Generalized Uhlenbeck-Goudsmit hypothesis 'Magnetic' S^{a} and 'Electric' Z^{a} Spins

TL;DR

This paper introduces a generalized hypothesis linking dipole moments and spin tensors, decomposes spin into magnetic and electric components, and suggests that electric dipole moments are related to a new electric spin component, challenging traditional symmetry notions.

Contribution

It formulates a generalized Uhlenbeck-Goudsmit hypothesis, decomposes the spin tensor into new electric and magnetic spins, and redefines the origin of electric dipole moments in a 4D geometric framework.

Findings

Electric dipole moments are determined by the electric spin Z^{a}.

Neither T nor P symmetries are valid in 4D spacetime, only world parity W.

The approach impacts elementary particle theories and EDM search experiments.

Abstract

In this paper, the connection between the dipole moment tensor D^{ab} and the spin four-tensor S^{ab} is formulated in the form of the generalized Uhlenbeck-Goudsmit hypothesis, D^{ab}=g_{S}S^{ab}. It is also found that the spin four-tensor S^{ab} can be decomposed into two 4-vectors, the usual `space-space' intrinsic angular momentum S^{a}, which will be called `magnetic' spin (mspin), and a new one, the `time-space' intrinsic angular momentum Z^{a}, which will be called `electric' spin (espin). Both spins are equally good physical quantities. Taking into account the generalized Uhlenbeck-Goudsmit hypothesis, the decomposition of S^{ab} and the decomposition of D^{ab} into the dipole moments m^{a} and d^{a}, we find that an electric dipole moment (EDM) of a fundamental particle, as a four-dimensional (4D) geometric quantity, is determined by Z^{a} and not, as generally accepted, by the spin $\mathbf{S}$ as a 3-vector. Also it is shown 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^{a}=-x^{a}, is well defined in the 4D spacetime. Some consequences for elementary particle theories and experiments that search for EDM are briefly discussed.