User:Ems57fcva/sandbox/time dilation

All observers can use this technique to set up their own temproal coordinate system. Note that in relativity for these temporal coordinate systems will not match up (unless the observers are at rest). For example, look at the case of a series of timing signals being sent out by on observer who is moving with respect to the original observer as seen by the original observer. The original observer will see a light signal emitted at time t3 arrive at time t4 and return to the moving observer at time t5. However, since the second observer was moving, the interval t4 - t3 will not be the same as the interval t5 - t4 for this original observer. However, the second observer will be assigning his own temporal coordinates to these events (T3, T4, and T5), and for him (since the speed of light is also c for him under the second postulate of special relativity) T4 - T3 = T5 - T4.

If the moving observer emitted a signal at T4, he would consider the emission of this signal to be simultaneous with the original observer's clock reading t4. However, since the original observer would see that event as being at (t3 + t5)/2, and of the above mentioend difference in the out-and-back times for the signals of the moving observer with respect to the original observer, the original obserer would not perceive this emission of this additional signal to be simultaneous with t4. This effect is called the relativity of simultaneity.