Measurement in quantum mechanics and classical statistical mechanics

Abstract

It is shown that the uncertainties (Δ P) 2 and (Δ Q) 2 in momentum and positiion of a quantum particle can always be expressed as the sum of a classical term and a quantum term. For quantum states characterized by a product Δ PΔ Q〉 h it is always possible to reduce the uncertainty in both P and Q by performing measurements of both of them with resolutions Δ P 0 and Δ Q 0 such that their product is of the order of h. These measurements do not bring into existence values of P and Q which were nonexisting before, as it is usually assumed, but merely restrict the region in phase space allowed for them. This analysis can be used to support the thesis that the old question of the state vector collapse can be solved within the frameworl of the formalism of quantum mechanics, since it arises from the irreversible character of the increase of knowledge.