vuquta Posted March 23, 2010 Posted March 23, 2010 Assume O and O' are clocks are in relative motion in the standard configuration. Assume the stationary frame is O. According to SR, when the clock O elapses t, the clock in O' elapses t/γ, thus, when the clock in O elapses tγ, the clock in O elapses t. That is simple time dilation. By the measure at c logic of SR, if light is emitted when O and O' are co-located, light proceeds spherically from the origin of each. This website shows this. http://casa.colorado.edu/~ajsh/sr/paradox.html Now, considering O', when its clock elapses r/c, light proceeds a distance r in all directions. This is the SR measure at c logic. OK, now for the experiment, when the clocks O and O' are co-located, light is emitted at the co-location point by O'. Only the positive x-axis will be considered. Let r be a chosen distance. 1) Allow the time γr/c to elapse in O. 2) By SR, light proceeds a distance γr in O. 3) Since γr/c elapses in O, then r/c elapses on the clock of O'. 4) By SR logic, when r/c elapses in O', light proceeds r in all directions. Hence, the light is a distance r from O' along the positive x-axis. 5) When γr/c elapses in O, O' is located at a position vt or v(γr/c) in the coordinates of O. 6) But, since r/c elapsed in O', then light is a distance r from O'. Therefore, in O light is a distance vt + r/γ from O or v(γr/c) + r/γ = γr( v/c + 1/γ²) Hence, gathering all the SR logic, when the clock of O elapses γr/c, light is located at γr( v/c + 1/γ²) and γr which is a contradiction.
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