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Philosophy

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    See Identity and Individuality in Quantum Theory Commented Jun 6, 2021 at 5:53
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    I have reservations about the idea of quantum physics as counter example to the law of identity. Sure one can often hear sentences like "the particle is both here and there" or "the particle went though both slits", but it appears to mostly be confusion raised by the fact that everyday language is not adapted to describe quantum reality (and how would it be, as all the reality we experience directly is macroscopic). But rigorously speaking, each particle or field has a well defined state vector and is rigorously defined as a mathematical object. Commented Jun 7, 2021 at 8:23
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    "But rigorously speaking, each particle or field has a well defined state vector and is rigorously defined as a mathematical object." --- not when multiple particles interact, they don't. Then we have only a state vector describing the whole. The motivation behind Schrödinger logic is that we should not speak of the identity of individual particles when they are indistinguishable by any measurement, even in principle. Commented Jun 7, 2021 at 14:51
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    @Hypnosifl Thanks. But even if our 'things' are bijections, it opens up a distinction between what we normally treat as 'objects' within our domain and these 'things'. I think Steven French is making a similar point in section 5 of the SEP article plato.stanford.edu/entries/qt-idind/#Self-Ind Commented Jun 7, 2021 at 18:25
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    @bumble I don't think it changes anything, because then this system of interacting particles is still a well defined set of numbers, always equal to itself and that can be used to conduct rigorous calculations. Again, the confusion arises from trying to instinctively grasp the idea of interacting particles, which escapes our capacity and depends on various interpretations of QM. But the mathematical object is unambiguous. Commented Jun 8, 2021 at 3:10