Dissecting’s Einstein’s Lightning Strike Example: Proof That His Light-speed Constancy Postulate Is Untenable
The example of two lightning strikes on a train given by Einstein is reviewed. He used his lightspeed postulate (LSP) to prove that events which occur simultaneously for one observer will not be so for another who is moving relative to him. It is shown that the LSP fails to correctly predict the speed of light emitted from a source which passes the observer at the same time that the light is emitted. The correct value is obtained when the Galilean Velocity transformation (GVT) is used, however, as shown by adding the distances traversed at any later time T by the light relative to its source and the source relative to the observer (cT + vT). When the GVT is applied instead in the train example, it is found that the lightning strikes do occur simultaneously for both the observer on the train and his counterpart at rest on the platform. Moreover, it is shown that the prediction of remote non-simultaneity (RNS) by the Lorentz transformation (LT) is not consistent with the Law of Causality. The latter requires that the rate of an inertial clock must remain constant for an indefinite period of time, thereby indicating that the ratio Q of the rates of any two such clocks (such as those used in the LT and the train example) must have a constant value. As a consequence, the following proportionality must exist for the elapsed times for a given event measured by the two clocks Δt’=Δt/Q. This relation, which is referred to as Newtonian Simultaneity, clearly eliminates any occurrence of RNS since Δt’ and Δt must either both have
null values or both non-null values on this basis. A replacement (Newton-Voigt transformation or NVT) for the LT is obtained by incorporating Newtonian Simultaneity with Einstein’s two postulates of relativity.