On Thursday, March 8, 2018 at 6:36:36 PM UTC-6, [email protected] wrote: > > > > 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 * >
The flow can be a path in a space with a Euclidean metric. On leaving JFK for Heathrow you fly pretty close to Iceland. It is just a minimal path on a sphere. That is another example. Time has not that much to do with it other than in the Lorentzian metric there is the light cone structure and hyperbolic transformations. LC > > 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.
