Do quantum propositions obey the principle of excluded middle?
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.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 DOI:
 10.48550/arXiv.1807.10127
 arXiv:
 arXiv:1807.10127
 Bibcode:
 2018arXiv180710127B
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 13 pages