What's the nothingness that our universe is expanding into?

[julcab12]

I guess we can ask this in a different way: is a universe with space, but without matter, energy and radiation possible in GR?

Nope. Nothing will cause the distortion or the curve so i don't know how will it work in GR. The model won't make sense at all. I bet you can figure that one out.^^

 

[PeterDonis]

is a universe with space, but without matter, energy and radiation possible in GR?

Yes. This universe is called "Minkowski spacetime", and is a valid solution of the Einstein Field Equation. This is why SR is a valid special case (or limiting case) of GR.

Nothing will cause the distortion or the curve so i don't know how will it work in GR.

This just means spacetime is flat, i.e., Minkowski spacetime. See my comment above.

 

[bahamagreen]

A usual verbal-logical approach might suggest that:

- if the universe is expanding
and
- if the universe is all there is
and
- if expansion requires expanding "into" anything
then
- the universe must be expanding into itself

There might be different ways to interpret whether that conclusion is meaningful or meaningless... I'm still thinking that a simple review of the current physics understanding of the answers to the deliberately naive questions in post #62 would help all around.

 

[PeterDonis]

if expansion requires expanding "into" anything

It doesn't. "Expansion" can be defined purely in terms of quantities intrinsic to the manifold.

 

[bahamagreen]

I find the phrase "mapping...onto itself" when searching on expanding mapping.
I find the Wiki definitions of:
homotopy - a continuous deformation...one function to another (in the same space?)
homeomorphism - a continuous deformation...one space to another

Are these what you mean by quantities intrinsic to the manifold?

 

[julcab12]

Yes. This universe is called "Minkowski spacetime", and is a valid solution of the Einstein Field Equation. This is why SR is a valid special case (or limiting case) of GR.
This just means spacetime is flat, i.e., Minkowski spacetime. See my comment above.

Yep. You're right (Sorry for that) i overstated the question thinking; 'If it has any physical meaning other than GR's mathematical model'. .

In the context of GR -- Field theory has that non-trivial vacuum solutions. Matter and energy has a gravitational potential which in term makes spacetime curved. In the absence of such gravitational effect (which we don't know if it will happen in reality or in the future) spacetime will appear flat.

 

[PeterDonis]

Are these what you mean by quantities intrinsic to the manifold?

No. I mean quantities that describe the intrinsic geometry of spacetime, or of families of curves in spacetime. One of these quantities is called the "expansion scalar" of the family of worldlines that describes "comoving" observers--i.e., observers that see the universe as homogeneous and isotropic. This quantity is positive, and provides an invariant way of specifying what "the universe is expanding" means.