The Logico-Algebraic Approach to Quantum Mechanics

Volume 5a of the series The University of Western Ontario Series in Philosophy of Science pp 1-26

The Logic of Quantum Mechanics

  • Garrett BirkhoffAffiliated withThe Institute for Advanced Study, Harvard University
  • , John Von NeumannAffiliated withThe Institute for Advanced Study, Harvard University

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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).