{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T00:30:45Z","timestamp":1780446645657,"version":"3.54.1"},"reference-count":26,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2010,3,8]],"date-time":"2010-03-08T00:00:00Z","timestamp":1268006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Despite the widely-held premise that initial boundary conditions (BCs) corresponding to measurements\/interactions can fully specify a physical subsystem, a literal reading of Hamilton\u2019s principle would imply that both initial and final BCs are required (or more generally, a BC on a closed hypersurface in spacetime). Such a time-symmetric perspective of BCs, as applied to classical fields, leads to interesting parallels with quantum theory. This paper will map out some of the consequences of this counter-intuitive premise, as applied to covariant classical fields. The most notable result is the contextuality of fields constrained in this manner, naturally bypassing the usual arguments against so-called \u201crealistic\u201d interpretations of quantum phenomena.<\/jats:p>","DOI":"10.3390\/sym2010272","type":"journal-article","created":{"date-parts":[[2010,3,8]],"date-time":"2010-03-08T11:22:08Z","timestamp":1268047328000},"page":"272-283","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Time-Symmetric Boundary Conditions and Quantum Foundations"],"prefix":"10.3390","volume":"2","author":[{"given":"Ken","family":"Wharton","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, San Jos\u00b4e State University, San Jos\u00b4e, CA 95192-0106, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2010,3,8]]},"reference":[{"key":"ref_1","unstructured":"Lanczos, C. (1970). The Variational Principles of Mechanics, Dover. [4th ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Schulman, L.S. (1997). Time\u2019s Arrows and Quantum Measurement, Cambridge University Press.","DOI":"10.1017\/CBO9780511622878"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1038\/127447a0","article-title":"The end of the world: From the standpoint of mathematical physics","volume":"127","author":"Eddington","year":"1931","journal-title":"Nature"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1007\/BF01397280","article-title":"ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik","volume":"43","author":"Heisenberg","year":"1927","journal-title":"Z. Phys."},{"key":"ref_5","unstructured":"Goldstein, H. (1980). Classical Mechanics, Addison-Wesley. [2nd ed.]."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/s10701-009-9398-2","article-title":"A novel interpretation of the Klein-Gordon Equation","volume":"40","author":"Wharton","year":"2010","journal-title":"Found. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"032110","DOI":"10.1103\/PhysRevA.75.032110","article-title":"Evidence for the epistemic view of quantum states: A toy theory","volume":"75","author":"Spekkens","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1103\/RevModPhys.38.447","article-title":"On the problem of hidden variables in quantum mechanics","volume":"38","author":"Bell","year":"1966","journal-title":"Rev. Mod. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1007\/BF00715107","article-title":"Time symmetry and interpretation of quantum mechanics","volume":"6","year":"1976","journal-title":"Found. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1007\/BF00717585","article-title":"Proof of a retroactive influence","volume":"8","author":"Reitdijk","year":"1978","journal-title":"Found. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1103\/PhysRevD.22.362","article-title":"Generalized absorber theory and the Einstein-Podolsky-Rosen paradox","volume":"22","author":"Cramer","year":"1980","journal-title":"Phys. Rev. D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/BF02082904","article-title":"Bell\u2019s theorem and Backwards-In-Time causality","volume":"22","author":"Sutherland","year":"1983","journal-title":"Int. J. Theo. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Price, H. (1996). Time\u2019s Arrow and Archimedes\u2019 Point, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780195117981.001.0001"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/0375-9601(96)00620-2","article-title":"Realism and time symmetry in quantum mechanics","volume":"A222","author":"Miller","year":"1996","journal-title":"Phys. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10701-006-9089-1","article-title":"Time-symmetric quantum mechanics","volume":"37","author":"Wharton","year":"2007","journal-title":"Found. Phys."},{"key":"ref_16","unstructured":"Miller, D.J. (2009, December 30). Quantum mechanics as a consistency condition on initial and final boundary conditions. Available online: http:\/\/arxiv.org\/pdf\/quant-ph\/0607169."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2315","DOI":"10.1088\/0305-4470\/24\/10\/018","article-title":"Complete description of a quantum system at a given time","volume":"24","author":"Aharonov","year":"1991","journal-title":"J. Phys. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"12049","DOI":"10.1088\/1742-6596\/67\/1\/012049","article-title":"Probabilites in the general boundary formulation","volume":"67","author":"Oeckl","year":"2007","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_19","unstructured":"Sutherland, R. (2009, December 30). Causally symmetric bohm model. Available online: http:\/\/arxiv.org\/pdf\/quant-ph\/0601095."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1086\/367875","article-title":"Fulling non-uniqueness and the unruh effect: A primer on some aspects of quantum field theory","volume":"70","author":"Arageorgis","year":"2003","journal-title":"Phil. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1103\/PhysRev.160.1113","article-title":"Quantum theory of gravity I: The canonical theory","volume":"160","author":"DeWitt","year":"1967","journal-title":"Phys. Rev."},{"key":"ref_22","unstructured":"Wharton, K.B. (2009, December 30). Extending Hamilton\u2019s principle to quantize classical fields. Available online: http:\/\/arxiv.org\/pdf\/0906.5409."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"B1410","DOI":"10.1103\/PhysRev.134.B1410","article-title":"Time symmetry in the quantum process of measurement","volume":"134","author":"Aharonov","year":"1964","journal-title":"Phys. Rev."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"22104","DOI":"10.1103\/PhysRevA.77.022104","article-title":"Exponential complexity and ontological theories of quantum mechanics","volume":"77","author":"Montina","year":"2008","journal-title":"Phys. Rev. A"},{"key":"ref_25","unstructured":"Evans, P., Price, H., and Wharton, K.B. (2010, February 01). New slant on the EPR-Bell experiment. Available online: http:\/\/arxiv.org\/pdf\/1001.5057v2."},{"key":"ref_26","unstructured":"Wharton, K. (, January June). Classical fields as the natural ontic structure for quantum theory. Presented at Perimeter Institute, quantum foundations seminar, Waterloo, OT, USA."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/2\/1\/272\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:01:40Z","timestamp":1760220100000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/2\/1\/272"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3,8]]},"references-count":26,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,3]]}},"alternative-id":["sym2010272"],"URL":"https:\/\/doi.org\/10.3390\/sym2010272","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,3,8]]}}}