On the physical interpretation of negative probabilities in Prugovecki's empirical theory of measurement

Abstract

We study the problem of a simultaneous measurement of incompatible observables in the framework of Prugoveckiis empirical theory of measurement (i.e., the theory where the irreducible errors in individual measurements ought to be taken into account). We propose a solution for the main problem of this theory: negative probability distributions that arise for some states in the probabilistic description of a simultaneous measurement. These probabilities have a meaningful frequency interpretation. However, limits of relative frequencies exist only in a generalized sense and this is only a chaotic oscillation from the ordinary point of view. We present a measurement (i.e., a preparation and determinative measurements) where negative and usual Kolmogorov probabilities might arise. We show that there are two roots of negative probabilities: disturbance effects and the finite exactness of a measurement. Resume : Nous Otudions le problme reliO aux mesures simultanOes diobservables