Mike_Fontenot
Registered Senior Member
[...]
Your quote,
I.e., According to HIM, she gets rapidly YOUNGER when he accelerates in the direction away from her.
[Bob-a-builder continues]
How would they see one another?
[end quote]
[I (Mike Fontenot) continue]
The traveler (he) never SEES the home twin (her) rapidly get younger. That may be the point you're missing.
Suppose that she sends him a video image that shows her holding a sign that states her age. When he receives that image, he knows that the image he sees and the age printed on her sign is NOT her age "right now" ... it gives her age when she transmitted the signal, which was a LONG time in the past. To get her age "right now", he must determine by how much she has aged during the transit time of the image, and then add that to her age at the time of transmission. If he does that correctly, he will calculate that she has gotten younger since the last time he went through this process.
But he don't have to go through the above process to determine her current age at any instant of his life. He can use the Lorentz equations, or even easier, the Minkowski diagram, or even easier, the CADO equation (which is easily derived from the Minkowski diagram) to determine her current age at any given instant in his life. All of the above options are described in detail in my webpage:
https://sites.google.com/site/cadoequation/cado-reference-frame
and in my paper
"Accelerated Observers in Special Relativity", PHYSICS ESSAYS, December 1999, p629.
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