Monday, July 2, 2007

Hidden variable theories

Hidden variable theories. In such theories the particles reaching the
barrier are not identical; they possess other variables in addition
to their velocities and, in principle, the values of these variables
determine the fate of each particle as it reaches the barrier; no
breakdown of determinism is required and the probability aspect
only enters through our ignorance of these values, exactly as in
classical physics. At this stage of our discussion readers are probably
thinking that hidden variable theories surely contain the truth,
and that we have not yet given any good reasons for abandoning
determinism. They are right, but this will soon change and we shall
see that hidden variable theories, which are discussed more fully in
Chapter 5, have many difficulties.
Before proceeding we shall look a little more carefully at our
potential barrer experiment. Since we are interested in whether or
not particles pass through the barrier we must have detectors which
record the passage of a particle, e.g. by flashing so that we can see
the flash. We shall assume that our detectors are ‘perfect’, i.e. they
never miss a particle. Then if we have a detector on the left of the
barrier it will flash when a particle is transmitted, whereas one on
the right will flash for a reflected particle. Suppose N particles, all
with the same velocity, are sent and suppose we see R flashes in the
right-hand detector and Tin the left-hand detector. Because every
particle must go somewhere, we will find

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