🚀 go-pugleaf

One caveat about applying `polarizer intuition' to electron spins:  you must
remember that the two independent `polarizations' of a spin-1/2 particle are
180 degrees apart, not 90.  If you want to see electrons that were spin-up in
the Z direction become spin-down, here's what you do:

1.) Measure their Z-spin (Stern-Gerlach apparatus) to ensure you have a beam
    of pure spin-up electrons;

2.) Put this beam through a perpendicular apparatus, measuring their X-spin.
    Half of the beam will be spin-left, and the other half spin-right, of
    course.

3.) Now run either beam through a second Z-spin apparatus, and you will find
    that half of the electrons are now spin-down, not spin-up.  Of course, a
    *close* examination of the angular momentum of the apparatus will tell
    you where the Z-spin disappeared to.

Leave out step 2, of course, and you will never see a spin-down electron at
step 3.  This is indeed just like what happens to photons, except that there
(since a photon has spin 1) the independent states are vertical and horizontal
polarization---only 90 degrees apart---and the intermediate step that allows
light to pass through crossed polarizers is at 45 degrees.

The rule that `rotational angle between orthogonal spin states is 90 degrees
divided by the spin of the particle' applies to gravitons as well, by the way.
If you aim a small graser (Spectra-Physics catalog, August 2291; I'll look
up the part number for you, but it will take a while) at a + polarizer, and
then an x polarizer, you will find that no gravitons get through.  If you
interpolate a `halfway' polarizer, twisted 22.5 degrees to the right, then
a quarter of the gravitons will sail right on through, even though the + and
x states, 45 degrees apart, are orthogonal.

What about gravitinos (hypothetical spin-3/2 particles)?  Well, my dissertation
is (loosely) about them, so I should be the right person to ask, but damfino.
Gravitinos are usually dealt with in quantum field theory by thinking of them
as `vectors of spinors', a rather adhoc way of applying what we think we
understand about spin-1 and spin-1/2 to a particle that has attributes of both.
It works just fine for calculating amplitudes of fundamental processes, and
supergravity even helps us get a handle on the divergences...but my intuition
about their Lorentz-group behavior is weak.  Hannu?




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imum Saeptum Paludosum | Joshua W. Burton  burton@het.brown.edu  (401)351-5908
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