How are times after time dilation resolved in relativity

[Bohandas]

It's my understanding that under relativity if two objects are moving relative to each other at an appreciable fraction of the speed of light they will both perceive time to be slowed down for the other. How does this work out if they meet up?

For example, if I make a round trip to a star five lightyears away from earth at 99.5 percent the speed of light, the earth will percieve it as taking ten years and time on my ship advancing at 1 tenth the rate (and also the ship all smooshed up). But equivalently I will experience the earth ans stars shifting a 0.5 lightyear distance (due to length contraction) and back and still see the earth's time moving at one tenth of my own.

Why doesn't this lead to an infinite regression?

[gomipile]

You haven't yet taken into account the effect that turning around at the destination has on the reference frames.

Look up the "twin paradox." There are some pretty good explanations on YouTube. I'm not sure which one I remember had a particularly good explanation, but I can't look it up right now.

[Bohandas]

each time you stopped (at the middle and at the end) time on the planet would rush forward four and a half years?

[Anymage]

If you assume instantaneous turning around (although this is minor in the overall scheme of things) and instantaneous transfer of information (this very much is not). Relativity breaks all over the place if you assume any instant transfer of information.

[Mastikator]

It's resolved with acceleration. Acceleration causes time to slow down, right now you're accelerating up against the gravity of the Earth. That acceleration does in fact cause time to move slower for you than if you were deep in intergalactic space.
It's too complicated for my tiny inferior brain to *understand, but here's a link https://en.wikipedia.org/wiki/Accele...al_relativity)


*Not really, I'm just too lazy at the moment

The one on the space ship will have experienced less time than the one on Earth because the space ship had to do a LOT of acceleration to reach 99.5% of the speed of light. That acceleration, then de-acceleration (still counts!) and then accelerating back and finally de-accelerating on arrival would resolve the paradox.

[gomipile]

I think this is the video I was thinking about earlier:

https://m.youtube.com/watch?v=6MfJ59lkABY

On further reflection, there are details I don't like, but the spacetime diagrams are decent for helping understand some aspects of this topic.

[jayem]

Very carefully, taking note as to exactly which inertial frame you are measuring in.
(and as noted in the twin paradox that involves 3 frames)

[Radar]

Very carefully, taking note as to exactly which inertial frame you are measuring in.
(and as noted in the twin paradox that involves 3 frames)

What is important though, is that all three frames of reference will agree on the ages once the twins meet back. Lorentz transformation changes which events at different places are coterminous, but it will never change what happens at one specific point in spacetime.