Space-time geometry in the absence of matter

In summary: It's something that emerges from the equations as you try to solve them. So I guess you could say that without a spacetime geometry, there would be no gravity. But I don't think there is a clear answer to your question.
  • #1
rodsika
279
2
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?
 
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  • #2
None of the universes discovered to date have been completely empty without matter.
 
  • #3
rodsika said:
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.

rodsika said:
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.
 
  • #4
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.

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?
 
  • #5
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?

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.
 

1. What is space-time geometry in the absence of matter?

Space-time geometry is a mathematical model that describes the structure of the universe in terms of three dimensions of space and one dimension of time. In the absence of matter, space-time is considered to be flat and follows the principles of Einstein's theory of general relativity.

2. How does the absence of matter affect space-time geometry?

In the absence of matter, space-time is not distorted by the presence of massive objects. This means that the geometry of space-time is simpler and easier to understand. Without the effects of gravity, space and time are considered to be independent of each other.

3. Can space-time still exist without matter?

Yes, space-time can exist without matter. In fact, the majority of the universe is made up of empty space. Space-time is a fundamental aspect of the universe and does not depend on the presence of matter for its existence.

4. What are some implications of space-time geometry in the absence of matter?

One implication is that the laws of physics, particularly Einstein's theory of general relativity, can be simplified and easier to study in the absence of matter. This can also help us understand the fundamental nature of space and time. Additionally, the absence of matter in space-time allows for the possibility of other phenomena, such as dark energy and dark matter, to play a larger role in the structure of the universe.

5. How does our understanding of space-time geometry in the absence of matter impact our knowledge of the universe?

Studying space-time in the absence of matter can give us a deeper understanding of the fundamental principles that govern the universe. It can also help us make predictions about the behavior of the universe, such as the expansion of space and the movement of celestial bodies. Additionally, it can aid in the development of new technologies and advancements in space exploration.

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