On Sat, Jan 5, 2019 at 7:15 PM Brent Meeker <[email protected]> wrote:
> > > 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] 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. > I recommend Relativity Visualized: https://www.amazon.com/Relativity-Visualized-Lewis-Carroll-Epstein/dp/093521805X Jason -- 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.
