this post was submitted on 29 Nov 2024
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Fuck geometry (lemm.ee)
submitted 1 month ago by [email protected] to c/[email protected]
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[โ€“] [email protected] 1 points 1 month ago* (last edited 1 month ago) (1 children)

It depends which metric definition are you using. The one I wrote is a pseudo-Riemannian metric that is not positive defined.

Normally physicists use that generalized metric definition because spacetime in most cases has a metric signature of (-1, 1, 1, 1). Points with zero distance are not necessarily the same point, they just are in the same null geodesic.

[โ€“] kogasa 1 points 1 month ago

You're talking about a metric tensor on a pseudo-Riemannian manifold, I'm talking about a metric space. A metric in the sense of a metric space takes nonnegative real values. If you relax the condition that distinct points have nonzero distance, it's a pseudometric.