Is the GR explanation for how gravity moves things?

[bcrelling]

Is this a simple GR explanation for how gravity moves things?

In SR, the dilation effects happen in a way such that the speed of light is maintained for all observers.

In GR, mass is considered denser regions of spacetime.

What I was thinking:
It takes longer for light to precipitate through denser regions of spacetime(gravitational fields) so the only way the speed of light can be maintained for all observers is if they move closer to one another- and so we get gravitational force.

Can anyone confirm or deny this?

 

[pervect]

I'm not aware of any creditable source that claims

In GR, mass is considered denser regions of spacetime.

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.

 

[bcrelling]

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.

Ok thanks, I must have heard that from a pop science source or something.

However the way light is bent by gravity is consistent with the way light is bent when passing into a denser medium. Also laws of refraction indicate that at a certain density change gradient total internal reflection happens- which would be analogous to a black hole's event horizon.

 

[A.T.]

However the way light is bent by gravity is consistent with the way light is bent when passing into a denser medium.

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.

 

[pervect]

Gravitation can be interpreted as varying density of a space-propertime manifold.

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.

 

[A.T.]

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.

 

[FredericGos]

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.

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

 

[Dale]

Gravitation can be interpreted as varying density of a space-propertime manifold.

I don't even think that space-propertime has a manifold structure, at least not one that corresponds to anything physical. Please provide a valid reference for this.

 

[martinbn]

What is space-propertime?

 

[A.T.]

I don't even think that space-propertime has a manifold structure, at least not one that corresponds to anything physical.

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

 

[Dale]

Ok thanks, I must have heard that from a pop science source or something.

However the way light is bent by gravity is consistent with the way light is bent when passing into a denser medium. Also laws of refraction indicate that at a certain density change gradient total internal reflection happens- which would be analogous to a black hole's event horizon.

It think that it is consistent in a hand waving analogy way, but I do not think that it is consistent in a quantitative way. At least, I have never read a valid reference that made that analogy and defended it quantitatively. So I would not rely on this idea for a black hole.

In particular, with a black hole even purely radial light cannot escape whereas total internal reflection never occurs for purely radial light. Also, inside the black hole light is forced inwards everywhere, whereas total internal reflection is only a surface effect.

 

[Dale]

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

A manifold is a topological structure with a notion of connectedness. In spacetime that mathematical notion of connectedness corresponds to physical events which could be joined by a continuous path.

I don't see any similar notion of connectedness in space propertime. Please don't claim that it is a manifold unless you can provide a valid reference supporting that claim.

 

[VeryConfusedP]

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.

 

[WannabeNewton]

What exactly is space propertime?

 

[Dale]

I just think calling gravity "spacetime curvature," which it is, is very tough to understand

Sure, but there is no reason to think that nature shouldn't be very tough to understand.

Did you have an actual question? We don't have answers for all questions, and not all of the answers we do have are easy, but there is no reason to think that you cannot learn the answers we do have as well or better than me or others here.

 

[PeterDonis]

calling gravity "spacetime curvature," which it is, is very tough to understand

Actually, the more precise way of stating this is that *tidal* gravity is spacetime curvature. So understanding spacetime curvature just means understanding tidal gravity. Kip Thorne, for example, spends a good deal of time in his book Black Holes and Time Warps talking about this. (If you're looking for a book about GR written for non-scientists, with a minimum of math, I would highly recommend Thorne's book, btw.)

 

[pervect]

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

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".