We study the effect of the environment on the process of the measurement of a
state of a microscopic spin half system. The measuring apparatus is a heavy
particle, whose center of mass coordinates can be considered at the end of the
measurement as approximately classical, and thus can be used as a pointer. The
state of the pointer, which is the result of its interaction with the spin, is
transformed into a mixed state by the coupling of the pointer to the
environment. The environment is considered to be a gas reservoir, whose
particles interact with the pointer. This results in a Fokker-Planck equation
for the reduced density matrix of the pointer. The solution of the equation
shows that the quantum coherences, which are characteristic to the entangled
state between the probabilities to find the pointer in one of two positions,
decays exponentially fast in time. We calculate the exponential decay function
of this decoherence effect, and express it in terms of the parameters of the
model.Comment: 41 pages, 1 figur
