[RobC (OP)]

Without using analogies can anybody explain what exactly spin is when it is referred to as a property of a particle.

[Ethos_]

Without using analogies can anybody explain what exactly spin is when it is referred to as a property of a particle.

Spin has to do with the angular momentum of the particle. This subject can get rather complex when one considers spin values and charges values of 1/3 and 2/3, associated with the quarks. I don't think we can describe this fairly without resorting to  "analogies" even though those analogies are not totally consistent with what experiment tells us.

Think in terms of a top spinning, but not with only a horizontal angularity. If you have ever looked at the motion of a gyroscope, it may suggest some similarity to particle spin with the exception that the particle can be viewed as a single entity where the gyroscope has different parts spinning around different axes.

The particle is viewed as a single part which may be spinning several different axes all at the same time. The quark having fractional spin rates would be an example of that type of spin I'm attempting to describe.

Naturally, these examples are not totally realistic but only a crude attempt at a description. I'm not sure a description can be rendered without some kind of analogy.

[agyejy]

Without using analogies can anybody explain what exactly spin is when it is referred to as a property of a particle.

No one actually knows. We know it is related to angular momentum which is why it is often introduced with analogies to things like tops or gyroscopes. But generally speaking it is not something that has an explanation in our current scientific framework. It is more of an observational fact like the speed of light. Although I believe an argument can be made about the rotational symmetries of nature requiring the fundamental particles must have quantized spin. I'm not very familiar with that type of reasoning though.

[alancalverd]

Alas, spin is itself an analogy. Subatomic particles behave as if they are spinning tops, so protons neutrons and electrons have a magnetic moment aligned with the spin vector and the Pauli exclusion principle, that no two electrons can occupy the same quantum state, is obeyed if electrons have spin quantum numbers of  ±½.