The electron spin(or for that matter spin of any elementary particle) is taken as its fundamental property. According to classical mechanics there should be a torque to cause spin. what is the source of this torque?

The electron spin(or for that matter spin of any elementary particle) is taken as its fundamental property. According to classical mechanics there should be a torque to cause spin. what is the source of this torque?
The analog between classical spin (physical rotation) and the quantum mechanical spin of elementary particles is subtle. But I think I can answer your question purely classical:
Torque is the cause of angular acceleration (change in the velocity of the spin). The spin of an elementary particle is always the same (at least it's quantized, meaning no continues angular acceleration being applied to it). No angular acceleration requires no torque .
I hope it's a satisfying answer. Why/how these particles have spin at all (when the source isn't torque), is an other, tougher question
I think the basic answer is that just because we call it spin doesn't mean it's actually spinning.
The electron has an inherent frequency/wavelength. When electrons are emitted in the form of beta rays, the wavelength lies in the UV region. Utilize this frequency and the size of an electron and you can picture an electromagnetic resonant field wave moving at or near the speed of light. You may be able to find your own picture of electron spin. Simply saying that it is an energy phenomenon doesn't give much perspective.
Actually the called "spin" of the basic particles relates to the magnetic moment of them which can be measured experimentally in their interactions with magnetic fields.
The problem is that current theories (as classical physics does) assume the elementary particles being "pointlike" (with no dimensions) and so there's the problem on how a magnetic moment can be generated by a point since in theory a magnetic field can only be generated by an element of electrical current which implies in some dimension since current=charge x displacement.
In classical physics, the definition of current is the number of electrons passing a certain point per unit time. However, that does not rule out a definition of electric current that also include spatial terms. In fact, that is exactly what my studies have involved    and using classical theory. There are many electrons involved in most any electrical current, so including spatial terms for each one would be quite a task. However, get down to one or two electrons and you have a much easier solution.
what is the most exclusive application of electron spin? how can electron spin then be interpreted.
I don't know of the most exclusive application, and it's usually described as "intrinsic", but the Einsteinde Haas effect "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics." The electron has a magnetic dipole moment too, which again suggests rotation. Pay special attention to "The factor of two difference implies that the electron appears to be twice as effective in producing a magnetic moment as the corresponding classical charged body" which relates to spin ½. A moebius strip has something like a spin ½ characteristic, and there is another type of electromagnetic current: displacement current. It "is not an electric current of moving charges, but a timevarying electric field", just like you get in an electromagnetic wave. So you should interpret electron spin in terms of an optical vortex. Without worrying about dimensionality, work this out: 4π / c^{1½ }. There's a small binding energy adjustment, but even without it you should recognise the number. Don't forget that spherical harmonics apply in the hydrogen atom. We can diffract an electron. It has a wave nature. It is not a point particle.
because the electron move back and forth in time its spin is ordenery but again because it superposition in time , now have many option . thanks
torque is only needed to change spin
Here's another number to work out: c^{½ }/ 3π
A guy called Andrew Worsley told me about it, he's using spherical harmonics not for a hydrogen atom, but for the particles themselves. I think it needs a bit more work, but I really think he's on to something.
I simply couldn't not reply to this post. Martillo raises a very interesting and pretty important question, for two reasons. The first being is that my theory http://www.thescienceforum.com/newh...icmoment.html states that there can be what is called a ''semimetric'' and in mathematics that has an appearance of ... these allow what are called spinmicroframes, two degrees of freedom inside of the particle (within the boundaries of it's compton wavelength) which means a particle is not zero dimensional at all. It can be one 1dimension or 2dimensions but not three or zero. It does not make sense to speak of time, as that is not an observable quantity.
this has been taken from work written by me
'' The classical electron, is believed to be a sphere with a radius of (e²/Mc²). This is not a measured value. It's a careful analysis of the dimensions of the equation of the radius which says it depends on the electron charge (squared) e² the mass M and the speed of light (squared) c². The quantity in the denominator Mc² actually makes up the rest energy of a particle E_0. The rest energy will be explained in greater detail in the Chapter discussing relativity.
The Classical Electron Radius is in fact 1/137 times larger than the Compton Wavelength. The Compton Wavelength is (h/Mc) where h is Plancks Constant and it has a value of 6.62606957(29)×10^(−34) j.s. The Compton Wavelength itself has a value for the electron as 2.4263102175±33×10^(−12) m (the value varies with different particles) and is a measure itself of the wavelength of a particle being equal to a photon (a particle of light energy) whose energy is the same as the restmass energy of the particle. Complicated? Yes it can be.
Basically, all particles have a wavelength. Photon's can never be at rest (again reasons why will be given in the relativity chapter), but the energy of a photon can be low enough to have it's wavelength match any particle who is at rest. It's often seen in the eye's of many scientists as the ''size'' of a particle. Actually, a more accurate representation of the size of an object would be the Reduced Compton Wavelength (reasons given in the chapter references under [1] ). This is just when you divide the Compton Wavelength by 2π and it gives a smaller representation for the mass of a system.
Now, going back to the electron, the electron as a sphere was accepted by most physicists until the age of the revolutionary quantum field theory. A physicist by the name of Wolfgang Pauli actually predicted a very strange property of all subatomic matter. Using careful experiments, he was able to deduct that particles behaved as though they possessed a spin, just like a spinning top or even better to imagine, the spinning surface of a planet like the Earth.
Wolfgang didn't actually name it spin however, that was later coined by Ralph Kronig, George Uhlenbeck, and Samuel Goudsmit in 1925 and then a mathematical theory was developed by Pauli in 1927. The classical idea of spin came from Noether's (a mathematician) ''generator of rotations'' where it describes a real physical rotation of quantum objects.
This idea soon ran into problems however, because modern quantum field theory did not really believe an electron was classical at all, possessing a radius. In fact, as far as physicists can tell, any attempt at measuring a radius for an electron failed and all experimental data seemed to suggest that the electron was really a pointlike system  that is , a particle which does not have any dimensions which we can obtain from the classical radius. It was just a point and thus some problems began to arise from the mathematical theory.
A classical radial system can indeed rotate like a planet. In fact, an electron under this theory could make a 360 degree turn in space and as would be expected would return to it's original orientation. However, for a pointlike system to achieve a rotation and return to it's original orientation it would need to make twice as much as this angle (720 degrees). See, pointlike systems when in accord to rotations don't act like classical radial systems.
So it seemed there was a problem. Either particles do not physically rotate yet still possess an angular momentum with a classical radius, or that quantum particles don't physically rotate but still have a quantum spin and intrinsic property no less. It was decided that spin could not be a real physical spin [2]. Instead, the classical electron would fall into the archives of physical curiosity and the idea that spin was some inherent, instrinsic and fundamental property would live on. I believe this might have been a mistake. The fact that we haven't been able to observe the radius as of yet should not indicate an electron has no size. In fact, scientists have just recently attempted to measure the shape of an electron by measuring it's wobble in a magnetic field.''
This magnetic dipole moment suggestion was a good one at that.
I think in the end of the day, we opted for dimensionless objects because they are easier to work with. I am sure objects of sufficiently small sizes could seem like to us to appear as though they act like they have no dimensions, when really they are just to small to observe as of yet. Indirect evidence like what you suggest here should not be ignored.
Could you tell me what initiates there spin?
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