Is the GR explanation for how gravity moves things?

I'm not aware of any creditable source that claims

GR in the standard treatment models the curvature of space-time via the Riemann curvature tensor. This is a rank 4 tensor with 4x4x4x4 elements (with about 20 different independent values). The important part of the Riemann curvature are the Ricci and the Einstein tensors, which around 10 degrees of freedom. None of these degrees of freedom is generally interpretable as a "density" to the best of my knowledge.

 

Gravitation can be interpreted as varying density of a space-propertime manifold. Fixed stationary objects closer to the mass advance slower along the the propertime axis, so they age slower (gravitational time dilation). If you let the object fall, it will deviate from the purely temporal path, towards the denser region, and therefore start moving in space.

Note: This is just an analogy. Worldlines in space-time are different than light-paths in space.

 

Do you have a reference for anyone who actually does this?

It sounds too oversimple to be useful to me, but I'm willing to look at published references.

 

It might be oversimplifying. It is meant as an alternative to embedding diagrams, which require a higher dimensional embedding space, so you can effectively just visualize a curved 2D slice. Epstein mentioned it in "Relativity Visualized", which is a pop-sci book without math.

 

But isn't the energy-momentum tensor on the other side of the equation about density? I thought that T00 was energy density?

 

What is space-propertime?

 

What do mean exactly by "manifold structure that corresponds to something physical"?

 

Ignorant people like myself, I believe, get a bit confused when professionally trained physicists like DaleSpam and Peter Donis, people who understand gravity entirely, try to explain gravity as spacetime curvature. Peter and many others have helped tremendously, but I just think calling gravity "spacetime curvature," which it is, is very tough to understand, when most people were taught that gravity is an apple being attracted to the earth's surface (and this CAN make some people believe that the apple, if dropped in space, would fall, fall, fall for eternity, as if space is some deep pit, when it's really just going to be suspended in space, as long it's removed from curvatures being created by other bodies of mass). That's what was so troubling for me. Honestly, I think it would be SO much easier if the word gravity was replaced with either Spacetime Curvature or some other word of phrase. The word gravity, for people like myself, is just far too associated with that dang apple that fell from that tree in England--Newtonian interpretations of gravity seem to confuse people like myself, thereby causing us not to catch on to Einsteinian gravity as quickly as we could. Additionally, I think the word WARPING of spacetime is much easier to understand for lay men like myself. I cannot completely visualize the curves demonstrated by Tensor Calculus, but the word "warping" is a word that my mind can identify with. I say, Okay, you have spacetime with no mass (perhaps in deep pockets of space) and it's smooth--that's how my brain understands it. But then with the presence of matter and energy, it becomes warped.

That's my two cents. I'm not saying I'm right in everything I said, but these ways of negotiating the concepts of general relativity satiate my mind.

 

What exactly is space propertime?

 

Yes, it's pefectly OK to say that matter has an energy density The simplest totally correct formulation I know of of GR is due to Baez, http://math.ucr.edu/home/baez/einstein/ "The Meaning of Einstein's Equation".

It uses the volume of a ball of free-falling coffee grounds, initially at rest and arranged in a sphere, to characterize the gravity of the matter contained within said sphere of weightless coffee grounds.

The second derivative of the volume of the sphere turns out to be equal to certain properties of the enclosed the matter - namely the sum of the energy density, or T^00, aded to the sum of pressures on all three axes (T^11, T^22 and T^33).

But I don't see how you'd go from "the second derivative of the rate of change of volume of a sphere of coffee grounds" to "density of space" offhand, if you're trying to put the equation in the form "density of space == density of matter".