The Twins Paradox and the speed of light

I knew I was wrong, I was just curious WHY I was wrong, so thanks for the correction.

Sort of, but it's damn difficult explaining this stuff back and forth in text like this. I should set up an EvC Skype account What we are doing is trying to construct a 4d path through space-time for each of our two twins, and then measuring the length of these paths. Artificially arranging a constant velocity trip to some star system, using infinite accelerations to generate that velocity, to reverse the direction at the star system, and then bring the twin to rest back at earth is one way to make life easy in working out the length of the total 4d path. But to say that the length of the path "depends" on the velocity at an particular point, is like... well, like the following:start at a point. Move distance . Turn through an angle and reverse for a distance . How far are you from the origin? Answer So does your distance from the origin depend on ? Well, sort of, but only if that is how you arrange your path. You could have spiralled out from your starting point for a distance , with say a widening of per revolution. Now the relation between and your distance back to the origin is totally different.What I'm trying to say, is that you are getting hung up on the precise way you are arranging your particular path through space-time that you are attributing to it importance that just isn't there.If you assume the infinite accelerations, then you are in the nice position of being able to work out the time difference from the velocities. But that is because you have given yourself these infinite accelerations to make the situation easy. The time dilation itself is not arising from the velocities even though we are using the values of the velocities to work out the total time difference.Am I making any sense?

After pondering this for quite a bit, and doing some reading, I came up with an alternate explanation that I'd like to try out on you.Using the equivalence principle method on the finite acceleration as applied, we find that the gravitational potential difference at turn around is actually related to the separation between the twins at the turn around point. In fact the relation ship is phi = (a * d), assuming a is a constant acceleration. This is enough to account for what I thought was an issue. There will indeed be longer aging differentials for longer 'straight line' trips using Einstein's GR solution.This means of course that the critic's objection to Einstein was completely off base. The SR result is completely understandable using GR and the equivalence principle. I'm sorry that I cannot give you back your five minutes.

I'm glad to hear it The point to take away is the fundemental difference between the observer dependent "explanations" and the actual 4d geometry of the situation, which is the true "physics" so to speak.

Well, I was able to do the 4d stuff for SR. I think my problem involved not applying the equivalence principle properly. But I get to fall back on actually being an engineer and not a scientist.