{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T00:28:36Z","timestamp":1776731316463,"version":"3.51.2"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,4]],"date-time":"2024-12-04T00:00:00Z","timestamp":1733270400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In certain established approaches to quantum gravity, such as causal set theory and causal dynamical triangulations, discrete spacetime structure is taken to be a primary feature, not a secondary effect of \u201cquantizing\u201d a pre-existing classical continuum-based theory, as is done in approaches such as string theory and loop quantum gravity. For a priori discrete models, the full quantum theory is often obtained via some version of Feynman\u2019s sum-over-histories approach, in which each \u201chistory\u201d is a discrete object viewed as a classical spacetime. Counterintuitive physical scenarios such as Schr\u00f6dinger\u2019s cat or the grandfather paradox are typically associated with either quantum effects or causality violations, but we demonstrate that equally bizarre scenarios can arise at a purely classical level in the discrete causal context due to symmetry considerations. In particular, the graph-theoretic phenomenon of pseudosimilarity leads to situations in which alternative events occurring at physically distinguishable locations in the universe can cause different parts of the universe to \u201cswap identities\u201d in a fugue-like manner alien to continuum-based theories. This phenomenon is perhaps best understood as an extension of the relativity principle, which we call relativity of identity.<\/jats:p>","DOI":"10.3390\/sym16121609","type":"journal-article","created":{"date-parts":[[2024,12,4]],"date-time":"2024-12-04T06:38:25Z","timestamp":1733294305000},"page":"1609","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Counterintuitive Scenarios in Discrete Gravity Without Quantum Effects or Causality Violations"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-4802-3864","authenticated-orcid":false,"given":"Benjamin F.","family":"Dribus","sequence":"first","affiliation":[{"name":"Department of Mathematics, William Carey University, Hattiesburg, MS 39401, USA"},{"name":"College of Osteopathic Medicine, William Carey University, Hattiesburg, MS 39401, USA"},{"name":"Foundational Questions Institute (FQxI), New York, NY 10163, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-7770-9837","authenticated-orcid":false,"given":"Jesiah T.","family":"Darnell","sequence":"additional","affiliation":[{"name":"Department of Mathematics, William Carey University, Hattiesburg, MS 39401, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Neil","family":"Goldsmith","sequence":"additional","affiliation":[{"name":"Department of Chemistry and Physics, William Carey University, Hattiesburg, MS 39401, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1103\/PhysRevLett.59.521","article-title":"Space-Time as a Causal Set","volume":"59","author":"Bombelli","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Gomberoff, A., and Marolf, D. (2005). Causal Sets: Discrete Gravity. Lectures on Quantum Gravity, Springer.","DOI":"10.1007\/b106494"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"024002","DOI":"10.1103\/PhysRevD.61.024002","article-title":"Classical sequential growth dynamics for causal sets","volume":"61","author":"Rideout","year":"2000","journal-title":"Phys. Rev. D"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1016\/S0920-5632(01)01903-X","article-title":"A Lorentzian cure for Euclidean troubles","volume":"106\u2013107","author":"Ambjorn","year":"2002","journal-title":"Nucl. Phys. B Proc. Suppl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"124044","DOI":"10.1103\/PhysRevD.85.124044","article-title":"Second- and first-order phase transitions in causal dynamical triangulations","volume":"85","author":"Ambjorn","year":"2012","journal-title":"Phys. Rev. D"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"171301","DOI":"10.1103\/PhysRevLett.95.171301","article-title":"Spectral Dimension of the Universe","volume":"95","author":"Ambjorn","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/BF00669395","article-title":"\u201cSuperconducting\u201d Causal Nets","volume":"27","author":"Finkelstein","year":"1988","journal-title":"Int. J. Theor. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"104029","DOI":"10.1103\/PhysRevD.77.104029","article-title":"Quantum graphity: A model of emergent locality","volume":"77","author":"Konopka","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s00220-006-0066-5","article-title":"A Domain of Spacetime Intervals in General Relativity","volume":"267","author":"Martin","year":"2006","journal-title":"Commun. Math. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Dribus, B.F. (2017). Discrete Causal Theory: Emergent Spacetime and the Causal Metric Hypothesis, Springer.","DOI":"10.1007\/978-3-319-50083-6"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Becker, K., Becker, M., and Schwarz, J.H. (2007). String Theory and M-Theory, Cambridge University Press.","DOI":"10.1017\/CBO9780511816086"},{"key":"ref_12","unstructured":"Rovelli, C. (2004). Quantum Gravity, Cambridge University Press. Cambridge Monographs on Mathematical Physics."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1103\/RevModPhys.20.367","article-title":"Space-Time Approach to Non-Relativistic Quantum Mechanics","volume":"20","author":"Feynman","year":"1948","journal-title":"Rev. Mod. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3839","DOI":"10.1088\/0264-9381\/20\/16\/320","article-title":"Evolution in Quantum Causal Histories","volume":"20","author":"Hawkins","year":"2003","journal-title":"Class. Quantum Gravity"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s10701-004-1944-3","article-title":"Quantising on a Category","volume":"35","author":"Isham","year":"2005","journal-title":"Found. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"816","DOI":"10.1017\/S0960129511000545","article-title":"Toward a Fundamental Theorem of Quantal Measure Theory","volume":"22","author":"Sorkin","year":"2012","journal-title":"Math. Struct. Comput. Sci."},{"key":"ref_17","unstructured":"Dribus, B.F. (2013). On the Axioms of Causal Set Theory. arXiv."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Dribus, B.F. (2017). Entropic Phase Maps in Discrete Quantum Gravity. Entropy, 19.","DOI":"10.3390\/e19070322"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1063\/1.522874","article-title":"A new topology for curved space-time which incorporates the causal, differential, and conformal structures","volume":"17","author":"Hawking","year":"1976","journal-title":"J. Math. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1063\/1.523436","article-title":"The class of continuous timelike curves determines the topology of spacetime","volume":"18","author":"Malament","year":"1977","journal-title":"J. Math. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1103\/PhysRev.184.1261","article-title":"Space-Time Code","volume":"184","author":"Finkelstein","year":"1969","journal-title":"Phys. Rev."},{"key":"ref_22","unstructured":"Myrheim, J. (1978). Statistical Geometry, CERN. CERN Preprint."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Levy, M., and Deser, S. (1979). Quantum Gravity: A Fundamental Problem and some Radical Ideas. Recent Developments in Gravitation, Springer. Proceedings of the 1978 Cargese Summer Institute.","DOI":"10.1007\/978-1-4613-2955-8"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Dribus, B.F. (2015). On the Foundational Assumptions of Modern Physics. Questioning the Foundations of Physics, Springer. The Frontiers Collection.","DOI":"10.1007\/978-3-319-13045-3_4"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1103\/PhysRevLett.11.237","article-title":"Gravitational field of a spinning mass as an example of algebraically special metrics","volume":"11","author":"Kerr","year":"1963","journal-title":"Phys. Rev. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2579","DOI":"10.1142\/S0217732309031958","article-title":"Discreteness without symmetry breaking: A theorem","volume":"24","author":"Bombelli","year":"2009","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Oriti, D. (2009). Does locality fail at intermediate length scales?. Approaches to Quantum Gravity, Cambridge University Press.","DOI":"10.1017\/CBO9780511575549"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"124031","DOI":"10.1103\/PhysRevD.88.124031","article-title":"Phenomenology of Space-time Imperfection II: Local Defects","volume":"88","author":"Hossenfelder","year":"2013","journal-title":"Phys. Rev. D"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Babai, L. (2016). Graph Isomorphism in Quasipolynomial Time. arXiv.","DOI":"10.1145\/2897518.2897542"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/0095-8956(88)90044-5","article-title":"The Asymptotic Number of Acyclic Digraphs II","volume":"44","author":"Bender","year":"1988","journal-title":"J. Comb. Theory Ser. B"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/12\/1609\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:46:39Z","timestamp":1760114799000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/12\/1609"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,4]]},"references-count":30,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["sym16121609"],"URL":"https:\/\/doi.org\/10.3390\/sym16121609","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,4]]}}}