As noticed above in general we expect . That means that if the experiment is repeated many times, then there will be particles that were not registered while close to the counter; they moved away, and they will never be registered in the future. The natural question then arises: is the very presence of the counter reflected in the dynamics of the particles that pass the detector without being observed? Or we can put it as a "quantum espionage" question: can a particle detect a detector without being detected? And if so - which are the precise equations that tell us how?.
To answer this question it is not enough to use the two postulates above. One needs to make use of the Event Engine of EEQT once more.
Our third postulate reads:
prior to any event, and independently of whether any event will
happen or not, the state of the system is described by the vector
undergoing the non unitary
evolution given by Eq. (2). It is not too
difficult to think of an experiment that will test this
Fig. 1 shows four shots from time evolution of a gaussian wavepacket monitored by a gaussian detector placed at the center of the plane. The efficiency of the detector is in this case ca. There is almost no reflection. The shadow of the detector that is seen on the fourth shot can be easily interpreted in terms of ensemble interpretation: once we count only those particles that were not registered by the detector, then it is clear that there is nothing or almost nothing behind the detector. However a careful observer will notice that there is a local maximum exactly behind the counter. This is a quantum effect, that of "interference of alternatives". It has consequences for the rate of future events for an individual particle.