On Tuesday, February 19, 2019 at 4:15:55 AM UTC-7, [email protected] wrote: > > > > On Monday, February 18, 2019 at 3:37:19 PM UTC-7, Brent wrote: >> >> >> >> On 2/18/2019 2:05 PM, [email protected] wrote: >> >> *Is it correct to say that in 3-space with the Euclidian metric the >> geodesic is the path determined by minimal distance between two points, >> whereas in 4-space with the Lorentzian metric it's the maximal distance? >> TIA, AG* >> >> >> That's right as far as it goes. "Geodesic" is a general term in >> geometry, applying to curved spaces as well as flat and it refers to paths >> that are extremal. So in general relativity there can be different >> geodesics between the same two events, each of which is a local extremal. >> > > *Do you mean the metric tensor differs, depending on the coordinate > system? TIA, AG * >
*I don't understand your comment. Curvature of space-time should be independent of coordinate systems, so how can there be different extremals for two fixed events in the manifold? AG* > >> 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.
