#### Mike_Fontenot

**Registered Senior Member**

Even in the CMIF simultaneity method, no one ever visually sees anyone getting younger, ever.

In my proof, I'm not assuming ANY simultaneity method. The only thing I assume is that Einstein's gravitational time dilation equation is valid. Here is a Wiki link that gives that equation:

https://en.wikipedia.org/wiki/Gravitational_time_dilation

Scan down to the first section ("Definition"), and find the first equation. In that equation, assume that "g" is constant, so the integration is trivial, and the time dilation equation simplifies to

T_d(h) = exp(gh),

(where I have also eliminated the "c" factor by using units of years and light-years). That equation says that the clock that is closest to the source of the gravitational field will run slower than the clock "h" lightyears farther from the source, by the factor exp(gh).

Then, I use the equivalence principle to replace the constant gravitational field g by a constant acceleration "A" of the two observers (the "HP" and "he") who are separated by the distance "d", giving me

T_d(d) = exp(Ad),

which says that the "HP", who is located "d" light-years behind "him", will age more slowly, by the factor exp(Ad), than "he" will.

That is the equation I use at the beginning of my proof.

In answer to your statement "Even in the CMIF simultaneity method, no one ever visually sees anyone getting younger, ever.", I say "No one has ever made use of the HP before, to find out!" But as I said in the proof, it would be absurd for anyone co-located with another person to ever contend that he sees the other person getting younger.

What I've really done, by doing a simultaneous and equal constant acceleration of "him" and the "HP", is to construct a coordinate system for the accelerating observer, analogous to the coordinate system that Einstein constructed for a perpetually-inertial observer. Of course, the clocks for "him" and the "HP" don't run at the same rate as the perpetually-inertial clocks do, but if "he" knows how to correct for the "HP" clock rate, it can serve as a coordinate system.