Questions about space and matter

[Histspec]

Another way to ask is is space an attribute of matter, or is it just something matter can occupy and shape? Intuitively I am inclined to think the former.

This is somehow related to Mach's principle (at least in Einstein's reading): Are all forms of gravitational fields, the spacetime metric, and the inertia of bodies, fully determined by the masses of the universe? A nice historical description of this problem was given by Janssen:
https://philsci-archive.pitt.edu/4377/
See particular section 5. Fourth attempt: Mach’s principle and cosmological constant.

Einstein initially hoped that Mach's principle holds in GR, but it was soon showed by DeSitter that GR allows for a solution with vanishing matter density, while at the same time a single test body retains its inertia. Einstein was not convinced, so he wrote to DeSitter in 1917:

It would be unsatisfactory, in my opinion, if a world without matter were possible. Rather, it should be the case that the $g_{\mu\nu}$ -field is fully determined by matter and cannot exist without the latter. This is the core of what I mean by the requirement of the relativity of inertia.

Anyway, there was nothing wrong with DeSitter's solution, which led Einstein (among other reasons) to abandon Mach's principle, so he wrote in 1954:

In my view one should no longer speak of Mach’s principle at all. It dates back to the time in which one thought that the “ponderable bodies” are the only physically real entities and that all elements of the theory which are not completely determined by them should be avoided. (I am well aware of the fact that I myself was long influenced by this idée fixe)

 

[PeterDonis]

it was soon showed by DeSitter that GR allows for a solution with vanishing matter density, while at the same time a single test body retains its inertia

De Sitter didn't have to show that: flat Minkowski spacetime is also such a solution. (So is Schwarzschild's vacuum solution, which was published in 1916, the first solution to be discovered, but nobody understood that at the time--this solution was only thought to be valid for the spacetime surrounding an ordinary non-rotating planet or star, and the fact that it can also describe a black hole was not realized for another two decades.)

What de Sitter showed (that Einstein didn't expect) was that adding the cosmological constant to the field equations still allowed solutions with nonzero spacetime curvature but no matter, in which test bodies retain inertia. Einstein had hoped that would not be the case, as Janssen remarks in the paper you reference.

 

[Tomas Vencl]

…….

The question is does matter "create" space(time)?….

I think that solving this guestion honestly is behind relativity framework, and needs deeper quantum gravity theory. For example:
https://en.wikipedia.org/wiki/Causal_dynamical_triangulation

 

[Histspec]

What de Sitter showed (that Einstein didn't expect) was that adding the cosmological constant to the field equations still allowed solutions with nonzero spacetime curvature but no matter, in which test bodies retain inertia. Einstein had hoped that would not be the case, as Janssen remarks in the paper you reference.

Yes, I should have added that DeSitter's vacuum solution is related to Einstein's modified field equations that include the cosmological constant. Anyway, the point is that GR solutions such as this contributed, at least in the long term, to Einstein's abandonment of his idea quoted above (inspired by Mach's principle), that the possibility of a world without matter is unsatisfactory and that the $g_{\mu\nu}$-field cannot exist without matter....

 

[PeterDonis]

GR solutions such as this contributed, at least in the long term, to Einstein's abandonment of his idea quoted above (inspired by Mach's principle), that the possibility of a world without matter is unsatisfactory and that the $g_{\mu\nu}$-field cannot exist without matter....

Yes, agreed.