Axiom System and Completeness Expression for Quantum Mechanics

Abstract

The standard axiomatization of quantum mechanics (QM) is not fully explicit about the role of the time-parameter. Especially, the time reference within the probability algorithm (the Born Rule, BR) is unclear. Using a plausible principle P1, about the role of probability in a physical theory, and a second principle P2 affording a most natural way to make BR precise, a logical conflict with the standard expression for the completeness of QM can be derived. Rejecting P1 is implausible. Rejecting P2 leads to unphysical results and to a conflict with a generalization of P2, a principle P3. It is thus made plausible that the standard expression of QM completeness must be revised. An absolutely explicit form of the axioms is provided, including a precise form of the projection postulate. An appropriate expression for QM completeness, reflecting the restrictions of the Gleason and Kochen-Specker theorems is proposed.

20 pages, no figures

References in corpus (8)

• Quantum probabilities as Bayesian probabilities
• Bell-Kochen-Specker theorem: A proof with 18 vectors
• Quantum correlations versus Multisimultaneity: an experimental test
• Does entanglement depend on the timing of the impacts at the beam-splitters?
• On a Time Symmetric Formulation of Quantum Mechanics
• Kochen-Specker Vectors
• Quantum entanglement with acousto-optic modulators: 2-photon beatings and Bell experiments with moving beamsplitters
• Relativistic nonlocality (RNL) in experiments with moving polarizers and 2 non-before impacts