system
Given the following post, respond as if you're commenting on Reddit:
human
How does time dilation work without a privileged reference frame?

If a traveler is moving at near light speed when he comes to a stop he sees that we have aged and he hasn't. But aren't we the ones moving according to his reference frame so when we stop why isn't he the one that's aged and we haven't?
gpt
This is the actual "paradox" of the twin's paradox. If you're both moving in a straight line at a constant velocity, you both see each other as time dilated. So if you place one twin on Earth, and the other on a spaceship that flies to Alpha Centauri and back (at constant speed for each leg), then both see each other as time dilated during both stages of the trip. So... who is older than the other?

It turns out the trick is that one twin *didn't* go at a constant velocity. By turning around and coming back, he's broken the symmetry, and made himself different from the other twin. Without a privileged reference frame, there is no universal difference between "stationary" and "moving", so we can't say who is moving and who is staying still. But we *can* say who has *accelerated* and who has stayed at a constant velocity.

You can imagine that each reference frame is represented by a train moving at a constant speed along an infinitely long and straight track. Without any privileged frame of reference (i.e. ignore the track itself), there's no way to tell if your train is moving, or if someone else's train is moving, or if they are both moving. But you *can* tell if somebody has changed trains!

Relativity says that all reference frames are equally true. But if you change reference frames, then you're no longer going to get consistent results: you have to do all the maths from one reference frame. So if you add up the time dilation from the travelling twin's point of view, you get the wrong answer.

In terms of the mathematics & physics of what's going on, the equations for how time differs between reference frames doesn't only include a time dilation term. It also includes an "out of sync" term. If time is running at different rates in different reference frames, then you need another term to account for how time becomes "unsynchronised" between frames of reference.

The time dilation term only depends on your relative speed - it doesn't depend on whether you are moving towards or apart from each other, or how far apart you are. But the "out of sync" term includes direction and position. This makes everything add up consistently so you get the travelling twin ageing less without any contradiction.