Generalization of the von Neumann theorems to irreproducible measurements within quantum field theory. IV

Abstract

It is shown that the theorem of the first part of this cycle of papers necessarily, by virtue of only the fundamental principles of quantum theory, implies the existence of two fundamentally different types of evolution of isolated quantum macrosystems, i.e., the S and PS evolutions of pure states. As for isolated quantum microsystems, they can only S-evolve. The paper considers the fundamental specific singularities of PS evolution, which follow strictly from the theorem itself, as well as its corollary, proved in the first part [1] of this cycle of papers, also only on the basis of the fundamental principles of quantum theory. These singularities consist in the fact that, regardless of the commutativity of any observable\(\mathop \xi \limits^ \wedge\) of a system described by a vector in physical Hilbert space with the S-operator of this system, the probability distribution of this observable\(\mathop \xi \limits^ \wedge\) during measurement (with an appropriate instrument Ξ), providing complete information about the ξ characteristic of the system, is not conserved during the process of PS evolution. Nor is even the expectation of the result of measurement of the observable\(\mathop \xi \limits^ \wedge\) conserved with time.