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Beyond Archimedean Space-Time Structure
University of Pretoria, South Africa.
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics. (mathematical modeling)ORCID iD: 0000-0002-9857-0938
2011 (English)In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1327, p. 520-526Article in journal (Refereed) Published
Abstract [en]

It took two millennia after Euclid and until in the early 1880s, when we went beyond the ancient axiom of parallels, and inaugurated geometries of curved spaces. In less than one more century, General Relativity followed. At present, physical thinking is still beheld by the yet deeper and equally ancient Archimedean assumption. In view of that, it is argued with some rather easily accessible mathematical support that Theoretical Physics may at last venture into the non-Archimedean realms. In this introductory paper we stress two fundamental consequences of the non-Archimedean approach to Theoretical Physics: one of them for quantum theory and another for relativity theory. From the non-Archimedean viewpoint, the assumption of the existence of minimal quanta of light (of the fixed frequency) is an artifact of the present Archimedean mathematical basis of quantum mechanics. In the same way the assumption of the existence of the maximal velocity, the velocity of light, is a feature of the real space-time structure which is fundamentally Archimedean. Both these assumptions are not justified in corresponding non-Archimedean models.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2011. Vol. 1327, p. 520-526
Keywords [en]
Archimedean and non-Archimedean models, string theory, Euclidean and non-Euclidean geometries, p-adic numbers, nonstandard analysis, existence of quanta of light, the velocity of light
National Category
Physical Sciences
Research subject
Natural Science, Physics
Identifiers
URN: urn:nbn:se:lnu:diva-16587DOI: 10.1063/1.3567483OAI: oai:DiVA.org:lnu-16587DiVA, id: diva2:472976
Conference
International Conference Advances in Quantum Theory, Vaxjo, SWEDEN, JUN 14-17, 2010
Available from: 2012-01-04 Created: 2012-01-04 Last updated: 2017-12-08Bibliographically approved

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Khrennikov, Andrei

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