|The spin of a particle can be measured in various ways. For
particles with magnetic moments, the spin determines the number of
different beams that come out when the particles travel through a
spatially varying magnetic field. (The number is 2s+1) (There are some
case, such as electrons, for which experimental complications get in
the way of the simple version of this experiment.) The spin of a
nucleus determines the number of magnetic resonance lines of an
electron near it, by the same formula and for essentially the same
reason. The number of different spin states shows up when you count
states in various thermodynamic problems, affecting equilibrium
concentrations. I've undoubtedly left off numerous other ways of
measuring spin. |
Total spin is definitely not conserved under various reactions. For example, two free radical molecules, each s=1/2, can combine to form an s=0 molecule. The average of the component of angular momentum, of which spin is one piece, along any direction is conserved, but quantum mechanics doesn't require that states have sharply defined values for those components. The spread around the average is not conserved, and it's part of what determines the total spin.
In the particular case you cite, you've noticed that something seems fishy. You're right- something else is needed to make it all balance out. The something else is a neutrino, also spin 1/2. So you have an odd number of fermions going to an odd number of fermions. That obeys another conservation rule (parity), which would be violated if an even number of fermions formed a fermion.
There's a theorem you can prove about the possible allowed values of spin (and all angular momentum for that matter) of a particle has to be a half-integer multiple of Planck's constant divided by 2pi, but the axioms you start with in order to prove this are called the commutation relations for the angular momentum operators. The reasoning is somewhat circular -- the angular momentum commutation relations are a very compact statement of angular momentum physics from which other results can be derived, but the reason we believe them is because experiment agrees with their predictions. It is also true that the angular momentum operators you can build out of the regular momentum operator in quantum mechanics for a single particle obey the commutation relations, so we have a certain confidence in them.
We say electrons have "spin 1/2" and we mean by that their spin angular momentum has magnitude (1/2)(h/2pi). Planck's constant can be measured in other ways and compared with the spin of the electron.
Some newer models predict "anyons", which are neither Fermions nor Bosons, but have spins which are not integer multiples of (h/4pi). These can exist in reduced dimensional spaces (2 space dimensions + 1 time dimension) which are approximately true for some condensed matter systems. These are "quasiparticles" which are really combinations of more normal particles (like electrons, or holes) and possibly excitations of the surrounding lattice. Sometimes it is a lot easier to think of an interacting system in terms of quasiparticles than in terms of each of the real particles that's there. But all real particles we know about are either Fermions or Bosons, which reduces the problem of measuring their spins to choosing among a few small integers times (h/4pi).
(republished on 07/21/06)
(published on 02/23/13)
(published on 03/11/13)