A question about curved space

[Half_Man_Half_Wit]

@Exapno_Mapcase

Describing space with a geometry seems to leave the basic question of what space is unresolved. The differences between geometries aren’t familiar and no matter which geometry actually describes the behavior of space it fails to explain what space is so as to be curved that way in the first place.

Well, I don’t think there really is anything that spacetime is apart from this geometry – i.e. apart from the gravitational field itself.

My representing space as fundamentally a series of mathematical points may not be going over with others, but it helps me.

The problem with this is, technically, it’s wrong – Einstein devised a rather clever argument, called the hole argument, which essentially shows that the notion of a ‘point on spacetime’ has no physical meaning – all one can really talk about are coincidences of spacetime trajectories, i.e. places where one thing meets another. The reason for that is essentially that general relativity is invariant under arbitrary coordinate changes.

[KellyCriterion]

Thank you for asking this question, Hambil.

That image has also bugged me each and every time I’ve seen it (link is broken for me but I know the image). I never would have had the capability/energy to put in to words like you did.