Spin as internal angular momentum

[Idoubt]

We say that spin is an intrinsic angular momentum which does not have anything to do with space. But is it possible that it is the orbital angular momentum of some internal constituent particles (a yet unknown fine structure)?

 

[Simon Bridge]

The spin is deduced from magnetic moment - so the "internal constituent particles" would also need to make up a distributed charge ... we know the charge on, say, and electron, as well as the spin - so we can work out how the charge must be distributed. The calculation shows that the possible internal particles are not so internal.

Anyway - we know about the finer structure of many particles with spin: like hadrons.

 

[Idoubt]

The calculation shows that the possible internal particles are not so internal.

Could you elaborate a little? Are you saying that the observed experimental data rules out a further fine structure for elementary particles in the standard model? I know that the existence of quarks were confirmed from high energy scattering from nucleons. My question is with the current experimental evidence how strongly will we say that a further fine structure is not possible.

 

[Bill_K]

We say that spin is an intrinsic angular momentum which does not have anything to do with space. But is it possible that it is the orbital angular momentum of some internal constituent particles (a yet unknown fine structure)?

Orbital angular momentum cannot be half-integer. If the electron were made of "smaller" particles, at least one of those particles would have to have half-integer spin.

Are you saying that the observed experimental data rules out a further fine structure for elementary particles in the standard model? I know that the existence of quarks were confirmed from high energy scattering from nucleons. My question is with the current experimental evidence how strongly will we say that a further fine structure is not possible.

To probe shorter distances you need higher energy. The highest energy we've explored in detail is ~ 10 TeV by the LHC, and there's no indication that the particles we currently believe are elementary might instead be composite. The electron is still pointlike, it shows no substructure down to a distance of at least 10^-17 cm.

 

[Simon Bridge]

Could you elaborate a little? Are you saying that the observed experimental data rules out a further fine structure for elementary particles in the standard model?

No - I am being much more specific than that: I am saying that the evidence is not consistent with the intrinsic magnetic moment being produced by internal components having some kind of rotation. The evidence so far pretty much rules out turning internal components as the source of the spin. Fundamental particles are just not big enough.

The calculation is http://physicspages.com/2013/04/11/magnetic-dipole-moment-of-spinning-spherical-shell/ - you could give it a go.

Anyway. We would expect that any further fine structure discovered for, say, an electron, would also show intrinsic angular momentum of the kind you are asking about in post #1. The concept of "intrinsic angular momentum" is very well established and so would take quite a lot to unseat it.

I know that the existence of quarks were confirmed from high energy scattering from nucleons. My question is with the current experimental evidence how strongly will we say that a further fine structure is not possible.

This is quite a different question from the one you started out asking - I will echo Bill_K on this one. Any sub-structure is certainly on scales less than 10^-17cm.

iirc: Hans Dehmelt got a Nobel Prize for getting this figure as the upper limit for the radius of an electron.
Other experiments in 1988 (same guy) suggests R_e<10^-20cm

If you represented an electron as a smallish pencil dot (0.2mm) - the atom it is part of, drawn to scale, would be a bit under a light-second across (2x10⁸m). I'm a bit tired so you may want to check that calculation.

It may help to think of fundamental particles as "carrying" angular momentum without classically rotating much as light carries regular momentum without having any mass. These are names we use for structures we find in the maths, names chosen for their physical effects.