Thursday, 1 August 2019

special relativity - How are the time dilation and the relativistic Doppler shift added together in what observers "see"?



I'm using the illustration from this question:


enter image description here


Suppose A and B are d light years away, and at rest. Then they symmetrically start to travel toward each other (symmetric acceleration process in negligible time) at a high speed v. How each one sees the other one's clock working?


"Always faster" and "always slower" are both logically impossible, since due to the symmetry, they must agree that same time has elapsed on both clocks when they meet. So it's either "always normal" or probably "faster for some time and slower for some time". What's the mathematical expression for the seeming rate of clocks?




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