Generalized Uhlenbeck-Goudsmit Hypothesis, ‘Magnetic ’ S a and ‘Electric ’ Z a Spins

In this paper the connection between the dipole moment tensor D and the spin four-tensor S is formulated in the form of the generalized UhlenbeckGoudsmit hypothesis, D = gSS . It is also found that the spin four-tensor S can be decomposed into two 4-vectors, the usual “space-space” intrinsic angular momentum S, which will be called ‘magnetic’ spin (mspin), and a new one, the “time-space” intrinsic angular momentum Z, which will be called ‘electric’ spin (espin). Both spins are equally well physical quantities. Taking into account the generalized Uhlenbeck-Goudsmit hypothesis, the decomposition of S and the decomposition of D into the dipole moments m and d we find that an electric dipole moment (EDM) of a fundamental particle, as a four-dimensional geometric quantity, is determined by Z and not, as generally accepted, by the spin S. Also it is proved that neither the T inversion nor the P inversion are good symmetries in the 4D spacetime. In this geometric approach only the world parity W , Wx = −x, is well-defined in the 4D spacetime. Different shortcomings in EDM experiments are discussed. One of the main shortcomings is that in all experiments the usual transformations of the 3D fields E and B (A. Einstein, Ann. Physik 17, 891 (1905)) are always considered as that they are relativistically correct Lorentz transformations (LT) of E and B. However, as proved in, e.g., T. Ivezić, Found. Phys. Lett. 18, 301 (2005), these transformations are not the LT and they drastically differ from the LT of the relativistically correct 4D electric and magnetic fields. This is an essential reason why the fact that no EDM has yet been found does not mean that there is no EDM of the size predicted in this paper. The other reasons are also discussed.