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dc.date.accessioned2020-04-27T18:53:51Z
dc.date.available2020-04-27T18:53:51Z
dc.date.created2019-06-21T15:55:09Z
dc.date.issued2019
dc.identifier.citationHelland, Inge Svein . Symmetry in a space of conceptual variables. Journal of Mathematical Physics. 2019, 60(5), 1-8
dc.identifier.urihttp://hdl.handle.net/10852/74885
dc.description.abstractA conceptual variable is any variable defined by a person or by a group of persons. Such variables may be inaccessible, meaning that they cannot be measured with arbitrary accuracy on the physical system under consideration at any given time. An example may be the spin vector of a particle; another example may be the vector (position, momentum). In this paper, a space of inaccessible conceptual variables is defined, and group actions are defined on this space. Accessible functions are then defined on the same space. Assuming this structure, the basic Hilbert space structure of quantum theory is derived: Operators on a Hilbert space corresponding to the accessible variables are introduced; when these operators have a discrete spectrum, a natural model reduction implies a new model in which the values of the accessible variables are the eigenvalues of the operator. The principle behind this model reduction demands that a group action may also be defined also on the accessible variables; this is possible if the corresponding functions are permissible, a term that is precisely defined. The following recent principle from statistics is assumed: every model reduction should be to an orbit or to a set of orbits of the group. From this derivation, a new interpretation of quantum theory is briefly discussed: I argue that a state vector may be interpreted as connected to a focused question posed to nature together with a definite answer to this question. Further discussion of these topics is provided in a recent book published by the author of this paper.
dc.description.abstractSymmetry in a space of conceptual variables
dc.languageEN
dc.titleSymmetry in a space of conceptual variables
dc.typeJournal article
dc.creator.authorHelland, Inge Svein
cristin.unitcode185,15,13,0
cristin.unitnameMatematisk institutt
cristin.ispublishedtrue
cristin.fulltextpostprint
cristin.qualitycode1
dc.identifier.cristin1706911
dc.identifier.bibliographiccitationinfo:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal of Mathematical Physics&rft.volume=60&rft.spage=1&rft.date=2019
dc.identifier.jtitleJournal of Mathematical Physics
dc.identifier.volume60
dc.identifier.issue5
dc.identifier.doihttps://doi.org/10.1063/1.5082694
dc.identifier.urnURN:NBN:no-77994
dc.type.documentTidsskriftartikkel
dc.type.peerreviewedPeer reviewed
dc.source.issn0022-2488
dc.identifier.fulltextFulltext https://www.duo.uio.no/bitstream/handle/10852/74885/2/SymmetryconcB.pdf
dc.type.versionAcceptedVersion
cristin.articleid052101


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