In a recent paper [Lett. Nuovo Cim. 41, 551-558 (1984)] the author presented his ''rotational relativity theory'', which is based on the constancy of the spin of the photon (in an analogous way as the special theory of relativity is based on the constancy of the speed of light). The underlying mathematical structure of this theory is the manifold \({\mathbb{R}}\times S^ 3\) equipped with the metric \(d\tau^ 2=dt^ 2- \gamma^{-2}(d\theta_ 1^ 2+d\theta_ 2^ 2+d\theta^ 2_ 3).\) Here the constant \(\gamma\) ''is not a universal constant but is characteristic to every particle in nature and is the maximum angular velocity the particle can have'' (quoted from the text); the one-forms \(d\theta_ i\) are not exact (!) and may be expressed using Euler angles \(\phi\), \(\vartheta\), \(\psi\) on \(S^ 3\cong SU(2)\) by \[ d\theta_ 1=\sin \vartheta \quad \sin \psi d\phi +\cos \psi d\vartheta,\quad d\theta_ 2=\sin \vartheta \quad \cos \psi d\phi -\sin \psi d\vartheta,\quad d\theta_ 3=\cos \vartheta d\phi +d\psi. \] The paper discusses the transformations, which leave the above mentioned metric invariant, and deals with some predictions of the new theory to experiments. The reviewer has to confess that the physical content of the theory remains somewhat mysterious to him.