Our first postulate reads: the coupling to a "yes-no"
monitoring device is described by an operator
in the Hilbert space .
In general may explicitly
depend on time but here, for simplicity, we will assume that
this is not the case. That means: to any real experimental
device there corresponds a . In practice it may be
difficult to produce the that describes exactly
a given device. As it is difficult to find the Hamiltonian
that takes into account * exactly* all the forces that
act in a system. Nevertheless we believe that an exact
Hamiltonian exists, even if it is hard to find or impractical
to apply. Similarly our postulate states that an exact
exists, although it may be hard to find or impractical
to apply. Then we use an approximate one, a model one.

It should be noticed that we do not assume that
is an orthogonal projection. This reflects the fact that our
device - although giving definite "yes-no" answers,
gives them acting upon possibly * fuzzy* criteria. In the
limit when the criteria become sharp one should think
of as , where
is a coupling constant of physical dimension
and **E** a projection operator. In the general case
it is usually convenient to write
where is dimensionless.

It is also important to notice that the property that is being
monitored by the device
need not be an * elementary* one. Using the concepts
of quantum logic (cf. [18,19]) the property need not
be * atomic* -
it can be a composite property. In such a case,
when thinking about physical implementation of the procedure
determining whether the property holds or no, there are two
extreme cases. Roughly speaking the situation here is similar to
that occurring in discussion of superpositions of state preparation
procedures. Some procedures lead to a coherent superpositions,
some other lead to mixtures. Similarly with composite detectors:
one possibility is that we have
a distributed array of detectors that can act independently of each
other, and our event consists
on activating * one of them*. Another possibility is
that we have a * coherent* distributed detector like a
solid state lattice that acts as * one* detector.
In the first case (called * incoherent*) will
be of the form

while in the second * coherent* case:

where are operators associated to individual constituents of the detector's array. More can be said about this important topic, but we will not need to analyze it in more details for the present purpose.

Thu Feb 22 09:58:31 MET 1996