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Identity and Indiscernibility in Quantum MechanicsQualitative Individuation of Same-Type Particles: Beyond Orthodoxy

Identity and Indiscernibility in Quantum Mechanics: Qualitative Individuation of Same-Type... [This chapter develops an alternative (“heterodox”) approach to quantum individuation, which is based on certain types of symmetric projection operators acting in tensor-product Hilbert spaces. The starting point is an analysis of the correct meaning of symmetric combinations of single-particle projectors. An interpretation supporting the claim that same-type particles may be distinguishable by their properties is proposed. Subsequently, a criterion of qualitative individuation based on symmetric projectors is formulated and defended. The main objection to the proposed approach is related to the issue of measurements. In response to this objection, it is argued that in the case of “indistinguishable” particles, measurements performed on the separate components of a composite system must be linked to distinct spatial locations. Therefore it is paramount to properly include the spatial degrees of freedom in the description of a joint state of same-type particles (such as the singlet-spin state). We make a distinction between the genuine singlet-spin state and the “pseudo” singlet state whose antisymmetry is purely “formal”. It is shown that in the case of the former state, all known facts regarding the measurement outcomes are recovered, under both the collapse and “unitary” interpretations of measurements.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Identity and Indiscernibility in Quantum MechanicsQualitative Individuation of Same-Type Particles: Beyond Orthodoxy

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References (8)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
ISBN
978-3-030-74869-2
Pages
103 –135
DOI
10.1007/978-3-030-74870-8_5
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter develops an alternative (“heterodox”) approach to quantum individuation, which is based on certain types of symmetric projection operators acting in tensor-product Hilbert spaces. The starting point is an analysis of the correct meaning of symmetric combinations of single-particle projectors. An interpretation supporting the claim that same-type particles may be distinguishable by their properties is proposed. Subsequently, a criterion of qualitative individuation based on symmetric projectors is formulated and defended. The main objection to the proposed approach is related to the issue of measurements. In response to this objection, it is argued that in the case of “indistinguishable” particles, measurements performed on the separate components of a composite system must be linked to distinct spatial locations. Therefore it is paramount to properly include the spatial degrees of freedom in the description of a joint state of same-type particles (such as the singlet-spin state). We make a distinction between the genuine singlet-spin state and the “pseudo” singlet state whose antisymmetry is purely “formal”. It is shown that in the case of the former state, all known facts regarding the measurement outcomes are recovered, under both the collapse and “unitary” interpretations of measurements.]

Published: Jan 3, 2022

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