The logic of quantum mechanics

Garrett Birkhoff

John von Neumann

pp. 1-26

in: Clifford A. Hooker (ed), The logico-algebraic approach to quantum mechanics I, Berlin, Springer, 1975

Abstract

One of the aspects of quantum theory which has attracted the most general attention, is the novelty of the logical notions which it presupposes. It asserts that even a complete mathematical description of a physical system S does not in general enable one to predict with certainty the result of an experiment on S, and that in particular one can never predict with certainty both the position and the momentum of S, (Heisenberg's Uncertainty Principle). It further asserts that most pairs of observations are incompatible, and cannot be made on S, simultaneously (Principle of Non-commutativity of Observations).