arXiv:1807.10127quant-ph
Do quantum propositions obey the principle of excluded middle?
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Abstract
The present paper demonstrates the failure of the principle of excluded middle (PEM) in the lattice of all closed linear subspaces of a Hilbert space (usually defined as quantum logic). Namely, it is shown that for a qubit, a proposition and its negation can be both false. Since PEM is the assumed theorem of quantum logic, this raises the question: If PEM holds in the orthocomplemented lattice of all propositions of the quantum system, then how the failure of PEM in quantum logic can be explained? Alternatively, if the propositions relating to the quantum system do not obey PEM, then what is the semantics of those propositions? Possible answers to these questions are analyzed in the present paper.
Statisticians have a saying, “all models are wrong, some are useful”. What we have is that math is useful for modeling physics. But it is just that, a model in so far as we know. Believing that math or logic is intrinsic to the universe is not all necessary to using math and…
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