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The standard expression for the Wigner rotation leads to incorrect result forthe wavefront rotation. The results for the Wigner rotation in the Lorentz labframe obtained by many experts on special relativity such as Moeller andJackson, are incorrect. They overestimate the angle of the Wigner rotation by afactor $\gamma$ compared to its real value, and the direction of the rotationis also determined incorrectly. In 1959, Bargman, Michel, and Telegdi (BMT)proposed a consistent relativistic theory for the dynamics of the spin asobserved in the lab frame, which was successfully tested in experiments. TheBMT equation naturally involves the Wigner rotation as the purely kinematicaddition to the Larmor rotation which, in turn, is a consequence of interactionof the intrinsic magnetic moment with the external magnetic field. It iscommonly believed that the BMT equation contains the standard (and incorrect)result for the Wigner rotation in the Lorentz lab frame. The existing textbooksthen suggest that the experimental test of the BMT equation is a direct proofof validity for the standard expression for Wigner rotation. Here we focus onthe analysis of the reason why authors of textbooks obtained an incorrectexpression for the Wigner rotation. We demonstrate that the notion that thestandard (incorrect) result for the Wigner rotation as an integral part of theBMT equation in most texts is based, in turn, on an incorrect physicalargument. The aim of the present paper is to analyze the complicated situationrelating to the use of the theory of relativity and, in particular, Wignerrotation theory, in accelerator physics.

Wigner Rotation: Theory and Application to Practical Relativistic Engineering Problems