  An experimental test of the "special state" theory of quantum measurement is
proposed. It should be feasible with present-day laboratory equipment and
involves a slightly elaborated Stern-Gerlach setup.
  The "special state" theory is conservative with respect to quantum mechanics,
but radical with respect to statistical mechanics, in particular regarding the
arrow of time. In this article background material is given on both quantum
measurement and statistical mechanics aspects. For example, it is shown that
future boundary conditions would not contradict experience, indicating that the
fundamental equal-a-priori-probability assumption at the foundations of
statistical mechanics is far too strong (since future conditioning reduces the
class of allowed states).
  The test is based on a feature of this theory that was found necessary in
order to recover standard (Born) probabilities in quantum measurements.
Specifically, certain systems should have "noise" whose amplitude follows the
long-tailed Cauchy distribution. This distribution is marked by the occasional
occurrence of extremely large signals as well as a non-self-averaging property.
The proposed test is a variant of the Stern-Gerlach experiment in which
protocols are devised, some of which will require the presence of this noise,
some of which will not. The likely observational schemes would involve the
distinction between detection and non-detection of that "noise". The signal to
be detected (or not) would be either single photons in the visible and UV range
or electric fields (and related excitations) in the neighborhood of the ends of
the magnets.
