Rubber Sheet Analogy: How Mass Bends Spacetime

[Abtinnn]

I have a question on GR.
To what extent is the rubber sheet analogy correct?
To be more specific, in that analogy, an object with mass M bends the 2-D space (the sheet) into a third dimension (the sheet goes downward). Does this imply that in out universe, an object with mass bends the spacetime into another extra dimension? Sorry about the wording of the question...

 

[A.T.]

https://www.physicsforums.com/threa...ace-thus-causing-gravity.803213/#post-5042220
https://www.physicsforums.com/threa...visualization-of-gravity.726837/#post-4597121

 

[Matternot]

Is it possible for us to know hyperbolic/Minkowski space looks like?

 

[phyzguy]

You shouldn't take this analogy very seriously. It is just a picture to help you see how curvature can alter the path of an object. There are several areas where the analogy breaks down:

(1) The curvature in GR is not a curvature of our 3-dimensional space. It is a curvature of our 4-dimensional space time. In fact, in the Solar System, for example, almost all of the curvature that causes the motion of the planets is curvature in the time components of the curvature tensor.

(2) It is possible for our 4-dimensional space time to be curved without being embedded in a higher dimensional space. You can't conclude that just because it is curved it must be curved in a higher dimensional space. We just use the curvature of a 2D membrane embedded in 3D space to help us visualize what is happening.

 

[Abtinnn]

Thanks a lot for the responses!

(2) It is possible for our 4-dimensional space time to be curved without being embedded in a higher dimensional space. You can't conclude that just because it is curved it must be curved in a higher dimensional space. We just use the curvature of a 2D membrane embedded in 3D space to help us visualize what is happening.

Is there a way for us to find out whether or not our spacetime is curved in a higher dimension?

 

[A.T.]

Is there a way for us to find out whether or not our spacetime is curved in a higher dimension?

Curved spacetime is a mathematical model of nature. In the GR version of that model no higher dimensions are assumed, because they are unnecessary. See:

http://en.wikipedia.org/wiki/Occam's_razor

However, embedding of curved 2D slices of spacetime into higher dimensional non-curved 3D spaces can be useful for visualization. And theories other than GR might postulate higher dimensional spaces, if it's necessary.

 

[phyzguy]

Is there a way for us to find out whether or not our spacetime is curved in a higher dimension?

Not that I am aware of. There are people looking for the imprint of collisions between our observable universe and other "multi-verses" that could have happened during the period of inflation. If these are found (they have not been), this might be evidence that our universe is embedded in a higher dimensional space.