Small-time behaviour of quantum nondecay probability and Zeno's paradox in quantum mechanics

Abstract

A detailed investigation of the small-time deviations of the quantum nondecay probability from a pure exponential is made to study their physical consequences. Specific consideration is given to the problem of the dependence of the lifetime on the characteristics of the measuring apparata whose possible occurrence has recently been pointed out. In particular we investigate the problem of the indefinite increase of the lifetime when the frequency of the measurement processes tends to infinity, an effect referred to as Zeno's paradox in quantum mechanics. It is shown that, if the uncertainty relations are properly taken into account, the arguments leading to the paradox are not valid. Moreover, by the same kind of arguments, it is shown that the dependence of the measured lifetime on the frequency of the measurement processes, even though present in principle, is practically not detectable. To verify experimentally that the reduction process is effective one must then resort to the comparison of an experiment with reductions with one in which no interactions with the environment take place.