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Time Dilation and the Spatial Interval for which dx/dt is Speed

Allen D. Allen
Year: 1988
Keywords: principle of relativity, special relativity, time dilation, Lorentz contraction, twin paradox
The principle of relativity requires that the speed v<A, B> of A with respect to B be the same as the speed v<A, B> of B with respect to A for all ordered pairs <A, B>. It also requires that the interval Deltax used to calculate dx/dt = v<A, B> be defined for a particular experiment by resting endpoints. The rest frame of the endpoints is preferred for the experiment in that only the Lorentz contraction of Deltax applies to dx/dt = v<A, B> = v<B, A>. Consequently, relativistic time dilation is asymmetrical, the clocks in the frame of Deltax running faster than the clocks in a moving frame for all observers. This is analogous to the way in which the zero-momentum frame must be used to predict the outcome of dynamic particle experiments. In general, the principle of relativity does not say that for a given experiment E there is no preferred frame R(E). Rather, it states that there is no one preferred frame R for all E; that is, no absolute frame.