What is the Cause of Space Expansion?

[timmdeeg]

What does not happen is that the expansion of space gradually pushes the Earth further away without gravity being able to do anything about it!

So, on the scale of the solar system, the expansion of space has a tiny, negligible effect.

I think what one can say for sure is that if we pick a region in the ideal fluid model which is comparable in size to the solar system then there would be tiny effect on this scale. But how would you justify a tiny effect on the scale of the solar system even though this is gravitationally bound?

 

[PeroK]

I think what one can say for sure is that if we pick a region in the ideal fluid model which is comparable in size to the solar system then there would be tiny effect on this scale. But how would you justify a tiny effect on the scale of the solar system even though this is gravitationally bound?

I'm not sure I understand your question. If space is expanding, then it's expanding at all scales. There's no justification needed. What is needed is a calculation to confirm that it has a negligible effect on a given scale.

 

[timmdeeg]

I'm not sure I understand your question. If space is expanding, then it's expanding at all scales. There's no justification needed. What is needed is a calculation to confirm that it has a negligible effect on a given scale.

Well I was reasoning that the accelerated expansion creates tidal forces. And that these are way too week to stretch gravitationally bound systems like the solar system at all, but am not sure if this is correct. Whereas the ideal fluid model lacks gravitationally bound systems by definition.

The solar system is part of the milky way. So the average density exceeds the critical density. From this I wonder whether we expect any expansion locally at all.

 

[PeroK]

Well I was reasoning that the accelerated expansion creates tidal forces. And that these are way too week to stretch gravitationally bound systems like the solar system at all, but am not sure if this is correct. Whereas the ideal fluid model lacks gravitationally bound systems by definition.

The solar system is part of the milky way. So the average density exceeds the critical density. From this I wonder whether we expect any expansion locally at all.

I understand your question and I don't know the answer. In our solar system you would have to combine the local Schwarzschild geometry with the expansion geometry in some way. But, both are idealised solutions to spacetime on vastly different scales. And, of course, the local expansion is/would be infinitesimal in any case.

 

[PeterDonis]

I was reasoning that the accelerated expansion creates tidal forces

It creates (more precisely, it is a form of) tidal gravity. But tidal gravity, in itself, is not a force. What are often called "tidal forces" are really internal non-gravitational forces inside objects that prevent the individual atoms of those objects from moving on the trajectories that they would move on if they were moving solely in response to tidal gravity.

these are way too week to stretch gravitationally bound systems like the solar system at all

If we ignore the fact that gravity is not a force in GR, and think of a gravitationally bound system like the solar system as being held together by internal forces, which prevent its parts from moving on the exact trajectories that they would move on in response to the tidal gravity created by accelerated expansion, then it is true that the effect of that tidal gravity on the bound system is way, way too small for us to measure. But in principle the effect is there.

However, gravity isn't a force in GR, and a full GR analysis of something like the solar system embedded in a universe with accelerated expansion requires finding an appropriate metric. As it happens, there is one, at least heuristically; see below.

In our solar system you would have to combine the local Schwarzschild geometry with the expansion geometry in some way.

The Schwarzschild-de Sitter geometry (basically Schwarzschild spacetime with a cosmological constant added) is a known exact solution. I haven't seen a detailed analysis done of the case where the cosmological constant is very small (so the solution can be approximated by Schwarzschild plus a small perturbation), but intuitively I would expect it to show basically what I said above: you would still have stable orbits, they would just have slightly different parameters for the same Schwarzschild mass.

 

[timmdeeg]

I haven't seen a detailed analysis done of the case where the cosmological constant is very small (so the solution can be approximated by Schwarzschild plus a small perturbation), but intuitively I would expect it to show basically what I said above: you would still have stable orbits, they would just have slightly different parameters for the same Schwarzschild mass.

As I understand it the FRW model predicts the dynamical evolution of the universe globally thereby assuming an average matter density. In our universe the data are consistent with the assumption of a small cosmological constant. In the milky way however the matter density is higher than the critical density. I'm not sure if the Friedmann equations can be applied locally. If yes then it seems that from this point of view the milky doesn't participate in the global expansion. Hm, perhaps overdensity and gravitationally bound means the same.

 

[PeterDonis]

As I understand it the FRW model predicts the dynamical evolution of the universe globally thereby assuming an average matter density.

I'm not sure if the Friedmann equations can be applied locally.

I wasn't talking about using the FRW model to model something like the solar system. I was talking about using the Schwarzschild-de Sitter model, which is different: it is basically a model of an isolated gravitationally bound system in the presence of a cosmological constant, which, with a suitably chosen (very small) value of the cosmological constant, is a reasonable approximation to a model of a bound system like the solar system in our universe.

 

[timmdeeg]

I wasn't talking about using the FRW model to model something like the solar system. I was talking about using the Schwarzschild-de Sitter model, which is different: it is basically a model of an isolated gravitationally bound system in the presence of a cosmological constant, which, with a suitably chosen (very small) value of the cosmological constant, is a reasonable approximation to a model of a bound system like the solar system in our universe.

Whereby regarding the cosmological constant there seems to be a bridge to the FRW model in this approximation.

I understand that one can't model a bound system using the FRW model. Would you say that any considerations by interpreting the Friedmann equations locally like I attempted in #41 don't make any sense? Strictly these equations are based on the assumption of ideal homogeneity. I'm interested if they nevertheless provide conclusions regarding local inhomogeneities such, as regions with "overdensity" don't participate in the accelerated expansion or as super voids would expand faster than the universe in average.

 

[PeterDonis]

regarding the cosmological constant there seems to be a bridge to the FRW model in this approximation.

You would want to use the value for the cosmological constant that corresponds to our best current FRW-based model, yes.

Would you say that any considerations by interpreting the Friedmann equations locally like I attempted in #41 don't make any sense?

You can interpret the Friedmann equations locally, but you have to meet the conditions, one of which is that the density is the same everywhere. If that condition is not met, the equations aren't valid. But if, for example, you have a spherically symmetric (another condition for the FRW model to be valid) "bubble" of uniform density inside a spherically symmetric universe of some other density, you can apply the Friedmann equations inside the "bubble" just fine. The problem with applying the Friedmann equations locally in our actual universe is that the density is very, very far from being uniform on local scales.

There is ongoing work to develop more sophisticated models, not using the precise FRW metric (but the models could be, I think, described as FRW plus perturbations), that allow for variations in density. But AFAIK nobody has tried to apply them on scales as small as a single galaxy; we are still talking scales of tens to hundreds of millions of light years.

 

[timmdeeg]

You can interpret the Friedmann equations locally, but you have to meet the conditions, one of which is that the density is the same everywhere. If that condition is not met, the equations aren't valid. But if, for example, you have a spherically symmetric (another condition for the FRW model to be valid) "bubble" of uniform density inside a spherically symmetric universe of some other density, you can apply the Friedmann equations inside the "bubble" just fine.

Ok and thanks, this clarifies my question.

 

[KurtLudwig]

Yes.
This isn't really a meaningful statement either way; you can't say space is being created and you can't say it isn't. "Space being created" isn't a well-defined concept.
No; spacetime is curved. Your intuitions are used to flat spacetime; they don't work in curved spacetime.
No. Depending on what theory of quantum gravity finally pans out, it might turn out that spacetime is a field, or at least that it can be usefully modeled as one. But that goes beyond GR. As far as GR is concerned, spacetime isn't a field either, it's just geometry.
Which ones?
This is a good example of why it's a bad idea to try to learn science from pop science books.
According to our best current understanding of quantum gravity, if spacetime (not space) is in fact quantized (which is a better word than "granular"), we would not expect to see effects due to that until we got down to length scales on the order of the Planck length. That's about 20 orders of magnitude smaller than the smallest length scales we can currently probe. So we don't have any expectation of being able to test for quantum effects of spacetime or gravity any time soon.

Another possible test would be trying to spot violations of Lorentz invariance; but so far no such violations have been observed.
These two statements are mutually inconsistent. Which one do you want to discuss?

What is time? How does time arise? Is time the count of cycles?

 

[Mordred]

Simply a measure of rate of change or duration. It isn't some mythical substance but another property. Even under spacetime as per GR this definition does not change.

 

[PeterDonis]

What is time?

You're the one that made statements about what it is. I just asked you to make up your mind which of the two inconsistent things you said you want to pick.

As far as GR is concerned, time is just like length, except it's measured along timelike curves instead of spacelike curves.

 

[KurtLudwig]

Thanks for your reply. I have read the article on Special Relativity in Wikipedia. I do not yet fully understand all of the mathematics involved.

 

[Mordred]

Wiki in this case isn't particularly helpful particularly with its latest modifications.

While I can't buy you a textbook, I can offer a link to an open source written by another forum member

http://www.lightandmatter.com/sr/