By Knebelman M. S.
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Extra info for Groups of Collineations in a Space of Paths
This paradox is completely foreign to the fundamental aether theory, where the energy is perfectly defined and depends on the speed of the body with respect to the aether frame. ) When the signal reaches point A, it is reflected in a mirror firmly attached to frame S1 at a point A′ in the frame which at this instant coincides with A. After reflection, the signal comes back to O′. 32 Joseph Lévy 1 - Real co-ordinates The ratio of the distances covered by the signal from O′ to A′ and from O′′ to A is equal to the ratio of the speeds of the signal with respect to S1 and to S2.
1) 2 / C2 O ' A ' = X 1r = A 0 1 − v02 Notice that, as we have seen in Chapter 3, real speeds are simply additive. On the contrary, as we will now see, only the apparent speeds obey a law of composition of velocities different from the Galilean law. Since the distance O′A′ is measured with a contracted meter stick in frame S1, the apparent distance X1app found by observer S1 will be: X 1app = 2 A 0 1 − v02 / C 2 V − v01 . 2) Now, in order to determine the time needed by the body to reach point A′, we must first synchronize two clocks placed at O′ and A′.
The answers to questions 2 and 3 will be given in detail in Chapter 6. In light of this new data, the Lorentz assumptions appear far better founded today than in the past. Nevertheless, as will be seen later, this statement applies to the Lorentz assumptions, but not the Lorentz-Poincaré transformations. 1-3 Here we propose to derive a set of space-time transformations that are valid in all inertial frames. This approach is parallel to, but different from Selleri’s work,28 since, here, we are dealing with the experimental transformations obtained from the usual Einstein-Poincaré method of synchronization, or from the slow clock transport method, which is almost equivalent, but not with the absolute synchronization procedure which would be difficult to apply experimentally.