Q-spaces and the foundations of quantum mechanics

Our aim in this paper is to take quite seriously Heinz Post's claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, qua...

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Detalles Bibliográficos
Publicado: 2008
Materias:
Fock space
Particle number
Quantum indistinguishability
Quasi-sets
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00159018_v38_n11_p969_Domenech
http://hdl.handle.net/20.500.12110/paper_00159018_v38_n11_p969_Domenech
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00159018_v38_n11_p969_Domenech
record_format dspace
spelling paper:paper_00159018_v38_n11_p969_Domenech2023-06-08T14:38:12Z Q-spaces and the foundations of quantum mechanics Fock space Particle number Quantum indistinguishability Quasi-sets Our aim in this paper is to take quite seriously Heinz Post's claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller's words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg's suggestion that new phenomena require the formation of a new "closed" (that is, axiomatic) theory, coping also with the physical theory's underlying logic and mathematics. © 2008 Springer Science+Business Media, LLC. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00159018_v38_n11_p969_Domenech http://hdl.handle.net/20.500.12110/paper_00159018_v38_n11_p969_Domenech
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Fock space
Particle number
Quantum indistinguishability
Quasi-sets
spellingShingle Fock space
Particle number
Quantum indistinguishability
Quasi-sets
Q-spaces and the foundations of quantum mechanics
topic_facet Fock space
Particle number
Quantum indistinguishability
Quasi-sets
description Our aim in this paper is to take quite seriously Heinz Post's claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller's words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg's suggestion that new phenomena require the formation of a new "closed" (that is, axiomatic) theory, coping also with the physical theory's underlying logic and mathematics. © 2008 Springer Science+Business Media, LLC.
title Q-spaces and the foundations of quantum mechanics
title_short Q-spaces and the foundations of quantum mechanics
title_full Q-spaces and the foundations of quantum mechanics
title_fullStr Q-spaces and the foundations of quantum mechanics
title_full_unstemmed Q-spaces and the foundations of quantum mechanics
title_sort q-spaces and the foundations of quantum mechanics
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00159018_v38_n11_p969_Domenech
http://hdl.handle.net/20.500.12110/paper_00159018_v38_n11_p969_Domenech
_version_ 1768546330791116800

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