Presence of a particle in a given space-time region and the continuous action of a particle detector

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Abstract
We attempt to answer several questions relating to the presence of a particle, with known initial state, in a given region of space during a given period of time. In the process, we try to extend the quantum theory of observation to the case in which the observation goes on continuously. Although this mode of observation is common in practice, the theory does not seem to describe it adequately. In general, questions like those that we are asking do not have simple, unambiguous answers in quantum theory. In order to approach such a question, we usually have to assume that the particle interacts with something in the space-time region of interest, and then to infer the probability of the particle's presence from the probability of its interacting with the other object. This fact suggests either that we are asking the wrong questions or that perhaps quantum mechanics should be regarded as a theory of interaction events rather than a theory of systems.