Auwvax.351
net.misc
utzoo!decvax!harpo!uwvax!doug
Tue May  4 20:15:15 1982
polarizers and the quantum watched pot

                       * this is the RIGHT article *

I think the answer to

------->      |/-    (>

is

       If the light is incident on the first filter with an
       intensity of I, then the light which passes through
       the middle filter leaves with an intensity of I * cos^2 (45)
       and the light which leaves the right-most filter has
       an intensity of I * cos^4 (45).

   ------------------------------------------------------------

Anyway, what's *really* interesting here is an extension to this problem.

It reminds me of an article I read a year or so ago in the American Journal
of Physics.  It purports to relate this sort of classical phenomena
to the quantum mechanical principle that "the closer you watch a state,
the less it changes".  As a matter of fact, in the limit where you
*continously* watch a state, the state never changes.  For example,
if you could continously watch a certain unstable nuclide it would
never decay (certainly a change of state).

The description of the classical experiment was this:

       Suppose you had a rectangular tube containing some
       optically active liquid.


               |               |
               |               |
               <------L-------->

       If the tube has length L, and the liquid is optically active,
       then linearly polarized light, say vertical, which passed
       through it would emerge at a polarization of some angle
       theta from the vertical:


       ----> | |               |    |   /
               |               |    |
               <------L-------->   (polarizer)

       A vertical polarizer positioned at the right side could be
       used to measure theta by seeing what fraction of the intial
       intensity of light gets through it.

       A SECOND vertical polarizer placed half-way through the tube
       would mean that a GREATER intensity of light would emerge
       from the far right polarizer than had the second polarizer
       not been there.

       That is, cos^4 (theta/2) is greater than cos^2 (theta).
       (at least for angles of interest in this problem).

       A third polarizer would mean even more got through.
       And so on, and so on.  Obviously in the
       limit of an infinite number of infinitely thin vertical polarizers
       throughout the whole liquid, the exact same intensity of light
       would emerge finally as intially was incident on the liquid.

The mathematics of closely watched quantum states is very
analagous.  The quantum mechanical state of a system changes
with time, however it changes less when more measurements are made
of it.

The quantum mechanical watched pot never boils.





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