On Sunday, January 6, 2019 at 12:13:16 AM UTC, Brent wrote: > > > > On 1/5/2019 1:28 PM, [email protected] <javascript:> wrote: > > The relation is provided by the metric. If you choose different >> coordinate systems (e.g. cylindrical or spherical or whatever) then there >> is different metric tensor. So the integral along the path of g_ab dx^a >> dx^b is the same. >> >> Brent >> > > *I assume you're showing why the proper time along a given path is the > same for all observers, and this has nothing to do with coordinate time > being unrelated to proper time. AG * > > > Coordinate time between events A and B is just delta(x^0) = x^0(B) - > x^0(A). Just like the longitudinal distance between LA and NY is > Long(LA)-Long(NY). But the driving distance between LA and NY depends on > the path you take and is an integral along that path which includes changes > in latitude: > > S^2 = INT_path g_ab dx^a dx^b = INT_path [ dlong*dlong*cos^2(lat) + > dlat*dlat] > > Notice the cos^2 factor because the space isn't flat. > > So in GR coordinate time is related to proper time; it contributes a term > in accordance with the metric that describes the curvature of the > spacetime. But there are other terms from the spatial coordinates and even > cross terms and the terms are weighted by the metric factors that describe > the shape of the space. > > Brent >
*I think you mean that coordinate time is related to proper time as a path is traversed, even though elapsed coordinate time is the same for all paths having the same initial and endpoints in spacetime. 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.
