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Suppose two children are standing 100m apart one of them starts running towards the other with relativistic speed...which clock would be slower?

Note- I thought this was similar to the twins paradox but according to the solution i found for the paradox some time is unaccounted because of change in velocity....this is obviously not the case here


marked as duplicate by CR Drost, G. Smith, John Rennie special-relativity Jun 2 at 10:33

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  • $\begingroup$ I got his answer but what if they stop and then compare? $\endgroup$ – Danish Jun 2 at 5:18
  • $\begingroup$ In that case, rotation of time axis would not be present right? $\endgroup$ – Danish Jun 2 at 5:20
  • $\begingroup$ You are right that if either twin accelerates, but they are basically at the same place as the other twin, the other twins clock does not move. There is another reason that the twin paradox starts with the twins comparing their clocks at rest: it is that they are then able to agree on what time the clocks are starting at. In some sense the only effect in relativity is this effect called the relativity of simultaneity: this time dilation effect is just a compounded version of lots of that effect stacked. They disagree about what simultaneous means at distant points in space $\endgroup$ – CR Drost Jun 2 at 5:29
  • $\begingroup$ So when the moving child stops and compares which clock will be slower? $\endgroup$ – Danish Jun 2 at 5:34
  • $\begingroup$ When they stop, they will both appear to be ticking at the same rate, but they might show a different number, Alice’s might show a time of 8, 9, 10 while Bob’s shows 10, 11, 12 at those same ticks. Now Bob explains this offset by saying that he set his to 0 when Alice’s was at 0 and her clock ticked slowly, 10s actually happened but her clock only ticked 8. Alice explains this offset by saying that Bob screwed up that first synchronization by starting early: When her clock read 0, Bob’s already read 5.6, then it slowly ticked 6.4 during the next 8s, coming to 12. Both explanations are correct. $\endgroup$ – CR Drost Jun 2 at 6:25

I assume the twins are originally stationary with respect to one another and their clocks are synchronized, which can be accomplished by exchanging light signals. Then if one of the twins accelerates toward the other, that twin's spacetime path is curved (non-geodesic) and hence will be shorter in proper duration, and when the running twin passes the stationary twin the running twins clock will be behind that of the stationary twin.

  • $\begingroup$ How can it be explained from the running twins point of veiw $\endgroup$ – Danish Jun 2 at 7:00
  • $\begingroup$ The running twin has to know relativity theory and so makes exactly the same analysis as anyone else. There is no special physics for a viewpoint. Viewpoints are related by Lorentz transforms, but you can't draw a nice spacetime diagram for a arbitrarily varying boost. $\endgroup$ – Brent Meeker Jun 3 at 17:44

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