Abstract
On the one hand, non-reflexive logics are logics in which the principle of identity does not hold in general. On the other hand, quantum mechanics has difficulties regarding the interpretation of ‘particles’ and their identity, also known in the literature as ‘the problem of indistinguishable particles’. In this article, we will argue that non-reflexive logics can be a useful tool to account for such quantum indistinguishability. In particular, we will provide a particular non-reflexive logic that can help us to analyze and discuss this problem. From a more general physical perspective, we will also analyze the limits imposed by the orthodox quantum formalism to consider the existence of indistinguishable particles in the first place, and argue that non-reflexive logics can also help us to think beyond the limits of classical identity.
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Notes
The indetermination of the values of incompatible pairs is a matter of principle. In fact, it is one of the fundamental physical principles from which the formal structure of the theory may be derived. In mathematical terms, observables linked by the Heisenberg principle do not commute and thus, physical magnitudes obey a non-commutative algebra—technically, the projectors in which they decompose are structured in a modular lattice in the finite case.
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Acknowledgments
This work was partially supported by the following grants: VUB Project GOA67; FWO-research community W0.030.06; CONICET RES. 4541-12 (2013-2014).
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da Costa, N.C.A., de Ronde, C. Non-reflexive Logical Foundation for Quantum Mechanics. Found Phys 44, 1369–1380 (2014). https://doi.org/10.1007/s10701-014-9848-3
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DOI: https://doi.org/10.1007/s10701-014-9848-3