Considerations of the temporal behavior of a quantum system lead to the association of a random process with each observable for which the ergodic properties are proved. (auth)
An analysis of some of the fundamental principles underlaying the construction of operators in quantum mechanics is given. Each operator is associated to a projection operator and these projection operators are shown to fulfill a set of properties formally identical to those of a probability field. It is shown that, by the introduction of a measure in configuration space it is possible to obtain complete sets of commuting observables having, within limits, preassigned spectra. The introduction of new operators by consideration of the groups expressing the symmetries of the system, is discussed. (auth)
Techniques previously developed for deriving a master equation to general order in the perturbation for the transition probability are now applied to the interference term. A master equation to general order for the partial interference term is obtained, which, in the limit of small perturbation, leads to a Pauli master equation for the interference term itself. The long-time behavior of the interference term is discussed. By means of these results, a complete master equation can be written without any random phase assumption. The ergodic behavior of a quantum many-body system is demonstrated for a large class of physical quantities, and the approach to microcanonical equilibrium is discussed. (auth)
The formal time symmetry of the quantum measurement process is extensively discussed. Then, the origin of the alleged association between a fixed temporal direction and quantum measurements is investigated. It is shown that some features of such an association might arise from epistemological rather than purely physical assumptions. In particular, it is brought out that a sequence of statements bearing on quantum measurements may display intrinsic asymmetric properties, irrespective of the location of corresponding measurements in time t of the Schrödinger equation. The situation of an observer performing two measurements in two opposite directions of t is eventually investigated. Essential differences are found between two descriptions of this situation: the internal one (taking only into account what is recorded in the observer's memory) and the external one (whereby the observer is considered as a quantum system ruled by the Schrödinger equation). Finally, a method allowing several observers to establish a correspondence between their memory sizes is analyzed. The most important facts that usually lead to the associating of a preferential temporal direction with quantum measurements may be inferred from this correspondence.