

Subatomic Particle Spin
Name: Dmytro H.
Status: student
Age: 17
Location: N/A
Country: N/A
Date: Sunday, September 15, 2002
Question:
I have seem many times, when it comes to a description of
subatomic particles, that they all have spin. What is spin? And
furthermore what is the difference between a particle that has a spin of
1 compared to one that has a spin of 1/2 or 0?
Replies:
Nobody really knows what spin is, much beyond the fact that it is an
attribute of
an elementary particle. Charge, mass, speed, energy, and angular momentum are
among other attributes. You've probably noticed that some of these attributes
are intrinsic to the particle and can't be changed (e.g., mass, charge), while
others can be gained and lost (e.g., speed, angular momentum). Spin is
actually
two attributes, one of which is intrinsic, the other of which can be
gained or lost.
More about this later.
Although we do not have a deep understanding of what spin is, we do have a
mathematical
description of how it behaves  in particular, of how the total spin of a
system of
particles depends on the spins of the constituents. This allows us to
compare spin's
behavior to the behavior of other things that we feel we understand
better. One thing
we have noticed is that spin behaves a lot like angular momentum (which
also is really
two attributes).
Angular momentum is a vector quantity (something that has both a magnitude
and a
direction, like velocity) that can take on only certain values in quantum
mechanics.
Think of angular momentum as an arrow of some length that can point in
different
directions, but you cannot ever have complete information about the
direction. In
particular, if you have measured the projection of the arrow along the z
axis, you have
gained a clue about what the total angular momentum might be, but you have
also destroyed
any information you might have had about its projection along any other axis.
Another thing we know about angular momentum is that, in quantum
mechanics, it cannot take
on just any old values, but only certain specific ones. If a particle has
three units of
total angular momentum, then its projection can be any of (3, 2, 1, 0,
1, 2, 3) and
that is it: projections must differ by an integer number of units. Very
weird, but quite
a handy fact: if you know that a particle's angular momentum can take on
only two different
projection values, then you know its total angular momentum must be 1/2,
and the projection
values are (1/2, 1/2). If you know there are three projection values,
then you know the
total angular momentum is 1, with projections (1, 0, 1).
Spin acts like this, so everything you've just learned about angular
momentum is also
true of spin. In fact the mathematical description of the way spin
behaves is so similar
to the math of angular momentum that we can even do a mathematical trick
that allows us to
pretend that spin and angular momentum can be added together. However,
the magnitude of
the spin quantum number is an intrinsic attribute of a particle. All
electrons have total
spin 1/2, with two possible projection values, as we've seen. The
projection can be changed,
but the total spin of 1/2 is fixed for all time. It is part of the
definition of an electron.
All photons have spin 0, and for them "projection" does not seem to make
much sense, but it is
clear anyway that the number of possible projection states is one.
A curious and very mysterious thing is that the quantum mechanical rules
for particles that
have integer spin are very different from the rules for particles with
halfinteger spin.
All the halfinteger particles (e.g., electron, proton, neutron) must be
distinguishable from
each other: if they are in the same system, they must differ in at least
one quantum number.
Not so for the integerspin particles (e.g., photon, meson, gluon). These
are allowed to be
indistinguishable, and they can all have the same quantum numbers
including position. It so
happens that particles with halfinteger spin are the particles we think
of as making up matter,
and the particles with integer spin are those we associate with forces.
Why spin should be the
thing that distinguishes stuff from the forces between stuff is
unfathomable to me, and that spin
should do this in such an apparently arbitrary way (halfinteger as
opposed to integer) suggests
to me that our understanding is fundamentally flawed, and that the real
answer to your question
 if we ever discover it  will be part of a deeper understanding of
/way/ more than spin.
Tim Mooney
Dmytro,
Most individual particles and combinations of particles produce a magnetic
field very much like that of a spinning ball of charge. At one time,
scientists assumed the charged particles had to be spinning to make this
magnetic field. Experiments and observations showed that this spin is most
easily described as an angular momentum. All particles have an "internal
angular momentum" that is a multiple of the same value. One times this
value came to be called spin 1/2, two times this quantity came to be called
spin 1, and so forth. We do not know whether particles actually spin
around, but they have an internal angular momentum and a magnetic field that
suggests it.
Quantum physics is the physics of individual particles and small
combinations of particles. Analysis of statistics indicated that some
particles could build up in huge numbers. Other particles cannot build up
so easily.
A particle with integral spin (0,1,2,...) is not in any way limited by other
particles of its own kind. At one location, you can have a huge number with
exactly the same energy, moving in exactly the same way. Photons of light,
neutrinos, and pions are such particles. These tend to be the communication
particles, the particles that spend most of their time passing between
things. These are called BoseEinstein particles, or bosons for short.
A particle with halfintegral spin (1/2,3/2,5/2,...) is very limited by
other particles of its own kind. If two such particles are at the same
location, something must be different about them. They may be "spinning" in
different directions. They may have different energies. They may be moving
in different directions. They cannot be identical in all ways. Protons,
neutrons and electrons are the most common such particles. These tend to be
the particles that build matter. These are called FermiDirac particles, or
fermions for short.
I do not expect anyone knows why bosons and fermions behave so differently
when in groups. Some physicists can quote statistical calculations that
show it must be true, but not why. It happens to be how the universe
behaves.
Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
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Update: June 2012

