Time Dilation and the Spatial Interval for which dx/dt is Speed
Allen D. Allen
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 vA, B of B with respect to A for all ordered pairs A, B. It also requires that the interval 
x used to calculate dx/dt = vA, 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 x applies to dx/dt = vA, B = vB, A. Consequently, relativistic time dilation is asymmetrical, the clocks in the frame of x 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.
A, B of A with respect to B be the same as the speed vA, B of B with respect to A for all ordered pairs A, B. It also requires that the interval x used to calculate dx/dt = vA, 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 x applies to dx/dt = vA, B = vB, A. Consequently, relativistic time dilation is asymmetrical, the clocks in the frame of x 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.