06-07-2016, 04:36 AM

First, in the Lorentzian interpretation time dilation is a real effect, moving clocks are slower, moving rulers are shorter.

Why does the moving observer come to a different conclusion? He assumes he is at rest. Then, he uses a synchronization procedure which makes sense only if you are at rest. If you move, you get the synchronization wrong. This becomes important if you change your speed. And, again, behave as if you would think you are in rest, despite the change. Then, the new synchronization is wrong too, but wrong in a different way. So, at the moment when he changes the speed, what he "assumes" to happen "now" changes. The difference becomes bigger with distance. So, if you jump up and down here on Earth when Andromeda is up, the synchronization with Andromeda oscillates with the amplitude of years. Of course, if you ignore this change of synchronization, you get a completely wrong result.

And this wrong result is the consequence of his combining two descriptions which contradict each other: That he is at rest when he flies away, and that he is at rest when he returns. If he errs consistently, so that he assumes he is at rest initially, but moves with double speed when he returns, he will assume that his clock is faster initially, but a lot slower during his return flight, and get the correct result.

Why does the moving observer come to a different conclusion? He assumes he is at rest. Then, he uses a synchronization procedure which makes sense only if you are at rest. If you move, you get the synchronization wrong. This becomes important if you change your speed. And, again, behave as if you would think you are in rest, despite the change. Then, the new synchronization is wrong too, but wrong in a different way. So, at the moment when he changes the speed, what he "assumes" to happen "now" changes. The difference becomes bigger with distance. So, if you jump up and down here on Earth when Andromeda is up, the synchronization with Andromeda oscillates with the amplitude of years. Of course, if you ignore this change of synchronization, you get a completely wrong result.

And this wrong result is the consequence of his combining two descriptions which contradict each other: That he is at rest when he flies away, and that he is at rest when he returns. If he errs consistently, so that he assumes he is at rest initially, but moves with double speed when he returns, he will assume that his clock is faster initially, but a lot slower during his return flight, and get the correct result.