Ibix
Science Advisor
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Just to illustrate @Dale's point, consider a kind of repeated twin paradox. We have triplets, one who stays at home (purple), one who travels at 0.6c (red) and one who travels at 0.8c (blue). At time zero the travellers set off and return simultaneously at some later time, shake hands, turn around and repeat their trips. Below is a regular Minkowski diagram (left) and an Epstein diagram (right)
Note how you can't see from the right hand diagram that the travellers meet at home. And if you want to do something like add radar pulses to illustrate the Doppler analysis of the twin paradox, you can't do it. Light like lines satisfy ##x=t+\mathrm{const}## so ought to be drawn horizontally, but then how do you draw a radar pulse reflecting off something and returning? That's what I meant about not really being able to do actual physics in this scheme.
Note how you can't see from the right hand diagram that the travellers meet at home. And if you want to do something like add radar pulses to illustrate the Doppler analysis of the twin paradox, you can't do it. Light like lines satisfy ##x=t+\mathrm{const}## so ought to be drawn horizontally, but then how do you draw a radar pulse reflecting off something and returning? That's what I meant about not really being able to do actual physics in this scheme.