First to the question: Maxwell equations do consider spin, or more appropriately helicity (= +/- 1). It is built into them -- both at the classical level, as well as the quantum. This is easy to see from the transformation properties of  E  (+/-) i B

Second to Stam's remark: I disagree. Spin arises if we look at the spacetime symmetries (at classical as well as quantum level). It is associated with the second Casimir invariant of the Poincare' algebra, while mass is connected with the first Casimir invariant. Historically, because for physicists spin entered via Pauli's theoretical suggestion in a quantum mechanical context one gets the impression that spin is necessarily of a quantum origin. In Physics, mostly through textbooks, there is a widespread misconception that spin is of quantum origin. Agree?

Yes, it's called quantum electrodynamics-when sources are included, that, also, are subject to quantum fluctuations. This is all known for something like seventy years now and is the subject of standard courses in physics. In the absence of sources it's a free field, subject to the constraints of gauge invariance and its quantization is, also, a textbook subject.

Yes, people have done it much before and they have also stolen the opportunity to name those generalized Maxwell's equations by their name. Dirac theory for spin-1/2 fields or particles, rather when an electromagnetic field is coupled to a spin-1/2 particle it's better known as the Pauli equations and when coupled to a field it's known as QED.  Similarly, Proca theory for spin-1 fields, Rarita-Schwinger for spin-3/2 fields and many more. All you have to do is to take those Lagrangians and replace the derivatives with co-variant derivatives, which are minimally coupled to the external gauge field and then play with that.

@Stam and Bikash: thank you for your answers. Yes we all know about Dirac and QED treatment to spin. But perhaps it would be interesting to ask whether it is possible to consider spin in terms of Maxwell equations. Furthermore, as we know electromagnetic interpretation of wavefunction is forbidden to discuss, and it also seems the same situation for electromagnetic description of spin.

And one more thing, in that cited paper Maknickas discusses the speed of quantum interaction, which until now it is considered as spooky action at a distance. What do you think? Thanks. Best wishes

Maxwell's equations are classical equations, spin isn't a classical quantity. So it doesn't make sense to consider them together in this way. The correct way has been known for decades, so it's more useful to study it and use it to solve problems, than trying to answer questions that are known to be meainingless.

Quantum entanglement is described in non-relativistic quantum mechanics, where there isn't any notion of locality in the sense of relativity. So the speed of transmission isn't defined. Another statement that can't be assigned meaining.

First to the question: Maxwell equations do consider spin, or more appropriately helicity (= +/- 1). It is built into them -- both at the classical level, as well as the quantum. This is easy to see from the transformation properties of  E  (+/-) i B

Second to Stam's remark: I disagree. Spin arises if we look at the spacetime symmetries (at classical as well as quantum level). It is associated with the second Casimir invariant of the Poincare' algebra, while mass is connected with the first Casimir invariant. Historically, because for physicists spin entered via Pauli's theoretical suggestion in a quantum mechanical context one gets the impression that spin is necessarily of a quantum origin. In Physics, mostly through textbooks, there is a widespread misconception that spin is of quantum origin. Agree?

The helicity states of the elctromagnetic field are classical notions, of course. However, the photon is not-it's a  quantum object. It obeys Bose-Einstein statistics, not Boltzmann statistics.And the relation between its spin and its statistics doesn't exist in classical physics, not even in non-relativistic quantume mechanics.

So while Maxwell's equations indeed don't need to be generalized, in order to describe the helicity states of the elctromagnetic field-they, already, do so-they do not describe individual photons and their spin, but macroscopic numbers of them, in coherent superpositions, that are identified as  electromagnetic waves. Individual photons are described by quantum electrodynamics.

Maxwell equations describe also collective phenomena of integer spin entities.. photons in the EM waves...

EM field is different, for the "virtual photons" which are responsible in QED of the fields of the charges it is difficult to define a spin..

@Stam, Dharam, Berna, Stefano: thanks for your answers. Yes, i can understand Stam's reasoning. But i tend to agree with Dr. Ahluwalia that there could be classical description of spin. Some people describe spin tensor, but i am not so familiar with. Another reasoning is that there exists formal correspondence between quaternion Dirac equation and Maxwell equations in quaternion space, see for example our paper as provided in the link below. Thanks

Article A Derivation of Maxwell Equations in Quaternion Space

The description of Maxwell's equations in terms of spinors can be found, for example,  in Bogoliubov and Shirkov's book on quantum field theory. It is an exercise in group theory, i.e. mathematics,  to write the equations of motion of a spin 1 particle in terms of  two spin 1/2 particles. However, one shouldn't confuse mathematics with physics. The two are distinct. Calling something ``classical'' or ``quantum'' doesn't mean anything, unless the terms are defined beforehand.

Spin of particles, so far is considered as intrinsic quantum number and has no classical analog (such as spinning of charge). 2x2 Paulie matrices and 4x4 Dirac spinners for electron include spin of electron. The relation of spin with Electromagnetism is not straightforward. This relation emerges in the form of us = magnetic moment of electron. This, not only is related to spin quantum no. (+-1/2) but to charge -mass ratio and g (=2) factor. us interacts with divergence of magnetic field B, rather than B itself (see Stern- Gerlach experiment). Further the magnetic moments of Proton and Neutron (being composite particles made up of quarks) have about 1000 time less than that of electron magnetic moment and with different g factors. To sum up spin, is not an isolated property but is part of wave function (roughly, when spin flips whole wave function flips) i.e. spin is embedded in complex way in wave function.

For more than 100 years, efforts are being made to understand some classical Electromagnetic (EM) mechanism of spin (and charge etc.) generation of electron. Apart from quantized nature of interactions, there are other bottlenecks which hinder us to apply classical Maxwell,s theory to explain intrinsic EM properties of particles. Quantum electrodynamics (QED) Mathematically, abelian gauge theory caters for EM interactions between particles in terms of photon exchange. However it does not explicitly include EM particle models to its theoretical framework. There are so many similar papers on the subject  you mentioned. More profound are articles on Maxwell’s-Dirac equations and their equivalence.

For classical electron EM model pl. read my article “ de Broglie wave and electromagnetic travelling wave model of electron and other charged particles” Physics Essays 01/2014; 27(1). DOI: 10.4006/0836-1398-27.1.146

Since Dirac spinors responsible for the spins can be expressed in terms of Quaternions and Maxwell gave its fist version of the equations in Quaternions it is maybe possible to express the integer and half spin particle behaviour in a unified way maybe with bi-Quaternions or Octonions...

I think gravity too is strongly influenced by angular momenta (spin)...

@Stefano, Mohammad and Stam and others: thank you for all your answers. Yes, Stam perhaps is right that all of these are just mathematical exercise. But in my humble opinion there is hidden quantum-classical corespondence, which still needs to be clarified. As pointed out by N. P. Landsman:

"The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has

to clarify it. " (see http://arxiv.org/pdf/quant-ph/0506082.pdf)

Another thing to consider is relation between classical and quantum electrodynamics. (See Mario Valente at http://arxiv.org/abs/1201.5536). It seems to me that this problem is not only a matter of mathematical curiosity. Best wishes

http://arxiv.org/pdf/quant-ph/0506082.pdf

@Christina: thank you for your paper. Best wishes

@Victor, "The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has".

By adding this you have expanded the scope of question to a vast extent. It is much more elaborate than including spin in Maxwell's Eqns.

Among all the theories, I consider Maxwell theory + Special theory of relativity SR ( an outcome of covariance of Maxwell's equations) the most profound theory. The QM and SR theories were founded simultaneously in end of 19th and beginning of 20th century. Both the theories were counter commonsense; however were accepted only because of their unprecedented success in verifying and producing the physical results. In SR the invariance/covariance of physical laws is an in depth phenomenon of nature equally applicable to classical and QM laws. i.e. only by applying invariance we can generate new physics (without knowing any underlying physical mechanism) The Schrodinger Eq. was invariant, noted by Dirac; who wrote relativistically invariant eq. which is foundation stone of QM. I must mention, if you look at basic derivation of Schrödinger and Dirac eqs., both of them used classical Hamiltonian ( Schrödinger used non relativistic and Dirac used relativistic.)

There are so many things I can mention about “interpretation” of QM. But one very basic is wave function psy itself. Lot of efforts were put in by many renowned scientists for interpreting psy,(some physical picture or wave shape in real space) but all in vain. What we know to date is that its “mod squared of psy” gives the probability density of quantum state. It is very use full though but the actual wave shape of psy is random (we don’t know made of what) knowledge of which is restricted by Heisenberg uncertainty principle i.e. we cannot probe the particles and processes below uncertainty limit.

My point of view is we must probe deeper into physical processes and interactions and understand these to very basic level (it is not 1914, it is 2014). I have already given link of my paper in one of above posts. It is here again.

http://physicsessays.org/browse-journal-2/product/153-18-malik-mohammad-asif-de-broglie-wave-and-electromagnetic-travelling-wave-model-of-electron-and-other-charged-particles.html

@Arno and Mohammad: thank you for your answers. Best wishes

@Victor and others: we are not converging to conclusion regarding gist of question "inclusion of (quantum) spin to Maxwell theory".  My vote is yes. I always welcome serious counter arguments.  

Mohammad,

Do we all converge on the following remark, please let me know.

Maxwell equations describe electromagnetic field. WE all agree on that. As to spin: Viewed in a quantum field theoretic context they carry spin 1. Agree? Viewed purely at the classical level, they follow as the massless limit of the (1,0)+(0,1) representation of the Lorentz symmetries. Again, spin 1.

To be precise, for massless particles it is better to talk of helicity rather than spin.

However, see my remarks in

http://arxiv.org/abs/hep-th/9509116

Paradoxical kinematic acausality in Weinberg's equations for massless particles of arbitrary spin (with D. J. Ernst), Mod.Phys.Lett. A7 (1992) 1967-1974