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submitted 3 weeks ago by muntedcrocodile@lemm.ee to c/science_memes@mander.xyz

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[-] OrganicMustard@lemmy.world 1 points 3 weeks ago* (last edited 3 weeks ago)

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.

[-] kogasa@programming.dev 1 points 3 weeks 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.