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The Present Situation in Quantum Theory and its Merging with General Relativity
Linnaeus University, Faculty of Technology, Department of Mathematics. Natl Res Univ Informat Technol Mech & Opt ITMO, Russia. (Int Ctr Math Modelling Phys & Cognit Sci)ORCID iD: 0000-0002-9857-0938
2017 (English)In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 47, no 8, 1077-1099 p.Article in journal (Refereed) Published
Abstract [en]

We discuss the problems of quantum theory (QT) complicating its merging with general relativity (GR). QT is treated as a general theory of micro-phenomena-a bunch of models. Quantum mechanics (QM) and quantum field theory (QFT) are the most widely known (but, e.g., Bohmian mechanics is also a part of QT). The basic problems of QM and QFT are considered in interrelation. For QM, we stress its nonrelativistic character and the presence of spooky action at a distance. For QFT, we highlight the old problem of infinities. And this is the main point of the paper: it is meaningless to try to unify QFT so heavily suffering of infinities with GR. We also highlight difficulties of the QFT-treatment of entanglement. We compare the QFT and QM based measurement theories by presenting both theoretical and experimental viewpoints. Then we discuss two basic mathematical constraints of both QM and QFT, namely, the use of real (and, hence, complex) numbers and the Hilbert state space. We briefly present non-archimedean and non-hilbertian approaches to QT and their consequences. Finally, we claim that, in spite of the Bell theorem, it is still possible to treat quantum phenomena on the basis of a classical-like causal theory. We present a random field model generating the QM and QFT formalisms. This emergence viewpoint can serve as the basis for unification of novel QT (may be totally different from presently powerful QM and QFT) and GR. (It may happen that the latter would also be revolutionary modified.).

Place, publisher, year, edition, pages
Springer, 2017. Vol. 47, no 8, 1077-1099 p.
Keyword [en]
Quantum theory, Quantum mechanics, Quantum field theory, Quantum gravity, Infinities, Measurement theory, Non-hilbertian state space formalism, Non-real numbers in physics, Emergent theory
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-67396DOI: 10.1007/s10701-017-0089-0ISI: 000405964600007OAI: oai:DiVA.org:lnu-67396DiVA: diva2:1135926
Available from: 2017-08-24 Created: 2017-08-24 Last updated: 2017-08-24Bibliographically approved

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CiteExportLink to record
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