Perhaps the most unsatisfactory aspects of quantum mechanics as we
learn it
in class rooms are two fold. First of all, one gets an
uncomfortable
impression that the instructor himself does not
understand exactly how
quantum mechanics goes over to classical
mechanics despite the standard lore
that big, heavy objects should
follow classical mechanics while small things
obey quantum law of
nature. The second, even more immediate discomfort comes
from part
about how measurement of a quantum state occurs, where we
must
assume that a wave-function collapses to an eigen-state of what
the
apparatus measures. Perhaps the most popular culmination of
these doubts can
be found in so-called Schroedinger's cat.
This sort of doubts naturally
raise questions regarding whether
quantum mechanics is a complete framework
of its own. It has lead
many researches astray into the obscure world of
philosophy. I
must emphasize that the purpose of this min-project is NOT
to
encourage such a dangerous path.
One, relatively new approach to
this sort of fundamental questions
is characterized by the word
"Decoherence." This approach tries to
answer such questions entirely within
the framework of quantum
mechanics, by showing how the environment with a
large number of
degrees of freedom remove coherence from the object that
interact
with these larger number of degrees of freedom. This
makes
possible a seamless transition from quantum mechanics to
classical
mechanics, and also clarifies a thing or two about the
measurement
procedure in quantum mechanics.
Try to follow the main
references below, present the ideas, the
computations, and the result.