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I was watching this Ted Ed video on Youtube about the twin paradox and found the explanation with the spacetime graph a bit confusing. At 3:00 in the video, they show a graph and explain how bursts are sent by each twin to measure how much time has passed for the other twin.

My understanding is that at least during the first leg of the journey (until the traveling twin turns back), both observers must feel like time slows down by the same amount for the other twin, since their relative speeds are the same. However, the video seems to indicate that Terra feels that one year has passed for Stella when 2 have passed on Earth. But Stella sees that one year has passed on earth when 4 have passed on the spaceship. This means Terra feels Terra's time going twice as slow, but Stella sees Terra's time going 4 times slower.

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In the diagram above (from the video), the first half of the journey doesn't seem symmetric. Is this right or is the explanation in the video incorrect?

ps: I also found some diagrams online that show this symmetry during the first half of the journey like the following and I'm asking if the video got it wrong and should have drawn it like this instead.

enter image description here

Qmechanic
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Sameeran Rao
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  • can include the leg length and the $\beta$ in the question. – JEB Apr 06 '23 at 16:47
  • Time never slows down. Time is that which the clocks show and each observer perceives their own clock as running at the same rate at all times. Both observers, however, are seeing the clock of the other observer initially red-shifted by Doppler effect. Doppler is symmetric. What is not symmetric is signal delay. As soon as the traveling observer changes direction, his Doppler jumps from red to blue-shifted. The Doppler signal of that stationary observer stays the same for a while, though, because the signal has to propagate the distance. The paradox simply fails to take delay into account. – FlatterMann Apr 06 '23 at 16:51
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    Without a more precise question one cannot answer this - I am not going to watch the video. But what FlatterMann writes is misleading. You do not have to talk about Doppler shift in the twin paradox (even if you do, the twins can account for this). The ultimate point is that the worldlines are not symmetric in spacetime. – SvenForkbeard Apr 06 '23 at 17:07
  • @SvenForkbeard Doppler is what observers actually see. They don't see "time dilation". I am simply giving an explanation for the twin paradox in actually measured quantities rather than in theoretically derived ones. I don't think that should be controversial. It may be unusual because most textbooks don't seem to do it that way. Please think about it some more. You will find that it's not a bad idea. – FlatterMann Apr 06 '23 at 17:15
  • @SvenForkbeard The whole video is about observation of regular light (radio?) pulses, so it correctly explains what the two twins observer. Of course, it fails to reveal the twin paradox. – JEB Apr 06 '23 at 17:20
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    Does this answer your question? How can time dilation be symmetric? – John Rennie Apr 06 '23 at 17:22
  • @JEB Sorry I assumed because of the title it had something to do with the twin paradox. @Flattermann Well in some sense the whole point of the twin paradox is that they do see time dilation, in the sense that they are not equal ages when the meet again. With all the best will in the world, talking about Doppler shifts does not `explain' the paradox, merely defers an explanation. However, drawing invariant lines (such as the light ray signals as on the diagram above) does help, because they explicitly show why the worldlines are not symmetric. – SvenForkbeard Apr 06 '23 at 17:25
  • @SvenForkbeard thanks for the feedback about question not being precise. I updated the question with some images. My question is about the lower half of the image (first leg of the journey only) and why the video shows time slowing down at different rates for the twins during this part. Thanks. – Sameeran Rao Apr 06 '23 at 17:29
  • @JEB "time dilation" denotes the effect of the Lorenz transformation on the ratio of the rate of two clocks that are moving relatively to each other but are in the same position. Doppler is what we actually observe when "looking" at a clock that is not in the same location. So while Lorentz transformations are great for theoretical arguments relating to the symmetry of e.g. fields, they do not represent actual physical observations. The explanation of the paradox is about what goes wrong with the mental model: it's the use of Lorentz rather than Poincare. Doppler IS the physics of Poincare. – FlatterMann Apr 06 '23 at 17:40

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