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Relativity of simultaneity is a direct consequence of Lorentz invariance.

Since Lorentz invariance has been demonstrated to extremely high precision experimentally, then we know by consequence that relativity of simultaneity is also a physically real phenomenon. It's not an illusion.

The best way of understanding the concept of a "NOW" moment in special relativity is to first get an understanding of Einstein's array of clocks, yardsticks, and "helper friends" (HF's) in an inertial reference frame. He said that all the clocks in that reference frame could be synchronized by sending light pulses between the various clocks, and by making use of the fact that in ANY inertial frame, any light pulse will move at 186,000 miles per second, according to all stationary observers in that frame.So how do we use that fact to get a "NOW" moment (extending throughout all space), according to some particular inertial observer (call him the "PO") in that frame? To make it simple, we can arrange for all HF's to always have the same age as the PO. If the PO wants to know the current age of some particular distant person (DP) when the PO is age "T", he just needs to ask the HF who happens to be momentarily colocated with the DP at that instant, "What was the age of the DP when you were "T" years old?".If we use the above procedure for several different inertial reference frames (that are moving with respect to one another), the PO's in those different frames (when they are momentarily co-located) will get DIFFERENT answers to the question "How old is that distant person, right NOW. But each of the PO's MUST conclude that the answer he got is completely real and meaningful to him, because it is based ONLY on the assumption that the speed of a light pulse is always equal to 186,000 miles per second in ANY inertial reference frame. If that assumption were wrong, then all of special relativity would collapse.But what about for an ACCELERATING observer (the AO)? Can a "NOW" moment be defined for him? The answer is YES! He can ALSO surround himself with an array of clocks and HF's, separated by constant distances. Those clocks (and the corresponding HF's ages) CAN'T be synchronized with his clock and his age (because they all run at different rates), but he IS able to calculate what the reading of each HF's clock (and each HF's age) is at any instant of his (the AO's) own age. That DOES establish a "NOW" moment (extending throughout all space) for him, and that "NOW" moment MUST be completely real and meaningful to him.When you use the above procedure, the result is the same as that given by the Co-Moving-Inertial-Frames (CMIF) simultaneity method. So the easy way to get the answer is to just use the CMIF method (and that is what Brian Greene is using in his "alien" scenario in his NOVA program to determine simultaneity at a distance). What the array of clocks method does is GUARANTEE that the result given by the CMIF method must be considered to be completely real and meaningful to the AO.The derivations of the above results are given in three viXra papers. The "overview" (short) paper is titled"Is the Equivalence Principle Schizophrenic? ... And a Summary, and a Correction", https://vixra.org/abs/2206.0133Michael Leon Fontenot

The material that I've posted above is actually NOT a new "theory".

The only original work I've had to do, is to first realize that the existing GTD equation (the well-known exponential version) is incorrect

What I've done is to show that an analogous thing can also be done for an accelerated frame of reference in special relativity. I.e., an array of clocks can also be set up for an accelerating observer.

That is possible by making use of a combination of the gravitational time dilation (GTD) equation

But there is a far more interesting question: What do two people on earth, who are moving with respect to one another in the direction of Andromeda, conclude about the current time on Andromeda?

The only remaining question, in my mind, about this thread is "What motivated the OP to ask his original question". My guess is that he had heard (perhaps from people like me) that if a person (he) suddenly changes his velocity with respect to a distant person (her), accelerating in the direction AWAY FROM her, that he will conclude that she suddenly gets YOUNGER during his acceleration

Mike is referring to the topic from which his last three posts were split (at your suggestion no less).

Quote from: MikeFontenot on 11/08/2022 21:19:52The material that I've posted above is actually NOT a new "theory".

You're calling the equivalence principle 'Schizophrenic' which is a form of science denialism. The topic is in new theories where it belongs.