Attempt at the logical explanation of the wave-particle duality

Jarosław Pykacz

pp. 269-282

in: Maria L. Dalla Chiara, Roberto Giuntini, Federico Laudisa (eds), Language, quantum, music, Berlin, Springer, 1999

Abstract

In the orthodox quantum logic approach to foundations of quantum mechanics originated by Birkhoff and von Neumann [1] the object called quantum logic is not a logic in the very sense of this word but an algebraic structure: orthomodular lattice or poset. These orthomodular structures, abstracted from structures of Hilbert spaces used to describe quantum phenomena are weakenings of Boolean algebras. They can be thought of as representing Lindenbaum algebras of systems of propositions about quantum objects, the propositions belonging to the quantum logic proper. Since Lindenbaum algebras of propositional systems which obey the rules of classical logic are Boolean algebras it is inferred that the quantum logic proper, whatever it means, is non-classical.