QUANTUM THEORY OF MEASUREMENT AND ERGODICITY CONDITIONS

Journal Article · Tue May 01 04:00:00 EDT 1962 · Nuclear Phys.

DOI:https://doi.org/10.1016/0029-5582(62)90528-X· OSTI ID:4811699

Daneri, A; Loinger, A; Prosperi, G M

Some criticisms to von Neumann's treatment of the measuring process are discussed. The problem is considered and investigated on the basis of an ergodic theorem. The measuring apparatus is schematized as a macroscopic system which possesses, besides the energy, at least another macroscopic constant of the motion. The value of this constant characterizes an invariant manifold ( channel '). In each manifold certain ergodicity conditions hold and there exists an equilibrium macro-state towards which the system evolves spontaneously. The apparatus is assumed to be initially in the equilibrium state belonging to a given channel and the interaction with the observed system determines a transition of the apparatus towards a state be longing to another channel, which depends on the initial state of the observed system. Then the apparatus evolves towards a new equilibrium state. The ergodicity conditions employed are sufficiently realistic, since it is proved that they are in particular satisfied by a certain class of Hamiltonians for which a master equation can be derived. (auth)

• Research Organization: Universita, Milan
• NSA Number: NSA-16-026439
• OSTI ID: 4811699
• Journal Information: Nuclear Phys., Journal Name: Nuclear Phys. Vol. Vol: 33
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

DIFFERENTIAL EQUATIONS
ENERGY
ERGODIC THEOREM
ERGODICITY
HAMILTONIAN
INTERACTIONS
MEASURED VALUES
MECHANICS
MOTION
PHYSICS
QUANTUM MECHANICS
STATISTICS
THERMODYNAMICS