On Fri, Jan 17, 2025 at 1:41 PM Alan Grayson <agrayson2...@gmail.com> wrote:
*> IMO SR can handle curved spacetime. All one has to do is make the > partitions very fine, so we're approximating inertial motion along very > short paths. AG * *All one has to do? Well yes but that's easier said than done, it took Einstein 10 years of grueling work to figure out exactly how to do it, and the effort nearly killed him, he got sick, lost 50 pounds and figured he would die soon. Fortunately he did not. One of the most difficult things he had to figure out was how to measure distance in 4D non-Euclidean spacetime that was curved in any given way that was useful and never produced self-contradictory results. Mathematicians insist that distance must have the following properties:* *1) Non-negativity: d(x,y) ≥ 0 2) Identity of indiscernibles: d(x,y) = 0 if and only if x = y 3) Symmetry: d(x,y) = d(y,x)4) Triangle inequality: d(x,z) ≤ d(x,y) + d(y,z)* *After years of false starts and dead ends Einstein eventually found a measuring stick that worked, it's called the Metric Tensor. * *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* tg1 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/everything-list/CAJPayv0z3OUqVet%3D1f-%2BQuGrS0eH2em_-brfmP__bNuxhXF%3DAA%40mail.gmail.com.
