Logical reformulation of quantum mechanics. I. Foundations
The basic rules of quantum mechanics are reformulated. They deal primarily with individual systems and do not assume that every ket may represent a physical state. The customary kinematic and dynamic rules then allow to construct consistent Boolean logics describing the history of a system, following essentially Griffiths' proposal. Logical implication is defined within these logics, the multiplicity of which reflects the complementary principle. Only one interpretive rule of quantum mechanics is necessary in such a framework. It states that these logics provide bona fide foundations for the description of a quantum system and for reasoning about it. One attempts to build up classical physics, including classical logic, on these quantum foundations. The resulting theory of measurement needs not to state a priori that the eigenvalues of an observable have to be the results of individual measurements nor to assume wave packet reduction. Both these properties can be obtained as consequences of the basic rules. One also needs not to postulate that every observable is measurable, even in principle. A proposition calculus is obtained, allowing in principle the replacement of the discussion of problems concerned with the practical interpretation of experiments by due calculations.
- Research Organization:
- Universite de Paris-Sud, Orsay (France)
- OSTI ID:
- 6279404
- Journal Information:
- J. Stat. Phys.; (United States), Vol. 53:3-4
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
QUANTUM MECHANICS
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CLASSICAL MECHANICS
EIGENVALUES
EIGENVECTORS
ELECTRON DETECTION
HAMILTONIANS
HILBERT SPACE
MATHEMATICAL MODELS
MEASURE THEORY
PHASE SPACE
PLANCK LAW
SCHROEDINGER EQUATION
STATISTICAL MECHANICS
TOPOLOGICAL MAPPING
WAVE PACKETS
BANACH SPACE
CHARGED PARTICLE DETECTION
DETECTION
DIFFERENTIAL EQUATIONS
EQUATIONS
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MATHEMATICAL OPERATORS
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PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
RADIATION DETECTION
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657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics