On Sunday, March 11, 2018 at 10:30:46 AM UTC-4, agrays...@gmail.com wrote: > > > > On Saturday, March 10, 2018 at 10:54:50 PM UTC-5, Brent wrote: >> >> >> >> On 3/10/2018 7:32 PM, agrays...@gmail.com wrote: >> >> >> >> On Saturday, March 10, 2018 at 10:09:45 PM UTC-5, Brent wrote: >>> >>> >>> >>> On 3/10/2018 5:04 PM, agrays...@gmail.com wrote: >>> >>> >>> >>> On Sunday, March 4, 2018 at 11:35:24 PM UTC-5, agrays...@gmail.com >>> wrote: >>>> >>>> I don't think so. I think its equations of motion mix time and space, >>>> so if time increases, spatial position must change. That is, the >>>> assumption >>>> that time increases, produces changes in spatial position. CMIIAW. AG >>>> >>> >>> Here's a related question; if you assume a 4d spacetime manifold, how >>> does one imagine the shortest path between two points, aka a geodesic path, >>> using the Lorentzian metric? AG >>> >>> >>> In the Lorentz metric a geodesic is the longest path between two >>> time-like events. >>> >>> Brent >>> >> >> Right; we've discussed this in the past. But if that's true, why choose >> motion along a geodesic in spacetime for a model of gravity >> >> >> He didn't "choose" it, it's implicit in the motion being force-free. As >> Russell pointed out it's implied by conservation of energy-momentum. >> >> Brent >> > > Where exactly is it argued that conservation of energy-momentum implies > motion along a geodesic in the absence of external forces? TIA, AG >

I suppose, for say a Lorentzian metric, one could define a geodesic as the path where the length between two points is maximal, that it's unique, and all other paths do not conserve energy-momentum. Offhand, the proof doesn't seem obvious. Does Epstein do it? AG > if it's the LONGEST path between two time-like events. Wasn't Einstein >> motivated by the fact that a geodesic along a sphere using the Euclidean >> metric for path length, is the SHORTEST distance between two points on a >> sphere? AG >> -- >> 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-li...@googlegroups.com. >> To post to this group, send email to everyth...@googlegroups.com. >> Visit this group at https://groups.google.com/group/everything-list. >> For more options, visit https://groups.google.com/d/optout. >> >> >> -- 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 post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.