On Mon, Dec 31, 2018 at 2:46 PM Brent Meeker <[email protected]> wrote:
> > *But you do know that the straightest path between events in Minkowski > spacetime * > You do know don't you that Minkowski space is non-Euclidean because it treats time differently than the other 3 dimensions but it is not curved so it is useful in Special Relativity but not in General Relativity or anything involving gravity. *> is the longest duration path don't you. * And I hope you know the path yielding the longest proper time duration is not the same as having the longest distance through spacetime as time is just one dimension and spacetime involves 4. If r is the distance in space and c the speed of light then the square of the distance in spacetime between two events is r^2-(ct)^2, so the largest possible t (proper time) will give smallest possible distance through spacetime. > > The Google definition seems not to consider mixed signature metrics. Google said a geodesic is the shortest distance between 2 points on a curves surface, time is just one dimension and you can't have a curved surface with just one dimension. > > in Minkowski space there is only one time-like geodesic that connects > any given pair of time-like separated events, True but curved spacetime is not Minkowski space and you can have more than one one time-like geodesic connecting them. > * > Even a twin paradox can be constructed this way by having the > traveling twin's velocity reversed by the gravity of massive body far from > the stay-home twin; which in GR is not a force.* > Then one twin would encounter a intense gravitational field that the other twin did not and gravity will slow down a clock just like moving fast will. > *What "Feynman's example"?* I posted it a few days ago. it comes from "Surely you're joking Mr. Feynman" he posed this puzzle to an assistant of Einstein: "Y*ou blast off in a rocket which has a clock on board, and there's a clock on the ground. The idea is that you have to be back when the clock on the ground says one hour has passed. Now you want it so that **when you come back, your clock is as far ahead as possible. According to Einstein, if you go very high, your clock will go faster, because the higher something is in a gravitational field, the faster its clock goes. But if you try to go too high, since you've only got an hour, you have to go so fast to get there that the speed slows your clock down. So you can't go too high. The question is, exactly what program of speed and height should you make so that you get the maximum time on your clock?"* *"This assistant of Einstein worked on it for quite a bit before he realized that the answer is the real motion of matter. If you shoot something up in a normal way, so that the time it takes the shell to go up and come down is an hour, that's the correct motion. It's the fundamental principle of Einstein's gravity--that is, what's called the "proper time" is at a maximum for the actual curve."* John K Clark -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
