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I'm having trouble getting my head around the time dilation paradox.

Observer A and B are at the same "depth" in a gravity well. Observer B then descends into the well. A will observe B's time as going slower than their own. B will observe A's time as going faster than their own.

What happens if B were to ascend the well back to A's depth, would B's local time speed back up to the same rate as A's, but B would be younger (relative to A)?

What about the paradox caused by relative motion (ignoring gravity)? If A is moving relative to B, A and B will both observe the other's time as going slower. If A and B were together initially, then B moves away and returns, do their clocks agree? they can't both be younger than each other :s (i get thats the paradox, but what explanation resolves it?)

Thanks

Andrew Bullock
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3 Answers3

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Calculations show that younger will be the observer who suffered accelerations/decelerations.

Vladimir Kalitvianski
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  • is there a lay explanation as to why? – Andrew Bullock Feb 01 '11 at 22:19
  • I do not think so. Such is our reality. – Vladimir Kalitvianski Feb 01 '11 at 22:23
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    I wish we could vote down comments! Yes, accelerated twin will be younger, but don't physics would be ridiculous if there was no explanation for that! I guess you can find your answer in any standard text on special relativity! Just go and look at the chapter on accelerated reference frames and see how time dilation goes there! – iii Feb 02 '11 at 01:26
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    @Sina Salek: there is an explanation, but I don't know how well it can be qualified as a "lay explanation". In a way, Vladimir is right, it's just the way nature is. But he could have added what it is that is more fundamental than the passage of time. Well, turns out that there is a speed that is invariant. It is this fact combined with the relativity of motion that forces us to the conclusion that time is not absolute and that different observers will record different times. It is a fact borne out by experience and the most basic explanationis invariant speed $c$ + relativity. – Raskolnikov Feb 02 '11 at 10:07
  • this seems to explain it fairly well http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity – Andrew Bullock Feb 02 '11 at 16:30
  • @Andrew - my answer has a lay interpretation (even more lay than the wikipedia explanation - although that is surprisingly quite readable for WP physics article) – HorusKol Feb 02 '11 at 22:44
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Answer to the first question: yes, B will be younger than A.

Ted Bunn
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As I've been brought to understand this - the person who has descended down the gravity and then returned has not been accelerating at a constant rate throughout the journey (the change in direction requires a change in acceleration), and this causes the differential aging.

This is the same thing for the original twin paradox where one of them travels at near light speed and then returns. This may be oversimplifying things - but you seem to be after a lay explanation.

HorusKol
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