A note on Lorentz transformations and simultaneity in classical physics and special relativity

Since early models of wave propagation in both stationary and moving media during the nineteenth century, the Lorentz transformation (LT) has played a key role in describing characteristic wave phenomena, e.g., the Doppler shift effect. In these models LT connects two different events generated by wave propagations, as observed in two reference systems and the synchronism is absolute. In relativistic physics LT implements the relativity principle. As a consequence, it connects two space-time event coordinates that both correspond to the same physical event and “absolute synchronization” is not allowed. The relativistic interpretation started from Einstein’s early criticism of the notion of “simultaneity” and Minkowski’s invariance of the space-time interval. In this paper, the two different roles of LT, i.e., in classical wave propagation theories and in relativistic physics, are discussed. Einstein’s early criticism is also re-examined with respect to LT in view of its significance for the notion of simultaneity. Indeed, that early criticism is found to be defective. Our analysis is also useful for general readers in view of its impact on modern speculations about the existence of a preferred system of reference Σ, where light propagation is isotropic, and related implications.