On 2/19/2019 3:15 AM, [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] <javascript:> 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
*
No. A tensor, like a vector, is a geometric object. It has different
representations depending on the coordinate system, but those
representations transform like a real object that is independent of the
coordinate system.
Brent
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