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It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of (...) No categories |
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It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of (...) |
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In this paper I consider the question of whether absolute discernibility is attainable in symmetric languages. Simon Saunders has proven that all facts expressible in first-order language with identity can be equivalently stated within its symmetric sublanguage. I use this result to show specifically how particles of the same type can be absolutely discerned in the permutation-invariant language of the quantum theory of many particles. No categories |
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The mathematical notion of a permutation of indices in the state description admits different physical interpretations. Two main interpretations analyzed in this paper are: exchange of essences and exchange of haecceities. It is argued that adopting the essentialist approach leads to the conclusion, contrary to the conventional wisdom, that quantum particles of the same type are sometimes discernible by their properties. The indiscernibility thesis can be supported only by the alternative interpretation in terms of primitive thisness. |
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In this work we discuss logical structures related to indistinguishable particles. Most of the framework used to develop these structures was presented in [17, 28] and in [20, 14, 15, 16]. We use these structures and constructions to discuss possible ontologies for identical particles. In other words, we use these structures in order to characterize the logical structure of quantum systems for the case of indistinguishable particles, and draw possible philosophical implications. We also review some proposals available in the literature (...) |
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