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Foundations of Physics

, Volume 38, Issue 8, pp 707–732 | Cite as

Axiomatic Quantum Mechanics and Completeness

  • Carsten HeldEmail author
Open Access
Article

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. From a probability principle P1 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. All three principles are shown to be without alternative. It is thus shown 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.

Keywords

Axioms of quantum mechanics Completeness Gleason’s theorem Kochen-Specker theorem Born rule Projection postulate Probabilities as dispositions 

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Copyright information

© The Author(s) 2008

Authors and Affiliations

  1. 1.Philosophisches SeminarUniversität ErfurtErfurtGermany

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