Repeated Measurements on Unstable System

Abstract

The observation of an unstable system often includes a premeditated interaction with its environment. In many cases, such as the detection of particles by tracemonitoring devices, the interaction with the surrounding medium can be described as a sequence of measurements performed on the system under consideration. The study of such situations is the main subject of this chapter. First we formulate the basic assumptions and derive the integral equations which yield the decay law of a system which suffers repeated measurements, in general, randomly and nonhomogeneously distributed. The existence of the solution to these equations, together with its simple properties, are established. Section 2 is devoted to a discussion of some important examples. The results show that the measured decay laws behave asymptotically exponentially in a certain sense and, moreover, that the measured decay rate may be influenced by structure of the measuring device, if the decay law of the same system undisturbed by the measurements is not purely exponential. This conclusion might be used for search of the non-exponentialities; in order to get some quantitative estimates of the effect, we treat in Section 3 a simple model describing the decay of charged kaons in a bubble chamber. It appears that even in an optimal experimental arrangement, the effect is so very small that it can hardly be observed. Section 4 is devoted to the treatment of the limiting case when the measurement frequency tends to infinity, which is sometimes used to describe the behavio ur of a system exposed to continual observation. This interpretation leads to some counterintuitive conclusions, which will be discussed and clarified.

“The ‘path’ emerges only if we observe it.”

W. Heisenberg