work on the foundations of statistical mechanics. In D. Rickles (Ed.), The Ashgate companion to contemporary philosophy of physics. Farnham: Ashgate.Google Scholar
  38. Greene, B. (1999). The elegant universe : Superstrings, hidden dimensions, and the quest for the ultimate theory. New York: W.W. Norton. ISBN 0-393-04688-5.Google Scholar
  39. Han, M. (2017). Einstein equation from covariant loop quantum gravity in semiclassical continuum limit. Physical Review D, 96(2), 024047.  https://doi.org/10.1103/PhysRevD.96.024047.CrossRefGoogle Scholar
  40. Han, M., & Hung, L.-Y. (2017). Loop quantum gravity, exact holographic mapping, and holographic entanglement entropy. Physical Review D, 95(2), 024011.CrossRefGoogle Scholar
  41. Hansen, D., Kubizňák, D., & Mann, R. B. (2017). Horizon thermodynamics from Einstein’s equation of state. Physics Letters B, 771, 277–280.  https://doi.org/10.1016/j.physletb.2017.04.076. ISSN 0370-2693.CrossRefGoogle Scholar
  42. Huggett, N. (2017). Target space is not equal to space. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 59, 81–88.CrossRefGoogle Scholar
  43. Huggett, N., & Vistarini, T. (2015). Deriving general relativity from string theory. Philosophy of Science, 82(5), 1163–1174.CrossRefGoogle Scholar
  44. Huggett, N., & Wüthrich, C. (2013). Emergent spacetime and empirical (in)coherence. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 44(3), 276–285.CrossRefGoogle Scholar
  45. Jackson, S., McGough, L., & Verlinde, H. (2015). Conformal bootstrap, universality and gravitational scattering. Nuclear Physics B, 901, 382–429.CrossRefGoogle Scholar
  46. Jacobson, T. (1995). Thermodynamics of spacetime: The Einstein equation of state. Physical Review Letters, 75(7), 1260–1263.CrossRefGoogle Scholar
  47. Jacobson, T. (2016). Entanglement equilibrium and the Einstein equation. Physical Review Letters, 116(20), 201101.CrossRefGoogle Scholar
  48. Kaufman, A. M., Tai, M. E., Lukin, A., Rispoli, M., Schittko, R., Preiss, P. M., et al. (2016). Quantum thermalization through entanglement in an isolated many-body system. Science, 353(6301), 794.  https://doi.org/10.1126/science.aaf6725.CrossRefGoogle Scholar
  49. Kim, J. (1998). Mind in a physical world: An essay on the mind–body problem and mental causation (Vol. 75). Cambridge: MIT Press.CrossRefGoogle Scholar
  50. Knox, E. (2013). Effective spacetime geometry. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 44(3), 346–356.  https://doi.org/10.1016/j.shpsb.2013.04.002. ISSN 1355-2198.CrossRefGoogle Scholar
  51. Knox, E. (2017). Physical relativity from a functionalist perspective. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics.  https://doi.org/10.1016/j.shpsb.2017.09.008. ISSN 1355-2198.
  52. Lam, V., & Esfeld, M. (2013). A dilemma for the emergence of spacetime in canonical quantum gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 44(3), 286–293.CrossRefGoogle Scholar
  53. Lam, V., & Wüthrich, C. (2018). Spacetime is as spacetime does. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics.  https://doi.org/10.1016/j.shpsb.2018.04.003. ISSN 1355-2198.
  54. Lashkari, N., McDermott, M. B., & Van Raamsdonk, M. (2014). Gravitational dynamics from entanglement “thermodynamics”. Journal of High Energy Physics, 2014(4), 195.CrossRefGoogle Scholar
  55. Le Bihan, B. (2018). Space emergence in contemporary physics: Why we do not need fundamentality, layers of reality and emergence. Disputatio, 10(49), 71–95.  https://doi.org/10.2478/disp-2018-0004.CrossRefGoogle Scholar
  56. Le Bihan, B., & Read, J. (2018). Duality and ontology. Philosophy Compass, 13(12), e12555.  https://doi.org/10.1111/phc3.12555.CrossRefGoogle Scholar
  57. Lewkowycz, A., & Maldacena, J. (2013). Generalized gravitational entropy. Journal of High Energy Physics, 2013(8), 90.CrossRefGoogle Scholar
  58. Linnemann, N. S., & Visser, M. R. (2018). Hints towards the emergent nature of gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 64, 1–13.  https://doi.org/10.1016/j.shpsb.2018.04.001. ISSN 1355-2198.CrossRefGoogle Scholar
  59. Maldacena, J. (1999). The large-N limit of superconformal field theories and supergravity. International Journal of Theoretical Physics, 38(4), 1113–1133.CrossRefGoogle Scholar
  60. Maldacena, J., & Susskind, L. (2013). Cool horizons for entangled black holes. Fortschritte der Physik, 61(9), 781–811.CrossRefGoogle Scholar
  61. Mertens, T. G., Turiaci, G. J., & Verlinde, H. L. (2017). Solving the Schwarzian via the conformal bootstrap. Journal of High Energy Physics, 2017(8), 136.CrossRefGoogle Scholar
  62. Nomura, Y., Salzetta, N., Sanches, F., & Weinberg, S. J. (2016). Spacetime equals entanglement. Physics Letters B, 763, 370–374.  https://doi.org/10.1016/j.physletb.2016.10.045. ISSN 0370-2693.CrossRefGoogle Scholar
  63. Oriti, D. (2014). Disappearance and emergence of space and time in quantum gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 46, 186–199.CrossRefGoogle Scholar
  64. Padmanabhan, T. (2005). Gravity and the thermodynamics of horizons. Physics Reports, 406(2), 49–125.  https://doi.org/10.1016/j.physrep.2004.10.003. ISSN 0370-1573.CrossRefGoogle Scholar
  65. Padmanabhan, T. (2010a). Equipartition of energy in the horizon degrees of freedom and the emergence of gravity. Modern Physics Letters A, 25(14), 1129–1136.  https://doi.org/10.1142/S021773231003313X. ISSN 0217-7323.CrossRefGoogle Scholar
  66. Padmanabhan, T. (2010b). Thermodynamical aspects of gravity: New insights. Reports on Progress in Physics, 73(4), 046901.CrossRefGoogle Scholar
  67. Pitowsky, I. (2006). On the definition of equilibrium. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 37(3), 431–438.  https://doi.org/10.1016/j.shpsb.2006.03.001. ISSN 1355-2198.CrossRefGoogle Scholar
  68. Polchinski, J. (1998). String theory: An introduction to the bosonic string (Vol. 1). Cambridge: Cambridge University Press. ISBN 0-521-63303-6.CrossRefGoogle Scholar
  69. Rangamani, M., & Takayanagi, T. (2017). Holographic entanglement entropy. Cham: Springer.CrossRefGoogle Scholar
  70. Read, J. (2016). The interpretation of string-theoretic dualities. Foundations of Physics, 46(2), 209–235. ISSN 1572-9516.CrossRefGoogle Scholar
  71. Rickles, D. (2013). AdS/CFT duality and the emergence of spacetime. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 44(3), 312–320.CrossRefGoogle Scholar
  72. Ridderbos, K. (2002). The coarse-graining approach to statistical mechanics: How blissful is our ignorance? Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 33(1), 65–77.  https://doi.org/10.1016/S1355-2198(01)00037-5. ISSN 1355-2198.CrossRefGoogle Scholar
  73. Rovelli, C. (2013). A critical look at strings. Foundations of Physics, 43(1), 8–20.  https://doi.org/10.1007/s10701-011-9599-3. ISSN 1572-9516.CrossRefGoogle Scholar
  74. Ryu, S., & Takayanagi, T. (2006). Holographic derivation of entanglement entropy from the anti-de sitter space/conformal field theory correspondence. Physical Review Letters, 96(18), 181602.CrossRefGoogle Scholar
  75. Sakharov, A. D. (1967). Vacuum quantum fluctuations in curved space and the theory of gravitation. Doklady Akademii Nauk SSSR, 177(1), 70–71.Google Scholar
  76. Sindoni, L. (2012). Emergent models for gravity: An overview of microscopic models. SIGMA, 8, 027.Google Scholar
  77. Sindoni, L. (2013). Horizon thermodynamics in pregeometry. Journal of Physics: Conference Series, 410(1), 012140. ISSN 1742-6596.Google Scholar
  78. Sklar, L. (1993). Physics and chance: Philosophical issues in the foundations of statistical mechanics. Cambridge: Cambridge University Press.  https://doi.org/10.1017/CBO9780511624933. ISBN 978-0-521-55881-5.CrossRefGoogle Scholar
  79. Smart, J. J. C. (2017). The mind/brain identity theory. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy (Vol. Spring 2017). https://plato.stanford.edu/archives/spr2017/entries/mind-identity/.
  80. Smolin, L. (2006). The trouble with physics: The rise of string theory, the fall of a science, and what comes next. Boston: Houghton Mifflin.Google Scholar
  81. Smolin, L. (2016). Holographic relations in loop quantum gravity. arXiv:1608.02932.
  82. Sorkin, R. D., & Yazdi, Y. K. (2018). Entanglement entropy in causal set theory. Classical and Quantum Gravity, 35(7), 074004.CrossRefGoogle Scholar
  83. Strominger, A., & Vafa, C. (1996). Microscopic origin of the Bekenstein–Hawking entropy. Physics Letters B, 379(1), 99–104.  https://doi.org/10.1016/0370-2693(96)00345-0. ISSN 0370-2693.CrossRefGoogle Scholar
  84. Susskind, L. (1995). The world as a hologram. Journal of Mathematical Physics, 36(11), 6377–6396.CrossRefGoogle Scholar
  85. Swingle, B., & Van Raamsdonk, M. (2014). Universality of gravity from entanglement. arXiv:1405.2933v1.
  86. ’t Hooft, G. (1994). Dimensional reduction in quantum gravity. In A. Ali, J. Ellis, S. Randjbar-Daemi, S. Weinberg, & Y. Lu (Eds.), Highlights of particle and condensed matter physics (Salamfest): Proceedings of the conference, ITCP, Trieste, Italy, 1993, number 4 in World Scientific series in 20th Cenutry Physics (pp. 284–296). World Scientific Publishing Co Pte Ltd.Google Scholar
  87. Teh, N. J. (2013). Holography and emergence. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 44(3), 300–311.CrossRefGoogle Scholar
  88. Unruh, W. G. (1976). Notes on black-hole evaporation. Physical Review D, 14(4), 870–892.CrossRefGoogle Scholar
  89. Van Raamsdonk, M. (2010). Building up spacetime with quantum entanglement. General Relativity and Gravitation, 42(10), 2323–2329.CrossRefGoogle Scholar
  90. Van Raamsdonk, M. (2011). A patchwork description of dual spacetimes in AdS/CFT. Classical and Quantum Gravity, 28(6), 065002.CrossRefGoogle Scholar
  91. Verlinde, E. (2011). On the origin of gravity and the laws of Newton. Journal of High Energy Physics, 2011(4), 29.CrossRefGoogle Scholar
  92. Verlinde, E. (2017). Emergent gravity and the dark universe. SciPost Physics, 3(2), 016.CrossRefGoogle Scholar
  93. Visser, M. (2002). Sakharov’s induced gravity: A modern perspective. Modern Physics Letters A, 17(15n17), 977–991.  https://doi.org/10.1142/S0217732302006886. ISSN 0217-7323.CrossRefGoogle Scholar
  94. Wallace, D. (2018). The case for black hole thermodynamics part I: Phenomenological thermodynamics. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics.  https://doi.org/10.1016/j.shpsb.2018.05.002. ISSN 1355-2198.
  95. Weinberg, S., & Witten, E. (1980). Limits on massless particles. Physics Letters B, 96(1), 59–62.  https://doi.org/10.1016/0370-2693(80)90212-9. ISSN 0370-2693.CrossRefGoogle Scholar
  96. Weinfurtner, S., Tedford, E. W., Penrice, M. C. J., Unruh, W. G., & Lawrence, G. A. (2013). Classical aspects of Hawking radiation verified in analogue gravity experiment. In D. Faccio, F. Belgiorno, S. Cacciatori, V. Gorini, S. Liberati, & U. Moschella (Eds.), Analogue gravity phenomenology: Analogue spacetimes and horizons, from theory to experiment (pp. 167–180). Cham: Springer International Publishing.CrossRefGoogle Scholar
  97. Weisberg, M. (2006). Robustness analysis. Philosophy of Science, 73(5), 730–742.  https://doi.org/10.1086/518628. ISSN 00318248, 1539767X.CrossRefGoogle Scholar
  98. Wimsatt, W. (1981). Robustness, reliability and overdetermination. In M. Brewer & B. Collins (Eds.), Scientific inquiry and the social sciences (pp. 124–163). San Francisco: Jossey-Bass.Google Scholar
  99. Wüthrich, C. (2017). Raiders of the lost spacetime. In D. Lehmkuhl, G. Schiemann, & E. Scholz (Eds.), Towards a theory of spacetime theories (pp. 297–335). New York: Springer.CrossRefGoogle Scholar
  100. Zwiebach, B. (2009). A first course in string theory (2nd ed.). Cambridge: Cambridge University Press.CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Philosophy and Religious StudiesNTNU – Norwegian University of Science and TechnologyTrondheimNorway

Personalised recommendations