@ rpenner:

That's incorrect and renders your understanding of SR highly suspect.

Sir, you have the right to suspect what you like personally; but the discussion points made will be the objective arbiter either way, irrespective of anyone's personal suspicions.

SR was formulated first in Cartesian coordinates and then in pure geometry. In either, inertial trajectories are modeled as straight lines. That why "frame" is synonymous with "inertial Cartesian coordinate system." But just because straight lines are special in Eucldiean and Minkowski geometries doesn't mean that other curves are not admissible in either system. What began with straight lines and circles was generalized to conic sections, spirals and (with the invention of calculus) general curves. SR is entirely capable of handling the mechanics of acceleration motion, so your peculiar objection to treating accelerated motion in flat space time in SR seems baseless and backward.

Sir, you are preaching to the converted on all that. I have not contended against any of those things you point out. Perhaps you may be conflating me and my discussion points with some other person or points you are discussing with that involves your points and arguments?

In any case, my point was that whatever the original SR relative-only constant-motion type construct, it had to be extended to include, by whatever means and maths, the non-SR-type info, the self-limiting to which previously made the original twins paradox so problematic when considered only as SR type scenario. The point I made was that such extension was motivated by the need to explain the real effects when all is said and done. And that real effect in the twins scenario can only be understood and explained if the GR type info is available and applied to whatever extended SR construct is the best for that purpose of dispelling the twins paradox.

Do you see what I am constraining my point to? In short, whatever extended SR maths is applied, it boils down to the fact that eventually and effectively, the whole picture (and not just infinitesimal path lengths in curved space) has to be considered (as per the overarching GR construct) if the real effects on the one twin and not the other is to be understood irrespective of any previous SR-type maths logical 'paradoxes'.

That is all I have pointed out, Sir.

"Real" (meaning achievable) accelerations are not necessary for analysis of the twin paradox for the geometric fact that the straight line is the longest path remains whether the alternative to inertial travel is smooth or piecewise continuous (modelling infinite acceleration).

No Sir, I don't mean that. I meant "real" as in actual respective inherent properties and parameters (accelerations or not, etc) of both twins involved (for contextual clarification re that please refer to my earlier posts to Consfused2 regarding that. Thanks).

And as for the modeling using calculus techniques, it makes no difference to the actual real effective outcome of the accelerations on whichever twin is affected.

It reminds me of the Zeno Paradox which 'mathematically proves' there can be no motion at all. Obviously such techniques may be useful and fit for purpose in certain limited path length treatments in a particular construct; but eventually the whole path length needs be considered if the analysis is to make real physical sense.

For example, one may 'treat' an infinitesimal length of the circle circumference as 'straight', but in reality overview when all the infinitesimal lengths are combined, one must have reproduced the original circle's inherent circumference properties and parameters; else one is left stuck in an analytical maths construct which makes no sense other than the limited 'fit for purpose' sort of sense within the limited construct used in exclusion of the overarching reality view of the full circle.

Similarly, Confused2 seemed to be having difficulties because he seemed to be stuck in the original SR-relativity-only self-limiting perspective, instead of continuing beyond to the overarching GR perspective which informs and expands the understandings, even though the limited view was 'fit for purpose' for what limited understandings purposes it was originally designed for but which is now made more realistic by the GR overview. As I pointed out.

I trust you now understand that that was all I pointed out. I have had no argument at all with the other things you now raised above which were beside the point I was making, Sir. Thanks. Best.