Foundations of Physics 38 (11):969-994 (2008)

Décio Krause
Federal University of Santa Catarina
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
Keywords Quasi-sets  Particle number  Fock space  Quantum indistinguishability
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DOI 10.1007/s10701-008-9246-9
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References found in this work BETA

The Emperor’s New Mind.Roger Penrose - 1989 - Oxford University Press.
Are Rindler Quanta Real? Inequivalent Particle Concepts in Quantum Field Theory.Rob Clifton & Hans Halvorson - 2001 - British Journal for the Philosophy of Science 52 (3):417-470.

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Citations of this work BETA

Is Identity Really so Fundamental?Décio Krause & Jonas R. Becker Arenhart - 2019 - Foundations of Science 24 (1):51-71.
Identity and Individuality in Quantum Theory.Steven French - 2008 - Stanford Encyclopedia of Philosophy.
Structural Realism and the Nature of Structure.Jonas R. Becker Arenhart & Otávio Bueno - 2015 - European Journal for Philosophy of Science 5 (1):111-139.

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