In special relativity what is the solution to the twins paradox?

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miser
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In Special Relativity, there is a famous problem called the twins paradox. One person is "stationary" and the other accelerates away in a rocket ship at near light speed, then comes back. The outcome would be that the stationary person would have aged more than the person on the rocket ship.

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The paradox is that, in special relativity, all references frames are equally valid, so from the rocket's perspective the stationary person isn't stationary at all, but is in fact the one who accelerates away and then comes back. Indeed there is no such thing as "stationary" in an absolute sense, but only as relative to other objects.

However, if they run the same calculations on each other, they would both predict that time has passed longer for themselves and less for the other, yet only one of them is correct.

Why is it that the "stationary" person would be correct, and how could the rocket person know that their calculation is wrong? Is there a way to determine it in purely relativistic terms, or is special relativity not relative after all (instead requiring an absolute frame of reference or absolute measurements of force, etc.)?
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Joinedup
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If they have a chat about their experience after meeting up again the one who was on the rocket will notice that the earth looked like it was accelerating away from him... But that he felt like he was accelerating. If he had an accelerometer, that would confirm that he had been accelerated.

The one who stayed on earth will notice that the rocket looked like it was accelerating away from him but that he felt no unusual acceleration. If he had an accelerometer that would also show no unusual acceleration.

Thats why it's not the same for both twins when they meet up.
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(Original post by Joinedup)
If they have a chat about their experience after meeting up again the one who was on the rocket will notice that the earth looked like it was accelerating away from him... But that he felt like he was accelerating. If he had an accelerometer, that would confirm that he had been accelerated.

The one who stayed on earth will notice that the rocket looked like it was accelerating away from him but that he felt no unusual acceleration. If he had an accelerometer that would also show no unusual acceleration.

Thats why it's not the same for both twins when they meet up.
I know that view is a common one, but I think it doesn't hold up under scrutiny.

The first potential issue is that it implies acceleration is an absolute property in the universe (i.e., it can be agreed upon by all inertial reference frames), which I'm not sure has a solid basis. For example, couldn't the accelerometer be equally triggered by a gravitational field acting upon the rocket and the rocket simply holding its ground? Who's to say it was acceleration or a gravitational field that caused the accelerometer to move, and how could different reference frames agree about it?

Secondly, we can restate the problem such that the accelerating rocket is the one that experiences greater passing of time. For example, we can say that this time there are two rockets near earth. One rocket is in a free fall orbit around earth (no acceleration, only free fall). The second rocket is about the same distance away from earth, but is firing its engines in a constant acceleration to resist the earth's gravity, but otherwise stays in the same place.

In that scenario, after the orbiting rocket took one trip around the earth, the accelerating rocket would have experienced greater passing of time relative to the free falling rocket, despite the opposite having been the case in the original thought experiment.
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