Varitaion on the twin paradox that just doesnt work out for me

[Natman3400]

So if you were to take the twin paradox, but make it so instead of the ship turning around and going to earth, the ship bends space through higher dimensions to return to Earth with no movement, what happens then? I'm sure this has been thought up of before, but i can't find an explanation that works out for me.

 

[atyy]

In all variations of the twin paradox, we assume the age of the twin is the proper time elapsed along his worldline. So define your spacetime metric (this can be curved and includee wormholes etc), define the worldline of each twin. The spacetime metric acts on every point of the worldline of each twin to produce a number, integrate that number along the worldline (there's a minus sign and square root somewhere, but that's a technicality), and you will get the age. This always works if the spacetime is classical and "given" by god as a background spacetime.

 

[Natman3400]

What i am saying is since both Earth and the ship can be considered to be traveling at near the speed of light, won't the ship see Earth as older then itself, and Earth see the ship as older then itself? In this case, what happens?

 

[atyy]

What i am saying is since both Earth and the ship can be considered to be traveling at near the speed of light, won't the ship see Earth as older then itself, and Earth see the ship as older then itself? In this case, what happens?

It has nothing to do with traveling near the speed of light. Travelling near the speed of light is frame-dependent, so it's "coordinate" time dilation, not real aging. The twin paradox is about real aging.

 

[Natman3400]

It has nothing to do with traveling near the speed of light. Travelling near the speed of light is frame-dependent, so it's "coordinate" time dilation, not real aging. The twin paradox is about real aging.

Mind explaining abit?

 

[Fredrik]

The motion of a classical particle is described by a curve in spacetime. In situations like the twin paradox, we don't care about the small differences between the motions of different component parts of the same object, so we treat all clocks, humans, spaceships etc., as particles. The motion of each object is then approximately described by a curve in spacetime.

One of the axioms of both SR and GR is that a clock measures the proper time of the curve that represents its motion. The twin paradox is just a scenario where two objects move as described by two different curves with the same endpoints. The standard twin paradox considers two curves in Minkowski spacetime, but if you want to consider another spacetime, that's fine. There is however no spacetime in which two objects are brought together without movement. No matter what coordinate system you're using, one of the objects is moving.

If one of the two twins leaves Earth the usual way, and returns through a wormhole, the curve that describes his motion can have a longer or shorter proper time than it would have had otherwise. Either way, you find that guy's final age by calculating the proper time of the curve that represents his motion.

 

[Dale]

since both Earth and the ship can be considered ...

The situation is not symmetric since the spacetime metric is asymmetric.

 

[georgir]

The problem is with your requirement for a magical instantaneous return trip.
And no, the problem is not in the "magical" part - we can easily close our eyes and ignore the fact that it can't exist. It is in the "instantaneous" part.

Instantaneous is just not well-defined. Once the traveling twin decides to return, there exist numerous different frames of reference, according to each of which a different point from the other twin's timeline is simultaneous with the traveler's "now". Which one will your magic chose? You can make an arbitrary pick and you will have some arbitrary answer to the question about their ages, but you can't expect us to give you a scientific argument for picking a "correct" one... it is just not well defined.

 

[John232]

I kind of sounds like a proposed mode of time travel done by traveling close to the speed of light near a large gravitational field. The twin that did the sling shot would be younger, but would somehow end up traveling back in time when he arrived at Earth.

Another one was if you could move an end of a wormhole near the speed of light then one end off it would have its time slow, so then you could travel through one end and arrive in another time comeing out of the other. Then if you brought them both together you would end up comeing out of the wormhole before you went in, but then what if you stopped yourself from going in after you had went through the wormhole already?