Mentor Note: This thread has been separated out of a previous one to keep discussion of this particular topic open, since the previous thread has been closed. Sorry, the opportunity to ask questions is just too hard to resist. I'm still searching for the right understanding of equivalence. Or that is what has got me in trouble. I had been picturing it as "there is no difference in the reality experienced by an object traveling in a curved (accelerated) world-line in a flat space-time and that experienced by an object traveling in a straight world-line (at rest) in a curved space-time" - and so the same mechanism must be at work in both cases. I must have that simplification wrong in a fundamental way somehow. This lead me to imagine that although no one of the travelling twin's accelerations, through which he's squeezing some time-savings out of flat [itex]M4 [/itex] space-time by taking a longer path than sis, would be a significant "bending" of space-time, but that integrated over his path the result would have to be equal (due to equivalence) to the curvature from mass that would have been required to provide the same difference of geodesic length if he had descended? from his sister (in altitude) in a curved space around that mass the whole time. I thought that was Einstein's "virtual field" allusion. So this is where your correction is very much to my confusion. Lot's to learn. But this has been a good set up for that chapter on curvature.