COMPARISONS, CONTRASTS, AND CONFUSIONS
A comparison of the SRT transformation (Lorentz transformation) and the MLET transformation (Selleri transformation) is shown in Figure 1. (The equations for both transformations are given in detail below.) The magic of SRT is also illustrated by the fact that the length contraction and clock slowing are symmetrical. Each frame sees clocks in the other inertial frame running slow and sees lengths contracted. The Selleri Transformation, which is used in the MLET, is reciprocal rather than symmetrical. The observer in the moving frame would see the clocks in the absolute frame run faster and would see lengths expanded. The apparent Lorentz transformation is obtained when the appropriate clock bias is added to the Selleri transformation. It is interesting to note that most standard methods of synchronization of clocks automatically supplies the exact clock bias needed to convert the Selleri transformation into a Lorentz transformation.
Though the practical effect of either SRT or MLET involves the Lorentz transformation when one wants to move from one inertial frame to another, the question of when to apply the Lorentz transformation has a dramatically different answer in the two alternate theories. In the MLET there is never any requirement that the Lorentz transformation be employed. One can pick any inertial frame one wants, assume that that frame is the absolute frame, and work exclusively in that frame. The apparent Lorentz transformation from the absolute frame to the chosen inertial frame leaves the apparent speed of light isotropic. Thus, in the chosen inertial frame the speed of light is assumed to be isotropic, clocks are assumed to run slow with speed in that frame, and lengths of moving objects are assumed to contract in the direction of their motion. Most important, an observer or sensor moving in that chosen frame will not see an isotropic light speed (i.e. there is no need for a further transformation to cause the observer or sensor to be stationary in his own frame).
However, in SRT, it is clearly taught as part of the theory that the observer’s (or sensor’s) inertial frame is the correct frame to employ. Thus, in theory, all sources and clocks must be mapped via the Lorentz transformation into the observer’s frame at all times. This is most clearly seen in the theoretical development of the Thomas precession.