Notes on von Neumann measurement scheme

Abstract

A quantum measurement scheme devised by von Neumann plays a central role in all considerations relevant to the measurement problem in quantum mechanics. Despite the fact that the scheme ultimately did not reach the anticipated goal, a view is still maintained, that at least the very approach to the solution of the problem is correct and does not rise any doubts about its consistency. However, a little critical check of a validity of the key assumptions, lying in the foundations of the scheme, casts some shadow on its physically unimpeachable status. Speaking explicitly, the use of such physically bad established notions as a quantization of a purely macroscopic object and an “ideal” measurement, although embodied in the proper mathematical formalism of quantum theory, as well as the over-simplified interpretation of the theory, characterize this measurement scheme as a purely theoretical construction, which is far away from the situation occurring in the case of real measurements.