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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?

Qmechanic
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Roberto Singer
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    Possible duplicate of What is the proper way to explain the twin paradox? – StephenG - Help Ukraine Apr 19 '19 at 02:34
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    No, these answers all assume from the getgo that one twin is accelerating and knows he is accelerating, and the other twin is stationary and knows he is stationary, and both observers agree on who is what. If all you know is that the other observer is accelerating, how do you measure which of the twins is really experiencing acceleration? The paradox arises when each twin assumes he is stationary/accelerating. If they agree on which is which its easy to make the calculations, but how can they objectively measure whose frame is consistently inertial? – Roberto Singer Apr 19 '19 at 02:44
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    @RobertoSinger Acceleration isn't subjective – BioPhysicist Apr 19 '19 at 03:18

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The resolution to the paradox is that, although velocity is relative, acceleration is in general not, so the situation is not actually symmetric. An easy way to see this is to imagine what you feel when your car accelerates: you feel your seat push you forward, or when you slam on the brakes you feel your seatbelt hold you back. You do not feel the same effects when you look at some other car that is accelerating "relative to you."

These are measurable effects, so each twin can independently determine whether she is herself accelerating, in addition to looking at the other twin's motion. Thus there is no ambiguity in which twin accelerates.

Note: I'm posting this answer because it is simple, even though this is indeed a duplicate of What is the proper way to explain the twin paradox. See the answers there for a more detailed description of what is actually going on.

Will
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