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I'm a beginner physics student only studying elementary AP-level physics and calculus, so when I came across the conceptual basis of the twins paradox I was, of course curious. People often explain the paradox away by explaining how the symmetry from each perspective is broken, without satisfactorily illustrating why. Before I ask my question I want to explain from my understanding-
So you have a twin on earth who understands that his twin is on a spaceship accelerating away arbitrarily close to the speed of light then returning home. He accelerates away and comes back, and I understand why the twin on the spaceship believes the other is older- Because on a spacetime diagram, we recognize that the axis flips and the twin on the ship understands that the relativistic affect on him will result in a difference.
So my question is: How do both observers figure out WHO is accelerating to begin with? To illustrate my problem with the paradox, I instead imagine two twins floating in space 1 meter apart in a vacuum, until one sees the other accelerate to near light speed. If we assume that the twins will return to their initial position at 1 meter apart, only ONE of them will age. The problem is figuring out who?
This is because: If twin A assumes he is stationary, and twin B assumes he is accelerating, then they can work out the respective maths. But what happens if both assume that they are accelerating, or that both are stationary? This is what results in the apparent paradox isn't it? So the real question should be: How do we know who is objectively accelerating?