Auwvax.349
net.misc
utzoo!decvax!harpo!uwvax!doug
Tue May  4 20:08:48 1982
polarizers and the quantum watched pot

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.
Notice that cos^4 (45) is greater than cos^2 (45) (for any angles you're
ever going to see in this problem).  That is, the intensity
of light passing through the whole collection of filters is GREATER
than the intensity of light which passed through just the middle one.

This means the presence of the middle filter actually "helped restore"
things to the initial state, if you look at it in a certain way.  Of
course, I'm ignoring simple attenuation of light through the substance
of the polarizer.

The reason I mention it, is 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).

By the way, 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.

        Using the sort of analysis above, we can see that 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. A third polarizer would mean even more.  
        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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