Relativity thought experiment

The paradox of each twin seeming have aged more slowly than the other is due to the fact that special relativity applies only when the two observers are moving at constant linear speeds relative to each other. Special relativity doesn't handle acceleration. Unlike velocity, acceleration is not relative.

At least one of the twins must undergo acceleration/deceleration in order for them to be reunited. Once that happens, special relativity no longer applies. That is why the paradox arises.

Bob Feduniak

[PairTheBoard]

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usmhot --


Incidentally, sincere apologies - I got it backwards in my original post - the twin on Earth would age more slowly than her space-faring counterpart. Time slows down in a gravity field relative to another point in space.

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I don't think so. The time dilation due to gravity is minimal. The time dilation due to velocity is the main thing. And we have proof with clocks sent into orbit. They no longer feel the force of gravity, but due to their speed they come back to earth having aged slower than their earth bound counterparts.

The Twin that travels out and back and spends time close to the speed of light is younger when he returns than his earthbound brother. And he never has to exceed 1g to do it. The more time he spends coasting near the speed of light the younger he will be than the earth he left behind when he returns. This is well known in relativity.

PairTheBoard

[PairTheBoard]

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The paradox of each twin seeming have aged more slowly than the other is due to the fact that special relativity applies only when the two observers are moving at constant linear speeds relative to each other. Special relativity doesn't handle acceleration. Unlike velocity, acceleration is not relative.

At least one of the twins must undergo acceleration/deceleration in order for them to be reunited. Once that happens, special relativity no longer applies. That is why the paradox arises.

Bob Feduniak

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I was with you until the second paragraph. What does the acceleration/deceleration have to do with anything. The twin on earth can experience identical acceleration in both directions due to gravity. I think the acceleration is irrelevant. It's the velocity of the traveler that causes him to age slower.

PairTheBoard

It is the velocity. The problem is that the two twins can't be brought back together without at least one of them experiencing acceleration/deceleration. Once that happens, special relativity ceases to apply. Without introducing acceleration/eeceleration into the picture, it's not possible to verify whether the twins have aged differently, so there's no paradox.

The fact that special relativity can't handle this sort of thing is one of the reasons that general relativity was developed. I don't recall how to apply general relativity to the twin paradox, and it's not even close to being intuitively clear to me.

Bob Feduniak

[Moon Double Comb]

The acceleration/deceleration is fundamental here, since it breaks the symmetry and special relativity is not applicable anymore. You need general relativity.

And although I'm not an expert on the subject, I think you're misinterpreting the gravity/acceleration relation. Gravity curves spacetime, so that an otherwise straight worldline through flat spacetime is seen as a curved worldline from a rest frame. While acceleration is a curved worldline in itself. So seen from a rest frame both are interchangeable.

I would venture to guess that if you apply general relativity to the twin paradox the twins either have the same age and are not spatially seperated OR have a different age and ARE spatially seperated.

[PairTheBoard]

Ok, the reason no one has ever been able to give me a simple explanation for this is because the explanation is not simple. This link goes into various explanations. It looks to me like the determining factors are the speed of the craft and the two directions - ie. "away from" and "back toward". But you guys can figure it out.

Twin Paradox


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