Mike_Fontenot said:
Just FYI:
... at any instant of his life, the traveler CAN, if he so chooses, decide to stop accelerating for more than a single momentary instant ... for some segment of his life ... before resuming accelerating again. He may not choose to ever do that, but he CAN if he wants. IF he does, he can make the SAME kind of observations and calculations that a perpetually-inertial observer who is (temporarily) co-located with him during that segment can make.
EDITs have been made in this post, and they are
highlighted ...
Mike, let me ask you ...
What's the difference between going inertial for 1 quintillionth of a microsecond, versus considering the velocity at a point on the x vs t position plot
while still non-inertial? I mean, from a standpoint of what twin B can do in that time, what's the diff?
On the one hand, I realize that while inertial, one is not dynamically changing in POV. On the other hand, there's not enough time for twin B to bounce any radar signals out and back off twin A, either way. Now, the LTs were designed for the all-inertial case, yes, however it seems to me that all heavenly bodies exist precisely where the co-located MSIRF observer says they do, including twin
B. Why not? Twin B and the MSIRF observer are "at that instant" colocated and of zero relative v. They are both then receiving the same light signals from their surroundings, including from twin A, so they should then see the heavens the same at that instant. If the MSIRF observer says twin A is currently right there, then although twin B may not know such from his own classical calculations, there's no good reason that twin B should disagree, because the special theory is rock solid. If they were of differing v when colocated, I'd contend differently, however they are not.
If twin B's calculations based upon his own measurements tell him something differently, then something is amiss. What's amiss IMO, is the fact that the non-inertial twin B deduces the twin A velocity
differently from observations and "calculations made in the classical way". Let's face it, he can't plug superluminal velocities into the LTs, nor should he try. His POV dynamically changes, which causes light's speed to appear variable across spatial expanse (but never at his own location). The reason he measures the A-velocity differently is because he (rather accidentally) accounts for length-contraction while ignoring dilation (and doppler effects). If he does not ignore said effects, and accounts for all of them, then he should obtain the relative A-velocity representing the current slope of the A-worldline. Events move in spacetime while non-inertial, and this cannot be ignored whether B is trying to determine the A-velocity from bounced radar signals, or determining the A-velocity from a space vs time plot after the fact, IMO.
Now I realize that you use the twin-A system as the reference for all future calculations as they go, so you do not have the superluminal problem. I'm just trying to nail down the reasoning as to why twin B should disagree with the MSIRF observer at their moiment of colocation, and how to justify a resolution of that matter in a way that all observers agree (as consistent with SR).
GrayGhost