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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

Danish
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  • I got his answer but what if they stop and then compare? – Danish Jun 02 '19 at 05:18
  • In that case, rotation of time axis would not be present right? – Danish Jun 02 '19 at 05:20
  • 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 – CR Drost Jun 02 '19 at 05:29
  • So when the moving child stops and compares which clock will be slower? – Danish Jun 02 '19 at 05:34
  • 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. – CR Drost Jun 02 '19 at 06:25
  • How can the initial synchronisatiob be affected? – Danish Jun 02 '19 at 06:43
  • Danish, if you are asking about the situation on the Earth and we consider the Earth to be perfectly spherically symmetric and ignore the effects of other celestial bodies, the answer is, if both children are at the same gravitational potential, whichever child that moves faster with respect to the center of the Earth will experience time to move slower. – Agerhell Jun 02 '19 at 12:39
  • Let us say that both children are at the equator, one of them one hundred meters to the east, and both are initally at rest with respect to the face of the earth. Both have clocks that intially run at the same rate. Now if the eastern child starts running to the west his clock is going to run faster as long as he does not move as fast as the Earth rotates (40 000 km/day). However, if the western child starts running towards the eastern child his clock is going to run slower because he is running in the same direction that the Earth is rotating in. – Agerhell Jun 02 '19 at 13:06
  • Ok so we have to take a third reference point right? – Danish Jun 02 '19 at 13:47
  • Yes you can say that. If you have a spherically symmetric gravitational field you take the center of mass as the reference point. Then it is GR though and not SR. Note that SR was developed before GR when the effects of gravity was not fully understood. – Agerhell Jun 02 '19 at 16:36

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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.

Brent Meeker
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  • How can it be explained from the running twins point of veiw – Danish Jun 02 '19 at 07:00
  • 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. – Brent Meeker Jun 03 '19 at 17:44