Modern physics tends to operate on the idea of geodesics and geometric determined flows. 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.
