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Causal Sets and an Emerging Continuum

Published 22 May 2024 in gr-qc and hep-th | (2405.14059v3)

Abstract: Causal set theory offers a simple and elegant picture of discrete physics. But the vast majority of causal sets look nothing at all like continuum spacetimes, and must be excluded in some way to obtain a realistic theory. I describe recent results showing that almost all non-manifoldlike causal sets are, in fact, very strongly suppressed in the gravitational path integral. This does not quite demonstrate the emergence of a continuum -- we do not yet understand the remaining unsuppressed causal sets well enough -- but it is a significant step in that direction.

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References (27)
  1. D. Malamet, J. Math. Phys. 18 (1977) 1399.
  2. L. Bombelli, J. Lee, D. Meyer, and R. D. Sorkin, “Space-Time as a Causal Set,” Phys. Rev. Lett. 59 (1987) 521.
  3. L. Bombelli, J. Henson, and R. D. Sorkin, “Discreteness without symmetry breaking: A Theorem,” Mod. Phys. Lett. A 24 (2009) 2579, arXiv:gr-qc/0605006.
  4. J. Myrheim, Statistical Geometry,” CERN Tech. Rep. CERN-TH-2538 (1978); available at https://cds.cern.ch/record/293594.
  5. D. A. Meyer, “The Dimension of Causal Sets,” Ph.D. thesis, MIT (1989); available at http://hdl.handle.net/1721.1/14328.
  6. S. Surya, “The causal set approach to quantum gravity,” Living Rev. Rel. 22 (2019) 5, arXiv:1903.11544.
  7. D. M. T. Benincasa and F. Dowker, “The Scalar Curvature of a Causal Set,” Phys. Rev. Lett. 104 (2010) 181301, arXiv:1001.2725.
  8. F. Dowker and L. Glaser, “Causal set d’Alembertians for various dimensions,” Class. Quant. Grav. 30 (2013) 195016, arXiv:1305.2588.
  9. L. Glaser, “A closed form expression for the causal set d’Alembertian,” Class. Quant. Grav. 31 (2014) 095007, arXiv:1311.1701.
  10. R. D. Sorkin, “Scalar Field Theory on a Causal Set in Histories Form,” J. Phys. Conf. Ser. 306 (2011) 012017, arXiv:1107.0698.
  11. S. Johnston, “Feynman Propagator for a Free Scalar Field on a Causal Set,” Phys. Rev. Lett. 103 (2009) 180401, arXiv:0909.0944.
  12. E. Albertini, F. Dowker, A. Nasiri, and S. Zalel, “In-in correlators and scattering amplitudes on a causal set,” Phys. Rev. D 109 (2024) 106014, arXiv:2402.08555.
  13. C. Moore, “Comment on ‘Space-time as a causal set’,” Phys. Rev. Lett. 60 (1988) 655.
  14. L. Bombelli, J. Lee, D. Meyer, and R. D. Sorkin, “Bombelli et al reply to Comment on ‘Space-time as a causal set’,” Phys. Rev. Lett. 60 (1988) 656.
  15. L. Glaser and S. Surya, “Towards a Definition of Locality in a Manifoldlike Causal Set,” Phys. Rev. D 88 (2013) 124026, arXiv:1309.3403.
  16. D. J. Kleitman and B. L. Rothschild, “Asymptotic enumeration of partial orders on a finite set,” Trans. Amer. Math. Soc. 205 (1975) 205.
  17. D. Dhar, “Entropy and phase transitions in partially ordered sets,” J.  Math. Phys. 19 (1978) 1711.
  18. H. J. Prömel, A. Steger, and A. Taraz, “Phase Transitions in the Evolution of Partial Orders,” J. Comb. Theory series A 94 (2001) 230.
  19. C. DeWitt-Morette, A. Maheshwari, and B. Nelson, “Path Integration in Non- Relativistic Quantum Mechanics,” Phys. Rept. 50 (1979) 255.
  20. S. Surya, “Evidence for a Phase Transition in 2D Causal Set Quantum Gravity,” Class. Quant. Grav. 29 (2012) 132001, arXiv:1110.6244.
  21. R. D. Sorkin, “Does Locality Fail at Intermediate Length-Scales,” in Approaches to Quantum Gravity, edited by D. Oriti (Cambridge University Press, 2009), arXiv:gr-qc/0703099.
  22. G. Brinkmann and B. D. McKay, “Posets on up to 16 Points,” Order 19 (2002) 147.
  23. S. Loomis and S. Carlip, “Suppression of non-manifold-like sets in the causal set path integral,” Class. Quant. Grav. 35 (2018) 024002, arXiv:1709.00064.
  24. A. Mathur, A. A. Singh, and S. Surya, “Entropy and the Link Action in the Causal Set Path-Sum,” Class. Quant. Grav. 38 (2021) 045017, arXiv:2009.07623.
  25. A. Belenchia, D. M. T. Benincasa, and F. Dowker, “The continuum limit of a 4-dimensional causal set scalar d’Alembertian,” Class. Quant. Grav. 33 (2016) 245018 arXiv:1510.04656.
  26. P. Carlip, S. Carlip, and S. Surya, “Path integral suppression of badly behaved causal sets,” Class. Quant. Grav. 40 (2023) 095004, arXiv:2209.00327.
  27. P. Carlip, S. Carlip, and S. Surya, “The Einstein-Hilbert Action for Entropically Dominant Causal Sets,” to appear in Class. Quant. Grav., arXiv:2209.00327.

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