Causal set dynamics: a toy model
Open accessAbstract
We construct a quantum measure on the power set of non-cyclic oriented graphs of N points, drawing inspiration from one-dimensional directed percolation. Quantum interference patterns lead to properties which do not appear to have any analogue in classical percolation. Most notably, instead of the single phase transition of classical percolation, the quantum model displays two distinct crossover points. Between these two points, spacetime questions such as `does the network percolate?' have no definite or probabilistic answer.
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References 15 · Cited by 7
Research works printed but not linked: 7
- Sorkin R D 1990 Spacetime and causal sets Proc. SILARG VII Conf. (Mexico)
- Borissov R and Gupta S Propagating spin modes in canonical quantum gravity Penn. State University Preprint gr-qc/9810024 · arXiv
- Kauffman S and Smolin L 1998 Combinatorial dynamics in quantum gravity Preprint hep-th/9809161 Several articles about directed percolation can be found in Kinzel W 1983 Percolation Structures and Processes (Annals of the Israeli Physics Society vol 5) ed G D Eulsher, R Zallen and J Adler (Bristol: Hilger) p 425 · arXiv
- Directed percolation was introduced by Broadbent S R and Hammerlsey J M 1957 Proc. Camb. Phil. Soc. 53 629
- Feynman R P and Hibbs A R 1965 Quantum Mechanics and Path integrals (New York: McGraw-Hill)
- Sorkin R and Sudarsky D 1999 Large fluctuations in the horizon and what they teach us about quantum gravity and entropy Preprint gr-qc/9902051 · arXiv
- Daughton A R 1993 The recovery of locality for causal sets and related topics PhD Dissertation Syracuse University
- Authors
- Criscuolo, A., & Waelbroeck, H.
- Affiliations
- Utrecht University (NL)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1999-01-01
- Volume
- 16
- Issue
- 6
- Pages
- 1817-1832
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2081219817
- Cited by
- 7
- References
- 15
- Citations by year
- 2021: 1 · 2018: 1
- FWCI
- 0.81
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Mathematics › Mathematical Physics › advanced mathematical theories
- Keywords
- causal sets, quantum percolation, directed percolation, quantum interference, phase transitions, crossover point, quantum gravity, discrete spacetime
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