Mathematical Results on the Foundations of Quantum Mechanics

Neumann, J. v., Wheeler, N. A.

Anders Wimo

Detlef Dürr, Dustin Lazarovici

John von Neumann

Boris Khots, Dmitriy Khots

This work considers the Lagrange function in classical mechanics and Hamiltonian equations of general relativity and quantum theory, in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics. Certain results and communications pertaining to solutions of these problems are provided.

Alexander A. Pechenkin

Quantum logic as it is presented in Birkhoff-von Neumann’s 1936 paper arose within the framework of the mathematical elaboration of the foundations of quantum mechanics. Birkhoff-von Neumann’s axiomatic was an alternative of the traditional formulation of foundations of quantum mechanics proceeding from the technique of the Hilbert space. It provided more economic formulation of the foundations of the theory. In Mackay’s writings it has been transformed into the axiomatic of quantum theory of probability. However, Mackay came back to the concept of Hilbert space as the fundamental for quantum mechanics. He also adopted the rules of super-selections in his presentation of the foundations of quantum mechanics. The contemporary approach to Birkhoff-von Neumann’s axiomatic is twofold: the criticism of their too rigid construction from the point of view of physics and the development in connection with mathematical intuitionism.