Seven Principles of Quantum Mechanics

Abstract

The list of basic axioms of quantum mechanics as it was formulated by von Neumann includes only the mathematical formalism of the Hilbert space and its statistical interpretation. We point out that such an approach is too general to be considered as the foundation of quantum mechanics. In particular in this approach any finite-dimensional Hilbert space describes a quantum system. Though such a treatment might be a convenient approximation it can not be considered as a fundamental description of a quantum system and moreover it leads to some paradoxes like Bell's theorem. I present a list from seven basic postulates of axiomatic quantum mechanics. In particular the list includes the axiom describing spatial properties of quantum system. These axioms do not admit a nontrivial realization in the finite-dimensional Hilbert space. One suggests that the axiomatic quantum mechanics is consistent with local realism.

7 pages, latex

References in corpus (3)

• Local Realism, Contextualism and Loopholes in Bell`s Experiments
• Towards Quantum Information Theory in Space and Time
• On Quantum Statistical Inference, I

Cited by in corpus (7)

• Time Irreversibility Problem and Functional Formulation of Classical Mechanics
• Quantum Mechanics from Focusing and Symmetry
• Extended statistical modeling under symmetry; the link toward quantum mechanics
• The bicomplex quantum Coulomb potential problem
• Quantum theory as a statistical theory under symmetry and complementarity
• Quantum theory as a statistical theory under symmetry
• An epistemic interpretation and foundation of quantum theory