Translational Inertial Spin Effect

Abstract

The following results are shown: (a) Contrary to widespread belief, two energy-momentum tensors $T^{\mathrm{ij}}$ and ${\Theta }^{\mathrm{ij}}$ with a divergenceless difference are not necessarily physically equivalent; in fact, they will not be equivalent if the flux $\int (T^{i\alpha }-{\Theta }^{i\alpha })d{s}_{\alpha }\mathrm{dt}$ through the external surface of some test body between an initial and a final state is nonzero. (b) It follows necessarily from basic postulates of the Dirac one-electron theory that Tetrode's asymmetrical energy-momentum tensor is physically the good one, and that, in the circumstances mentioned above, use of the symmetrized ${\Theta }^{\mathrm{ij}}=\frac{(T^{\mathrm{ij}}+T^{\mathrm{ji}})}{2}$ tensor would yield a wrong result for the variation of the energy-momentum between states 1 and 2. (c) This being so, a macroscopic experiment based on ferromagnetism or ferrimagnetism can be devised, which demonstrates these facts as a measurable "translational inertial spin effect." (d) It is highly plausible that the above predictions, based on the one-particle electron theory, would be valid in the framework of the many-particle electron theory obeying Fermi statistics (the argument is based on the so-called bound-interaction hyperquantized formalism). The last point can be verified experimentally.