The discussion centers on the nature of spacetime geometry in the absence of matter, exploring whether spacetime exists independently of matter and how it behaves in a completely empty universe. Participants examine concepts from general relativity (GR) and consider hypothetical scenarios regarding the relationship between spacetime and matter.
Participants express multiple competing views regarding the existence and nature of spacetime geometry in the absence of matter. The discussion remains unresolved, with no consensus reached on the implications of a completely empty universe.
Limitations include the dependence on definitions of "empty" and "geometry," as well as the unresolved nature of the hypothetical scenarios presented.
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.rodsika said:Hi, is Spacetime geometry there even without the presence of matter or does matter produced Spacetime?
rodsika said:Or in other words. If the universe is completely empty without matter. Is there a Spacetime geometry?
bcrowell said: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.
rodsika said: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?