The Twin Paradox and Absolute Reference Frames in General Relativity

[CJames]

This article discusses a special case of the twin paradox in which the accelerated twin ages faster than the inertial twin: http://www.physorg.com/news163738003.html

According to the article, if you have two observers orbiting a planet, and one of them decelerates to land on the planet, than the twin who doesn't decelerate will age slower.

But then they say this:

By presenting a scenario in which the accelerated twin is older at the reunion, the scientists show that the final time difference between the twins often depends only on their velocities as measured with respect to an absolute standard of rest, and not on acceleration.

Absolute standard of rest? That just doesn't sound right. But if it's wrong, why IS the inertial reference frame aging slower? The article claims that it's okay to talk about absolute reference frames in GENERAL relativity. Is this true?

 

[ZikZak]

Yeah, that wording in particular made me go look up the original paper on arxiv. But indeed, that is the wording that the authors use. Ick. What they mean by "absolute rest" is that they do the calculation in the rest frame of the gravitating body.

The result is hardly surprising. In SR, the nonaccelerating twin will always be older, but that changes in GR. In GR, geodesics are still the paths of extremal aging, but because of curvature, that extremum need no longer be a maximum, and for orbiting bodies is frequently a saddle point. In fact, I think MTW give this exact example somewhere... ya, section 13.4.

 

[A.T.]

Absolute standard of rest? That just doesn't sound right. But if it's wrong, why IS the inertial reference frame aging slower? The article claims that it's okay to talk about absolute reference frames in GENERAL relativity. Is this true?

They are arguing about the 'cause' for the different aging of the twins, it terms of: "Is it acceleration or is it absolute movement?". But rules of thumb like these are to simplistic.

Proper time intervals are defined by the paths trough spacetime and depend also on the space time metric. But I don't see how this implies absolute rest. It is often just more convenient to do the calculation in the frame of the mass causing the spacetime curvature.

 

[George Jones]

Short answer: a geodesics worldline from event p to event q has maximum elapsed proper time for all worldlines from p to q if and only if there are no conjugate points between p and q.

I hope to write a much longer post about this, but the posts I hope to write don't always happen.

 

[A.T.]

Short answer: a geodesics worldline from event p to event q has maximum elapsed proper time for all worldlines from p to q if and only if there are no conjugate points between p and q.

Does this mean that the worldline has to be the only geodesics between p and q ?

That's what I was thinking too, because in the given case there can be different geodesics paths besides orbiting: swinging trough the center of the planet, being thrown up away from the planet and return. I assume they all have a different proper time interval, so they cannot all maximize it.

 

[CJames]

Thanks for the help!

ZikZak:

In SR, the nonaccelerating twin will always be older, but that changes in GR. In GR, geodesics are still the paths of extremal aging, but because of curvature, that extremum need no longer be a maximum, and for orbiting bodies is frequently a saddle point.

With my very vague understanding of physics, let me see if I'm understanding you correctly. By saying that an orbiting body may be in a saddle point, are you saying that this means that acceleration in one direction will decrease aging, while acceleration in another direction will increase aging?

George Jones:

Short answer: a geodesics worldline from event p to event q has maximum elapsed proper time for all worldlines from p to q if and only if there are no conjugate points between p and q.

I think I'm getting you. If I want to go from Florida to Washington, there is a geodesic connecting them across the united states, and a geodesic connecting them going all the way around the planet. If I'm following the geodesic that goes all the way around the planet, it'll be longer than even a very twisty road that doesn't leave the united states.

In four dimensions, if I compare two curves beginning and ending on the same two points, the longer curve will have traveled through more space and less time. So a longer curve means aging less. If space itself is curved, it makes sense that I could draw a curve that doesn't follow a geodesic but is shorter than one that is a geodesic, and therefore I would be describing an accelerating object which is aging faster than an object in free fall.

Did I butcher that?