Note 83 — Chapter XXIV · THE POSTULATE OF EQUIVALENCE

Here the reader may well question our right to argue as though velocities combined in the classical way, when the whole significance of the special relativity theory has been to deny the validity of the classical transformations. In point of fact the objection would be legitimate; and in all rigour the Einstein-Lorentz transformations should be applied for each successive instantaneous velocity of the enclosure. But it so happens that when the Einstein-Lorentz transformations are applied to a transverse beam of light, it is found that for low velocities of the enclosure the bending is practically the same as it would have turned out to be had we followed the classical rule of composition. In other words, had the motion of the enclosure been uniform, the transverse ray of light as measured in the enclosure would have been inclined much as in classical science. Indeed, were it not that the relativity transformations entailed a variation in the slant of a ray of light moving transversally, the theory would be incompatible with the well-known phenomenon of astronomical aberration.