Quotation from the paper:
What is spin?
[Ohanian H.C. – Amer. J. Phys., June 1986, v. 54, № 6, p.500]:
(According to N. Bohr) “After the short period of confusion, caused by the temporary limitation of clarity, there was common the agreement about the replacement of concrete means reached by abstract mathematical symbols. Especially this concerns the picture of rotation, which was substituted with the mathematical characteristics of the representations of a group of rotations in the three-dimensional space”. (In: Theoretical physics in the twentieth century. / ed. M. Fierz, V.F. Weisskopf. - New York: Interscience, 1960, p. 216.]).
Thus, physicists gradually began to consider a spin as the deep quantum property of electron, which has inaccessible physical explanation.
According to the predominant opinion, spin of electron or any other particle is certain mysterious internal torque of the momentum, for which it is not possible to construct the real physical picture and does not exist classical analog. Nevertheless on the basis of calculation, executed by Belinfante in 1939 [Belinfante F.J- Physica, 1939, v.6, p.887], it is possible to show that spin can be considered as the angular momentum, generated by the circulating of the energy flow in the field of electron wave. In exactly the same manner [Gordon W. - Z. Phys., 1928, v.50, p.630] the magnetic moment of electron can be considered as that created by the circulating flow of charge in the field of its wave. This approach gives intuitively attractive picture it denies “internal” nature of spin and magnetic moment, connecting them not with the internal structure of electron, but with the structure of the field of its wave. Furthermore, if we compare the calculations of the angular momentum in the Dirac and electromagnetic fields, then it becomes obvious that electron spin is completely analogous to the angular momentum of the classical circularly polarized wave.
As basic element in the Belinfante calculation is the use of the symmetrized tensor of energy-momentum. From the field theory it is well known that it is possible to construct several tensors of energy - momentum, each of which satisfies the conservation law \ partial _ \ nu T^ {\ mu \ nu} =0, and also gives the same resulting energy \ left ({\ int {T^ {00} d^3x}} \ right) and momentum \ left ({\ int {T^ {k0} d^3x}} \ right) as the canonical tensor of energy-momentum. All these tensors are distinguished by the terms of form \ partial _ \ alpha U^ {\ mu \ nu \ alpha}, which are antisymmetric on the last two indices \ left ({U^ {\ mu \ nu \ alpha} =-U^ {\ mu \ of alpha \ nu}} \ right), therefore the conservation law \ partial _ \ nu \ partial _ \ alpha U^ {\ mu \ nu \ alpha} of =0 is identically carried out. Belinfante showed that with the aid of the suitable selection of term \ partial _ \ alpha U^ {\ mu \ nu \ alpha} always it is possible to construct the symmetrized tensor of energy-momentum \ left ({T^ {\ mu \ nu} =T^ {\ nu \ mu}} \ right). Its advantage is the fact that the angular momentum, calculated directly from the momentum density of T^ {k0}, remains.
It could be that it turned out, it would make sense to think electron as two massless points rotating around each others with the speed of light. At least to the extent that if you are merely interested about the relationship of the mass, size and angular momentum.
