Simultaneity, Time Dilation and The Lorentz Transformation

The underlying basis for the predictions of non-simultaneity and time dilation in relativity theory is discussed. It is pointed out that Einstein based his conclusions entirely on the Lorentz transformation (LT). He claimed that once one assumes the constancy of the speed of light for all observers (at the same gravitational potential), there is no choice but to replace the Galilean transformation (GT) of classical physics by the LT. Lorentz pointed out as early as 1899, however, that the equations of the LT can only be specified to within a common factor ε based on this information alone. While Einstein mentioned this degree of freedom in his 1905 paper, he presented an argument that he felt settled the issue in favour of the LT (ε=1). The latter choice has the theoretical advantage of guaranteeing Lorentz invariance for the relativistic space-time transformation, but it also rules out the principle of simultaneity of events for observers in relative motion, a position that was revolutionary at the time he presented it. Another consequence of the LT is that it implies that the ancient principle of the objectivity of measurement no longer applies when two observers are in relative motion. For example, it becomes necessary to assume that each observer find that the other's clock is running slower than his own.