On Thursday, March 8, 2018 at 2:52:11 PM UTC-5, Lawrence Crowell wrote: > > Modern physics tends to operate on the idea of geodesics and geometric > determined flows. >
*Do you agree that the fact that the flow is geodesic is ultimately a postulate, and the existence of the flow is rooted in the monotonic increase of time? AG * A geodesic is "determined" from an initial point, which can just be a point > where data is specified instead of some point of origin, where the position > on a manifold and the tangent vector are specified. From there the dynamics > is completely determined. For a quantum system things are more nuanced with > there being a bundle of paths with some congruent condition given by > diffeomorphism and Weyl transformations "modded out." > > In spacetime and general relativity these geodesic flows obey the geodesic > deviation equation dU/ds = R(UV)V, and are determined by the curvature of > spacetime. Here U = dx/ds is the relative velocity between two test masses. > Now we might imagine a tether between these two test masses. Now their > relative separation distance is constant and the two masses are not on a > geodesic path. However, the center of mass of the two are on a geodesic. > The individual masses are then on nongeodesic paths due to the material > forces of the tether. > > LC > > On Thursday, March 8, 2018 at 6:24:59 AM UTC-6, [email protected] wrote: >> >> >> >> On Wednesday, March 7, 2018 at 11:04:09 PM UTC-5, Brent wrote: >>> >>> >>> >>> On 3/7/2018 5:39 AM, [email protected] wrote: >>> >>> *Thanks for your time and effort, but I don't think you understand my* >>> *question. Suppose a test particle is restrained spatially, say in * >>> *the Sun's gravitational field. When released, it starts to move >>> (toward * >>> *the Sun). How does GR explain this motion? By the advance of time? AG* >>> >>> >>> Time was advancing all along. Your restraint was a force causing the >>> particle to follow a non-geodesic path through space-time. When you >>> released it, it then followed the "straightest path possible", i.e. a >>> geodesic. >>> >>> Brent >>> >> >> So time is the "culprit". What has this resumption of spatial motion >> (along a geodesic in spacetime) have to do with conservation of momentum, >> if at all ? TIA, 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 [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.
