Relativistic spin operator must be intrinsic

Highlights: • We derive the properties that a relativistic intrinsic concept must obey. • We show that three-vector spin definitions fail to be intrinsic. • Intrinsicality is used as a condition to obtain a unique relativistic spin operator. • A consistent intrinsic model for the electromagnetic-spin interaction is presented. Although there are many proposals of relativistic spin observables, there is no agreement about the adequate definition of this quantity. This problem arises from the lack of consensus concerning the properties that such an operator should satisfy. Here we present how to overcome this problem by imposing an unquestionable condition about the nature of the relativistic spin observable: it must be intrinsic. The intrinsicality concept is analyzed in the relativistic classical limit and then it is extended to the quantum regime to approach the relativistic spin problem. This approach rules out three-vector proposals of relativistic spin observables and leads to a unique satisfactory definition that, besides being intrinsic, also possesses interesting physical features such as covariance and consistency of predictions in the non-relativistic limit. To support the results from an operational perspective, a consistent observer-independent model for the electromagnetic-spin interaction is also presented.