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[...]What does HF see on her display? Does HF see that she is now slightly younger than 20?[...]

A Possible Proof That Negative Ageing Doesn't Occur In Special Relativity

It is well-known that two stationary clocks at different positions in a gravitational field will run at different rates. The clock that is closer to the source of the gravitational field will run slower than the clock that is farther from the source of the field.Because of the equivalence principle, it is also true that if two clocks that are separated by a fixed distance "d" ly are both accelerated with a constant equal acceleration of "A" ly/y/y, the trailing clock runs slower than the leading clock, by the factor exp(Ad).

Because of the equivalence principle, it is also true that if two clocks that are separated by a fixed distance "d" ly are both accelerated with a constant equal acceleration of "A" ly/y/y,

Now, suppose that he and his helper then both start accelerating at a constant "A" ly/y/y toward the right.

A Possible Proof That Negative Ageing Doesn't Occur In Special RelativityMichael Leon FontenotAccording to the CMIF (Co-Moving-Inertial Frames) simultaneity method, an observer (he) who accelerates in the direction away from a distant person (she) will conclude that she rapidly gets YOUNGER during his acceleration. But I think I may have found a counterexample that shows that such an accelerating observer does NOT conclude that.[...]

Had anyone said that it did?

Andromeda 'paradox' is one of the more classic examples.I am walking one way, and simultaneously (relative to my immediate inertial frame), the Andromeda race has launched a fleet against Earth. Now I turn around and walk the other way, and simultaneously (relative to my new immediate inertial frame), the Andromeda race is still in the process of making the decision to launch the fleet a month from now. By my act of turning around, I have 'caused' the Andromeda race to age (relative to me) negative one month.

These sorts of RoS things seem to keep Mike up at night, and all his threads are about ways to resolve this problem that isn't actually a problem.

But the problem that I see is that many physicists DON'T accept the CMIF method

the part of CMIF that says that the distant person can get younger

It's now looking like to me that Einstein's 1907 method of defining an array of clocks for an accelerating observer agrees completely with the CMIF method. If so, that means that CMIF is the law of the land, no further assumptions required. I can also now see what the error in my proof (that negative ageing doesn't occur) was. Details to follow.

I've had a new thought that is seeming "air tight" to me:If some person (the "HF") is momentarily co-located with the home twin (she), the HF cannot possibly witness her age to instantaneously change at that instant, either positively of negatively. That would be an absurdity.The distant accelerating observer (the "AO") is able to say that the HF always shares his (the AO's) notion of "NOW". Therefore the AO must also conclude that the home twin's age didn't instantaneously change (either positively or negatively) at that instant.If the above argument is correct, then the CMIF simultaneity method can't be correct.

Quote from: MikeFontenot on 07/08/2021 18:02:43Because of the equivalence principle, it is also true that if two clocks that are separated by a fixed distance "d" ly are both accelerated with a constant equal acceleration of "A" ly/y/y, the trailing clock runs slower than the leading clock, by the factor exp(Ad).You made the same assertion in June, the OP of this topic.This makes no mention of gravity, so the equivalence principle is irrelevant.

Because of the equivalence principle, it is also true that if two clocks that are separated by a fixed distance "d" ly are both accelerated with a constant equal acceleration of "A" ly/y/y, the trailing clock runs slower than the leading clock, by the factor exp(Ad).

The fact that it is not correct DOESN'T prove that she never abruptly gets older

I think the only way to prove that she doesn't abruptly get older

Immediately before the speed change, she is co-located with HF1. Immediately after the abrupt speed change, she is co-located with HF2.

But I HAVEN'T been able to find a flaw in my original proof that she can't abruptly get younger, according to the AO.

Quote from: MikeFontenot on 27/08/2021 23:50:48The fact that it is not correct DOESN'T prove that she never abruptly gets olderCouple of issues with that wording.[...]2) Your conclusion " she never abruptly gets older" is worded as if it was some kind of metaphysical fact instead of a relation to something. So say "she never abruptly gets older relative to AO's worldline, or AO's CMIF as you seem to prefer naming it.

The result (assuming I haven't made a mistake somewhere) is unexpected and disturbing.

My analysis found that the age change of the HF, produced by an instantaneous velocity change by the AO and the HF, from zero to 0.866 lightseconds/second (ls/s), directed toward the home twin (her), is INFINITE!

The equation you're using gives the rate of age change relative to AO, but you are interpreting that as an age change, not a rate of age change.