That elementary particles could "spin", in the sense of rotating, as you mention, and this faster than light is quite a bold assertion that no data supports.

The word "spin" has a very special meaning with regards to elementary particles. In QM it is one of the "quantum numbers". This one relates to "angular momentum", which may be what gives the impression that they rotate. Moreover, in QM, moving particles are not localized (non local wave packets) in a manner that makes rotating meaningless.

In electromagnetism, the concept of "spin" is related to the relative magnetic polarity of elementary particles, which allows electrons, for example to associate in parallel or anti-parallel spin alignment. The macroscopic fields of magnets for example, are due to numerous electrons in the material being forced aligned in parallel spin. Ref: CRC Handbook of Chemistry and Physics, section 12.

As for same charge particles to be attracted due to their magnetic fields, it is not excluded that co-valent bounding that allows atoms to associate in molecules could be due to such an anti-parallel alignment of the spins of both electrons involved. The same for pair filling of electronic orbitals in atoms.

As recently as 2014, it was experimentally demonstrated that the magnetic fields of 2 electrons belonging to two different atoms, that were kept captive in mutual parallel alignment interacted as a function of the inverse cube of the distance between them:

http://www.nature.com/articles/nature13403.epdf?referrer_access_token=yoC6RXrPyxwvQviChYrG0tRgN0jAjWel9jnR3ZoTv0PdPJ4geER1fKVR1YXH8GThqECstdb6e48mZm0qQo2OMX_XYURkzBSUZCrxM8VipvnG8FofxB39P4lc-1UIKEO1

This means that a very short distance, antiparallel spin alignment attraction will dominate over same charge Coulomb inverse square repulsion.

That elementary particles could "spin", in the sense of rotating, as you mention, and this faster than light is quite a bold assertion that no data supports.

The word "spin" has a very special meaning with regards to elementary particles. In QM it is one of the "quantum numbers". This one relates to "angular momentum", which may be what gives the impression that they rotate. Moreover, in QM, moving particles are not localized (non local wave packets) in a manner that makes rotating meaningless.

In electromagnetism, the concept of "spin" is related to the relative magnetic polarity of elementary particles, which allows electrons, for example to associate in parallel or anti-parallel spin alignment. The macroscopic fields of magnets for example, are due to numerous electrons in the material being forced aligned in parallel spin. Ref: CRC Handbook of Chemistry and Physics, section 12.

As for same charge particles to be attracted due to their magnetic fields, it is not excluded that co-valent bounding that allows atoms to associate in molecules could be due to such an anti-parallel alignment of the spins of both electrons involved. The same for pair filling of electronic orbitals in atoms.

As recently as 2014, it was experimentally demonstrated that the magnetic fields of 2 electrons belonging to two different atoms, that were kept captive in mutual parallel alignment interacted as a function of the inverse cube of the distance between them:

http://www.nature.com/articles/nature13403.epdf?referrer_access_token=yoC6RXrPyxwvQviChYrG0tRgN0jAjWel9jnR3ZoTv0PdPJ4geER1fKVR1YXH8GThqECstdb6e48mZm0qQo2OMX_XYURkzBSUZCrxM8VipvnG8FofxB39P4lc-1UIKEO1

This means that a very short distance, antiparallel spin alignment attraction will dominate over same charge Coulomb inverse square repulsion.

Quantum mechanical spin is something different than mechanical momentum.  Think instead about photons: they have a spin, yet they are non-magnetic and chargeless.  On the other hand they are carriers of both electric and magnetic field, aren't they?

The question can't be given any meaning, for fundamental particles, like quarks and leptons, since they are points, they don't spin in the classical sense of the word. So the opening statement is incorrect. Now one can ask whether a classical, charged sphere can rotate very fast and what would the electric and magnetic field look like. This is a standard exercise, cf., for instance, http://www.hep.princeton.edu/~mcdonald/examples/rotatingshell.pdf for the case of a shell and here, http://arxiv.org/pdf/1010.1917.pdf for a sphere.

Yet I venture to suggest that the quantum spin of fundamental particles is closer related to the mechanical angular momentum than you think and therefore it is closer related to the speed of light. This relationship is a bit more complicated than it sounds as well as the same surprisingly accurate relationship between rotation speed of black holes and speed of light. Roughly speaking, for fundamental particles probably it is the result of vibrations and beating of several frequencies.

 Yes, the classical view of the spinning "spin" is wrong.

 But it is an interesting question that if the magnetic interaction can be stronger than electric interaction in particle system.

 The electric potential is proportional to 1/r and magnetic dipole-dipole potential is proportional to 1/r^3. Therefore the magnetic interaction is supposed to become stronger at some small r.

 For ground state positronium case, its mean radius is R=1x10^(-10)m and the electric potential energy is -6.8eV.  On the other hand, the potential energy of its magnetic spin-spin interaction is +3.6x10^(-4) eV for singlet state. Therefore, at

 r

Dear Fumihiko, please note that the "electric" Coulomb force obeys the inverse square interaction rule (1/r^2), not the simple inverse rule (1/r).

If interested, unless I am mistaken, the distance at which the magnetic inverse cube interaction apparently starts to dominate as two elementary electromagnetic particles, electrons for example, are forced to close in on each other is illustrated in Figure 1 in section VII of this paper:

http://www.ijerd.com/paper/vol7-issue5/H0705050066.pdf

@Fumihiko Suekane:  1. comparing potential energies says nothing whether the interaction is attractive or repulsive.  Attraction or repulsion means force or, in other words, the (spatial) derivative of potential.  2. Even in classical picture the force between magnetic dipoles depends not only on their separation but also on their relative orientation, try it with two identical permanent magnets. Moreover: this force is not  necessarily directed along the line connecting them.  3. It is true that a positronium in its triplet state (parallel spins of its constituents, S=1) lives roughly one thousand times longer than para-positronium (S=0) but it nevertheless decays into 3 photons. Supposed magnetic force doesn't work efficiently enough, even at small distances, to prevent the anihilation.

Last but not least: the radius and diameter are not synonyms.

Dear Andre and Marek,

Thank you for pointing out some issues in my answer. The answer may have mixed up the usage of the words "potential energy" and "force", carelessly. I was intending to use potential energy throughout the discussion. Therefore, the r dependence of the Coulomb potential energy is 1/r.

1. Yes, the force is F=-dV/dr and generally the signs of F and V do not have direct correspondence. However, for electro-magnetic potential case, we define such a way that the positive potential monotonously decreases with respect to the distance r and reaches 0 at the infinite distance and the negative potential, vice versa. Therefore, the signs of F and V are the same. (For the strong interaction, this is not the case.)

2. If we think about the potential energy, the states are quantized into only two energy eigenstates, singlet and triplet. The positronium system is governed by the quantum mechanics rather than classical picture. Therefore, my understanding is that it is not necessary to think about arbitral relative orientation in this case.

3. I am not sure about this point. But the lifetime of the o-positronium and p-positronium can be calculated analytically using QED and if we study the calculation process in detail, we will be able to understand this. 

4. I am not sure this point, too. But it might be better to have used the "diameter" of the positronium rather than "radius", since the distance between the electron and positron correspond to the diameter. (This is not the case for the hydrogen atom.)

Dear Fumihiko,

I'm sure you are aware that potential (energy) is determined up to an arbitrary constant and only its differences are important, not only in electrostatics.  For example, we are used to speak about gravitational potential as having the shape 1/r but we compute it in relation to the ground we are standing on, no matter whether we are at the sea level or at 10th floor of high building.

Indeed, there is no clear relative orientation in quantum picture of two interacting spins s=1/2, except for "parallel" and "antiparallel" being the eigenstates of such a system in a free space.  But what about the case of higher spins?  Troublesome ...

 It is evident that the classical picture of the spin of a particle like that of a rotating body, is not helpful and even dangerous because missleading. Spin emerges from quantum relativistic considerations and quantities like the Dirac anamalous magnetic moment is a clear signature of how the classical intuition may fail in describing these quantities.

But even admitting that sitting on the frontier of a rotating electron one experiences a periferical velocity larger than c, at the same time the emerging inertial forces induce new effects which hardly fit into the simplified model you have in mind.

The best

G. Dattoli

Dear Giuseppe!

You said accurately: " It is evident that the classical picture of the spin of a particle like that of a rotating body, is not helpful ..."

Why does the Isospin-model of particles based on this classical picture?

Best Regards

Hans

The isospin has nothing to do with a rotating body, it realizes the invariance of the strong forces under charge reflections.

But such an invariance (some time referred as invariance by rotation in the isospin space) should be understood in abstract terms, not in a physical space.

Any two level quantum system can be described with a formalism similar to that of spin, but this does not imply that the dynamics of a two level system is rotation.

Furthermore physical space rotation are ruled by the SO(3) group spin transformation by SU(2), which are not the same thing.

Regards

Pino