On 1/5/2019 4:56 PM, [email protected] wrote:
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, *
Right. They are related, but not in a simple way. Each increment of coordinate time along the paths contributes to the increment of proper time, but it is only one term of several.
Brent -- 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.
