Concerning this attitude of there being a 'correct' method, I wonder what you mean by 'correct'. The only interpretation of that assertion is that the method corresponds to some metaphysical truth, but the method chosen is not consistent with any suggested metaphysics in any known philosophical interpretation except possibly solipsistic-idealism where Alice in fact doesn't exist at all when not directly experienced, and not even then in the same way you exist. This method you've created is not consistent with your claims in your paper and posts, and that makes it irrational.
section 13 said:
I don't believe that my home twin ceases to exist whenever we are separated.
OK, that sort of eliminates the solipsistic idealism. That fit well with the CMIF method, but not the others. The universe is all about me.
she must be a specific age right now. So I believe she must have some specific current age. Her current age is not just one of a set of equally good "conventions" of simultaneity, as many physicists believe. Therefore there must be a single, correct simultaneity method.
All this adds up to an assertion about some kind of objective (independent of viewpoint) ordering of all events in the universe. This is an absolutist stance, and the view says that there is an objective ordering, even if the ordering cannot be experimentally determined. This is a rational stance, and one held by a different set of physicists than the ones you mention that take a relative view, which you call a 'set of equally good "conventions" of simultaneity', which seems to be a strawman way of putting it because there seem to be only three conventions used in practice, and neither is on your list.
So, given your chosen premise that she must be a specific age right now, you've effectively asserted an objective ordering, and then you create a method that isn't objective. That's the part that isn't rational. You get the absurdities that Neddy and yourself point out: Two comoving observers using the same method and getting different answers. You call it a disagreement interval, which effectively admits that your assertion that Alice being a specific age right now to be a false assertion. You're contradicting your own premises.
If she's a specific age right now, then nothing you are doing right now (like moving this way or that) should have any effect at all on her age.
I now suspect that it may be impossible to prove which simultaneity method is the correct one. I DO believe that there IS one and only one correct simultaneity method in special relativity, but we probably just can't know what that correct method is. All we can do is choose which of the known methods we each want to use, based on which one we believe has the most desirable characteristics. I think my method's characteristics are the most desirable among the four simultaneity methods that I'm aware of (CMIF, Dolby&Gull, Minguizzi, and mine): mine is (1) causal, (2) it produces an ACD that is always continuous and piecewise-linear, and (3) it never produces negative ageing of the home twin
You forgot 4) Doesn't violate your stated premise that Alice has an actual age right now. Your method violates that, and Minguzzi does not.
But remember that I said that the physicists (both absolutists and relativists) tend to use only one of three methods for any practical purpose? All three of those methods satisfy your 3 points, and one satisfies the 4th one that includes your absolute premise.
Method 1: (the most commonly used method): Her age is as we see it. If I move away quickly, her age rate drops significantly, mostly due to Doppler effect.
I pointed out this method in an earlier post. Everybody is looking at Betelgeuse right now because it suddenly got uncharacteristically dimmer and they're wondering if it's about to go supernova. I found 50 link to articles about it and not one of them says that it might have gone supernova 650 years ago. They all say it might go any time now (It probably isn't). That's all using method 1. Ditto for all the news about the black hole mergers.
This method fails the test of commutivity. If I am 16 and she appears 8, then she, at 8, will see me as perhaps 4. This criteria was not one of your 3+1 points. Your method fails it as well. The method doesn't work over large distances.
Method 2: Frame of home base, the place where the reunion takes place. That's almost always Earth mean frame. This method is commutative, and works well locally but not over large distances. More precisely, all computations are done relative to the frame in which the departure event and the reunion event are at the same spatial location.
Method 3: Comoving coordinate system: The age of every event is the spacetime interval between the big bang and that event. This is a favored method for very large scale, and because it is the only method that foliates all of spacetime, it is favored by many absolutists. It is commutative. Drawback is that it isn't inertial. Two stationary objects tend to separate over time. An inertial object with no forces acting on it tends to slow over time, losing kinetic energy. All this is pretty non-Newtonian. The method is rarely used for local computations like trips to nearby galaxies and such.
The first two methods cannot be 'the correct' absolute method since neither foliates all of spacetime.
