Abstract
In this paper I discuss some metaphysical consequences of an unorthodox approach to the problem of the identity and individuality of “indistinguishable” quantum particles. This approach is based on the assumption that the only admissible way of individuating separate components of a given system is with the help of the permutation-invariant qualitative properties of the total system. Such a method of individuation, when applied to fermionic compositions occupying so-called GMW-nonentangled states, yields highly implausible consequences regarding the number of distinct components of a given composite system. I specify the problem (which I call the problem of fermionic inflation) in detail, and I consider several strategies of solving it. The preferred solution of the problem is based on the premise that spatial location should play a privileged role in identifying and making reference to quantum-mechanical systems.
Highlights
Quantum mechanics teaches us that particles of the same type can occupy only those joint states that are either symmetric or antisymmetric
Even without entering the intricate discussions on assorted grades of discernibility and their role in establishing the individuality of quantum objects, we may notice that the broad metaphysical picture emerging from the orthodox view is rather bizarre
Consider spin | ↑x, which is possessed by some system of degree one. Which system would it be: “up” or “down”? Nothing in the formalism that we have introduced so far can determine whether spin | ↑x should be paired up with | ↑z or with | ↓z
Summary
Quantum mechanics teaches us that particles of the same type can occupy only those joint states that are either symmetric (bosons) or antisymmetric (fermions). If the state of N bosons (fermions) results from the symmetrization (antisymmetrization) of a direct product of N orthogonal states, it can be formally proven that individual particles possess well-defined and discerning properties corresponding precisely to the initial, pre-symmetrization states. This fact gives formal support to the intuitively straightforward observation that an electron detected in a bubble chamber has a location property that distinguishes it from any other electron in the universe. I call this issue the problem of fermionic inflation, and I will consider several strategies of how to deal with it
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