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I'm trying to learn relativity theory on my own (special to begin with) and there's one basic misconception in my efforts.

Consider the usual setup for twins paradox, but let for now forget the accelaration part. I only want to separate the directions of movement. When the twins are moving apart from each other we know that the time for the travelling twin flows more slowly than for the stationary one. Then again it flows more slowly for stationary one also, when as far as the travelling one view is concerned. Yet they're both right. My interpretation folows that the information of time on Earth is transferred by light, so delay stacks with growing distance and it occurs evenly for both observers. Up to here everything fits to the theory.

When the direction of movement is however changed to the opposite, the light gets to both observers faster. Then both of them should see events happening faster. That implies the whole delay would cancel out. That's obviously not coherent with relativity theory at all.

I would like to aks why is this interpretation wrong and what is the right one then. I'm aware I think of it in a wrong way, but each time I try to explain it to myself I loop back to the same setup. I just keep getting back to this exact point whenever I'm like 'ok, I think I got it'. Should I just read further to general ralativity in pursuit of the answer? Or it's elementary misunderstanding, which is going to block any following concepts anyway?

I came across this post: What is time dilation really? It's well explained here, but the thing strictly connected to my question is omitted. That is the minus sign in Minkowski metric. What I've done above is just that this sign depends on velocity sign.

EDIT:

Clarification:

Put in ither words I meant Twin A stays on Earth and twin B travells away and comes back. Imagine being B on you're only interested in the rate of things happening on Earth. I agree that the rate will be perceived slower when travelling away, but it should be perceived faster when heading towards. It's fully analoguous to sound and Doppler's effect, when approaching I can hear higher frequency than when going away from the source. Quesion can be hence restated: why the analogy with sound doesn't apply?

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  • $\begingroup$ youtube.com/watch?v=0iJZ_QGMLD0 $\endgroup$ – Brad S Jul 7 '17 at 20:47
  • $\begingroup$ Thanks, I've watched that video already. Rephrasing my question in terms video: why is the time rotated backwards on the combeback? I would draw it the same way as it is in the first part of the journey. $\endgroup$ – piwox Jul 7 '17 at 20:58
  • $\begingroup$ Well this doesn't answer your question, but you can't draw it the same way. The axes are x and t and the origin is with respect to the earth observer. So to move away from earth is in the positive x direction and to return to earth is back from the positive direction to the origin. To, kind of, answer your question; Time dilation is a result of special relativity. It is a direct observation of the constancy of the speed of light or causality. If you haven't already, read this: en.wikipedia.org/wiki/Time_dilation $\endgroup$ – Brad S Jul 10 '17 at 13:24
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When the direction of movement is however changed to the opposite, the light gets to both observers faster. Then both of them should see events happening faster. That implies the whole delay would cancel out. That's obviously not coherent with relativity theory at all.

Each observer is stationary and everything else is moving, in each individual inertial (constant speed) frame. If both observers are heading back towards Earth from the same distance, and the same speed, they will both agree on the rate that things are happening on Earth, from their point of view.

No matter what velocity you travel at, (any direction, any speed), you need the Lorentz transformations to reconcile your measurements with somebody else in a frame of reference moving relative to you. I guess that you are thinking of the classical Doppler effect, but really it's the relativistic Doppler effect that's important here. You will need to slog through this Relativistic Doppler Effect This explains the difference

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  • $\begingroup$ That's not quite what I meant. Twin A stays on Earth and twin B travells away and comes back. To clarify: imagine being B on you're only interested in the rate of things happening on Earth. I agree that the rate will be perceived slower when travelling away, but it should be perceived faster when heading towards. It's fully analoguous to sound and Doppler's effect, when approaching I can hear higher frequency than when going away from the source. Quesion can be hence restated: why the analogy with sound doesn't apply? $\endgroup$ – piwox Jul 7 '17 at 20:35
  • $\begingroup$ Sorry, my first draft of the answer was way too long winded. No matter what velocity you travel at, (any direction, any speed), you need the Lorentz transformations to reconcile your measurements with somebody else in a frame of reference moving relative to you. I guess that you are thinking of the classical Doppler effect, but really it's the relativistic Doppler effect that's important here. You will need to slog through this en.wikipedia.org/wiki/Relativistic_Doppler_effect. This explains the difference $\endgroup$ – user154420 Jul 7 '17 at 20:53
  • $\begingroup$ Btw I also self study, and if I had a dollar/euro for every wrong assumption I have made......... Relativity Demystified by McMahon is excellent for learning the basic math and Susskind Stanford lectures on youtube are useful. Also Sean Carroll's pdf on GR is free online. Best of luck with it. $\endgroup$ – user154420 Jul 7 '17 at 21:08
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    $\begingroup$ Thanks a lot, that Wiki article on Doppler's effect in a way helps to distinct light propagation from time dilation itself. I tried to make them equivalent, which turns out not to be a case. Since sorted out, it should be easier now to dig further. I flipped through the referenced literature and it seems extremely useful. Thanks and good luck with your investigation, too . $\endgroup$ – piwox Jul 7 '17 at 22:17

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