Space-time geometry in the absence of matter

[rodsika]

Hi, is Spacetime geometry there even without the presence of matter or does matter produced Spacetime?

Or in other words. If the universe is completely empty without matter. Is there a Spacetime geometry?

 

[Dale]

None of the universes discovered to date have been completely empty without matter.

 

[bcrowell]

Hi, is Spacetime geometry there even without the presence of matter or does matter produced Spacetime?

GR describes spacetime as having its own dynamics. For example, you can have spacetimes that have negligible matter in them, but that have all kinds of complicated, interacting gravitational waves. In this sense, GR is non-Machian: http://en.wikipedia.org/wiki/Mach's_principle If there is some small matter content, then you can have observers, and they can observe the dynamics of this universe, which proceeds without any significant effect from matter.

Or in other words. If the universe is completely empty without matter. Is there a Spacetime geometry?

If it's really, truly, literally *completely* empty, then you can't have observers, so there would be no way to measure its geometry. If it's only *approximately* empty, then you can have all kinds of spacetimes -- there are many, many known vacuum solutions to the Einstein field equations. If you impose homogeneity and isotropy, then you can get the Milne model http://en.wikipedia.org/wiki/Milne_model , or, I think, variations on that theme with different topologies.

 

[rodsika]

GR describes spacetime as having its own dynamics. For example, you can have spacetimes that have negligible matter in them, but that have all kinds of complicated, interacting gravitational waves. In this sense, GR is non-Machian: http://en.wikipedia.org/wiki/Mach's_principle If there is some small matter content, then you can have observers, and they can observe the dynamics of this universe, which proceeds without any significant effect from matter.



If it's really, truly, literally *completely* empty, then you can't have observers, so there would be no way to measure its geometry. If it's only *approximately* empty, then you can have all kinds of spacetimes -- there are many, many known vacuum solutions to the Einstein field equations. If you impose homogeneity and isotropy, then you can get the Milne model http://en.wikipedia.org/wiki/Milne_model , or, I think, variations on that theme with different topologies.

Does Spacetime geometry only cause gravity or does it also produce positions of objects too? For example. Supposed just for sake of discussion, there was matter like a Cat but without the presence of spacetime geometry. Would the cat dissolve into a blob of matter soup (due to the absense of the geometry and possibly positions) or would the cat still have positions but just lack gravitational influence?

 

[bcrowell]

Does Spacetime geometry only cause gravity or does it also produce positions of objects too? For example. Supposed just for sake of discussion, there was matter like a Cat but without the presence of spacetime geometry. Would the cat dissolve into a blob of matter soup (due to the absense of the geometry and possibly positions) or would the cat still have positions but just lack gravitational influence?

I don't think there is any way to answer that, because we don't have any physical theory that doesn't have a spacetime geometry. The difference between GR and other well established theories is that in GR, the spacetime geometry is not fixed a priori.