From: mcirvin@scws1.harvard.edu (Mcirvin)
Newsgroups: alt.sci.physics.new-theories
Subject: Re: Spin Numbers
Date: 15 Nov 92 23:00:25 GMT
Organization: Harvard University Science Center

In article <corey.0f73@amiganet.chi.il.us> corey@amiganet.chi.il.us (Corey Sweeney) writes:
>Would somebody like to explain spin to me?  I've heard of it for years but i
>never found out what it was.
>
Here's the basic idea.  In classical physics there's a quantity called
angular momentum that is possessed, among other things, by spinning
objects; it's the angular velocity times the moment of inertia, which
depends on the distribution of mass. 

Now, in quantum mechanics, if you try to calculate the angular momentum
due to its orbit of something like an electron in an atom, you find that
the possible values of that angular momentum are integer multiples of
hbar (= Planck's constant h/2pi).  This is the quantum-mechanical 
equivalent of the ordinary sort of angular momentum; something's rotating
or moving around in such a way that it possesses angular momentum,
speaking very roughly.

However, after a while it became clear that this was not the whole
story; various experiments seemed to imply that electrons had an 
additional angular momentum of hbar/2, one-half the usual quantum
of orbital angular momentum.  Attempts to describe this in terms of
some kind of physical rotation of whatever the electron was made of
failed, since the electron was known to be small enough that it would
have to rotate faster than light.  So it was proposed that in addition
to orbital angular momentum, it was possible for objects to have a
kind of intrinsic angular momentum known as spin. 

Spin comes in integer or half-integer multiples of hbar, and which it is
has profound implications for the way identical particles behave in a
system.  Particles whose spin angular momentum is (n+1/2)hbar where n is
an integer obey the Pauli exclusion principle, for instance; they are
forbidden to occupy the same quantum state.  They are called fermions,
or Fermi-Dirac particles, after the people who studied their statistics
in detail.  Particles whose angular momentum is n*hbar are called
Bose-Einstein particles, or bosons.  They have a pronounced tendency
to be in the same quantum state.  The reason for the difference is
sufficiently obscure that it doesn't generally come up until graduate
courses in quantum field theory; it turns out to be necessary to have
this sort of behavior if you want to construct a reasonable relativistic
quantum theory.

Quantum-mechanical angular momentum, whether spin or orbital, behaves in
a funny way.  Classically angular momentum is represented as a vector
that points in a direction perpendicular to the plane of rotation, using
a right-hand rule.  In QM the components of this vector end up having
uncertainty relations between them; if you measure the z component, say,
the x component becomes uncertain.  The other odd thing is that no matter
what component you measure-- the x component or the y component or the
component in a direction 37.8 degrees off the y axis in the z direction--
you will always get an integer or half-integer multiple of hbar!  In the
case of electron spin this is particularly strange, since the only possible 
values are plus or minus hbar/2; these possibilities are sometimes called
"up" and "down."  No matter how you define "up," you'll always measure the
electron spin as "up" or "down." 

To find out more, read volume III of the Feynman Lectures on Physics.
It discusses quantum mechanics using spin as a starting point, since
spin systems provide the simplest example of most of the unique features
of quantum mechanics, such as uncertainty relations, quantum operators,
and quantum-mechanical dynamics.
r 
-- 
Matt McIrvin