Why isn't all relativity completely symmetrical? Shouldn't the principle of the twins paradox apply to every instance of special relativity?

Question

The twins paradox arises from the idea that anything moving relative to another thing should experience time dilation.

Meanwhile, anything moving relative to another thing is stationary from its own frame of reference.

The most common solution to the twins paradox I've found is that acceleration of the rocket plays a part, either extending the problem to general relativity or forcing us to consider the Earth's frame of reference as it is 100% certainly not accelerating.

It seems to me, however, that the paradoxical aspect of the twins paradox applies to anything moving anywhere, regardless of acceleration.

If you calculate time dilation perceived by something moving relative to you, and then calculate time dilation from the frame of reference inside that 'moving' thing, then surely you both have reason to think you are older than the other.

So how can you ever use special relativity to solve a problem? From both perspectives, they should be older than the other. How do we know which one is actually older, even when neither thing is accelerating?

I am stuck. Help.

Answer 1

The whole point of the usual resolution of the twin paradox is that the situation is not symmetric: one twin experiences acceleration, and the other does not.

In a truly symmetric situation (neither twin accelerates) then the twins never meet again, and so the question of "which one is older" has no absolute answer; it depends on what direction in spacetime you choose as the time axis, and each twin has a different preferred choice for that. It's like if the two twins each chose different directions for "north" (one using magnetic north, and the other using celestial north). They will come up with different answers as to how far north of them some object is, but neither one is "correct"; they're just using different coordinate systems.