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Name: Dmytro H.
Status: student
Age: 17
Location: N/A
Country: N/A
Date: Sunday, September 15, 2002

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?

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 half-integer spin. All the half-integer 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 integer-spin 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 half-integer 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 (half-integer 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


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 Bose-Einstein particles, or bosons for short.

A particle with half-integral 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 Fermi-Dirac 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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