2000 character limit reached
Causal Sets and an Emerging Continuum (2405.14059v3)
Published 22 May 2024 in gr-qc and hep-th
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.
- D. Malamet, J. Math. Phys. 18 (1977) 1399.
- L. Bombelli, J. Lee, D. Meyer, and R. D. Sorkin, “Space-Time as a Causal Set,” Phys. Rev. Lett. 59 (1987) 521.
- 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.
- J. Myrheim, Statistical Geometry,” CERN Tech. Rep. CERN-TH-2538 (1978); available at https://cds.cern.ch/record/293594.
- D. A. Meyer, “The Dimension of Causal Sets,” Ph.D. thesis, MIT (1989); available at http://hdl.handle.net/1721.1/14328.
- S. Surya, “The causal set approach to quantum gravity,” Living Rev. Rel. 22 (2019) 5, arXiv:1903.11544.
- D. M. T. Benincasa and F. Dowker, “The Scalar Curvature of a Causal Set,” Phys. Rev. Lett. 104 (2010) 181301, arXiv:1001.2725.
- F. Dowker and L. Glaser, “Causal set d’Alembertians for various dimensions,” Class. Quant. Grav. 30 (2013) 195016, arXiv:1305.2588.
- L. Glaser, “A closed form expression for the causal set d’Alembertian,” Class. Quant. Grav. 31 (2014) 095007, arXiv:1311.1701.
- R. D. Sorkin, “Scalar Field Theory on a Causal Set in Histories Form,” J. Phys. Conf. Ser. 306 (2011) 012017, arXiv:1107.0698.
- S. Johnston, “Feynman Propagator for a Free Scalar Field on a Causal Set,” Phys. Rev. Lett. 103 (2009) 180401, arXiv:0909.0944.
- 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.
- C. Moore, “Comment on ‘Space-time as a causal set’,” Phys. Rev. Lett. 60 (1988) 655.
- 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.
- L. Glaser and S. Surya, “Towards a Definition of Locality in a Manifoldlike Causal Set,” Phys. Rev. D 88 (2013) 124026, arXiv:1309.3403.
- D. J. Kleitman and B. L. Rothschild, “Asymptotic enumeration of partial orders on a finite set,” Trans. Amer. Math. Soc. 205 (1975) 205.
- D. Dhar, “Entropy and phase transitions in partially ordered sets,” J. Math. Phys. 19 (1978) 1711.
- H. J. Prömel, A. Steger, and A. Taraz, “Phase Transitions in the Evolution of Partial Orders,” J. Comb. Theory series A 94 (2001) 230.
- C. DeWitt-Morette, A. Maheshwari, and B. Nelson, “Path Integration in Non- Relativistic Quantum Mechanics,” Phys. Rept. 50 (1979) 255.
- S. Surya, “Evidence for a Phase Transition in 2D Causal Set Quantum Gravity,” Class. Quant. Grav. 29 (2012) 132001, arXiv:1110.6244.
- 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.
- G. Brinkmann and B. D. McKay, “Posets on up to 16 Points,” Order 19 (2002) 147.
- 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.
- 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.
- 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.
- P. Carlip, S. Carlip, and S. Surya, “Path integral suppression of badly behaved causal sets,” Class. Quant. Grav. 40 (2023) 095004, arXiv:2209.00327.
- 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.
Collections
Sign up for free to add this paper to one or more collections.