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Identity and Indiscernibility in Quantum MechanicsThe Heterodox Approach to Absolute Discernibility and Entanglement

Identity and Indiscernibility in Quantum Mechanics: The Heterodox Approach to Absolute... [We start this chapter with a logical theorem showing the possibility of expressing facts of absolute discernibility in symmetric sentences (sentences built with the help of permutation-invariant formulas). In the subsequent sections, we address the issue of the scope of absolute discernibility for same-type particles under the unorthodox approach to individuality proposed in the previous chapter. It is proven that “indistinguishable” fermions are always discerned by their properties, which are sometimes non-maximally specific (i.e. represented by many-dimensional projectors). In the case of bosons, we formulate a general criterion of discernibility, and we identify some states in which bosons are not absolutely discernible, other than simple products of identical states. The chapter also contains an extensive analysis of the concept of entanglement applied to “indistinguishable” particles (sometimes referred to as GMW-­entanglement). We formulate several equivalent criteria of GMW-entanglement for bosons and fermions, and we compare entanglement with discernibility. We also show that typical GMW-non-entangled states, despite being formally non-­factorizable, do not give rise to non-local correlations violating Bell’s inequalities.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Identity and Indiscernibility in Quantum MechanicsThe Heterodox Approach to Absolute Discernibility and Entanglement

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References (7)

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
137 –175
DOI
10.1007/978-3-030-74870-8_6
Publisher site
See Chapter on Publisher Site

Abstract

[We start this chapter with a logical theorem showing the possibility of expressing facts of absolute discernibility in symmetric sentences (sentences built with the help of permutation-invariant formulas). In the subsequent sections, we address the issue of the scope of absolute discernibility for same-type particles under the unorthodox approach to individuality proposed in the previous chapter. It is proven that “indistinguishable” fermions are always discerned by their properties, which are sometimes non-maximally specific (i.e. represented by many-dimensional projectors). In the case of bosons, we formulate a general criterion of discernibility, and we identify some states in which bosons are not absolutely discernible, other than simple products of identical states. The chapter also contains an extensive analysis of the concept of entanglement applied to “indistinguishable” particles (sometimes referred to as GMW-­entanglement). We formulate several equivalent criteria of GMW-entanglement for bosons and fermions, and we compare entanglement with discernibility. We also show that typical GMW-non-entangled states, despite being formally non-­factorizable, do not give rise to non-local correlations violating Bell’s inequalities.]

Published: Jan 3, 2022

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