Using General Relativity to analyze the twin paradox

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what physical thing is happening to the "traveling twin" in a single acceleration step
He's accelerating. :wink: That is, he is "changing direction" in spacetime, so his worldline is curved, not straight. More precisely, his worldline has two straight segments with a curved segment in between; the curved segment is where he is accelerating. The stay-at-home twin's worldline is straight the whole time.

If you mean, what causes him to accelerate, anything that causes him to feel a force will work: he can fire rockets, he can be pushed by a giant laser, he can turn on an electromagnet in his ship and get deflected by an external magnetic field, etc.

which is dependent on energy, by which time dilation and length contraction occur
Time dilation and length contraction don't depend on "energy". The stay-at-home twin never expends any energy--his worldline is straight the whole time--but he still is time dilated and length contracted relative to the traveling twin.

that is not a local space-time "bending" moment
As long as the energy the traveling twin needs to expend to curve his worldline is small enough, it will have negligible effect on the spacetime geometry. But SR doesn't explain why this is true; SR just assumes it (and assumes that we are only dealing with situations where all the energies are small enough). To explain why energies that are small enough don't affect the spacetime geometry, you need GR; the Einstein Field Equation, which tells you how much spacetime curvature is produced by a given amount of energy, is part of GR, not SR.
 
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It's certainly possible to verify if a calculation method that is claimed to work indeed works. I provided two references that verified that Einstein wasn't bluffing, for those who hold that Einstein's description is too vague to verify. :wink:
They made a lot of assumptions in the German-to-Math translation. I am not saying that their assumptions are bad ones, but I still hold that his description is too vague to verify.
 
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Neither Einstein, nor Moller, nor Builder brought them up in this context.
Clearly Einstein did. That is what he was referring to when he said "gravitational field". I showed in his technical paper where he stated that explicitly, but even just his pop-sci paper makes it clear from the way he describes the properties of the gravitational field.

there remain fictional terms in his description with magical effects.
With this I think it is time to close this thread. This now primarily about Einstein's word-choice and not about physics, and this type of language is deliberately unhelpful. Let's keep future threads to actual physics and not semantics.
 
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