Is gravity really a force of universal attraction?

[Pesj]

One popular and credible theory on the overall shape of the universe is the positively curved universe. In my mind that is the 3-sphere which is connected and finite sort of like in the balloon analogy. And the following discussion regards such a universe I think.

As I understand the regular discussion about expansion and gravity; a certain amount of mass would eventually stop the expansion of space and turn the process into a crunch. If gravity extends in all directions between all things (massive objects) shouldn´t the overall attraction or slowing of expansion due to gravity be zero. What I mean is that the attraction along one direction cancels the effect of gravity in the opposite direction for objects on roughly the opposite side of the 3-sphere. So on the universal scale the attraction cancels out and the amount of mass is irrelevant (at least the gravitational effects) for the rate of expansion. Or not? If the overall attraction would be sort of zero, what is being observed regarding expansion and curvature would be in a different light I guess. It would happen no matter how much matter there is.

Haven´t seen a discussion about this and i´m interested in hearing some input on this idea.

 

[hadsed]

Well you would think that inflation would decelerate, but there's this pesky thing about it and that is that it isn't decelerating. I'm not sure at the moment what the mainstream idea amongst expert cosmologists is because it seems like it's constantly changing, but I would think that the more logical conclusion would be the heat-death of the universe. Having said that, your explanation would make sense if it were not for the weird 'properties' or 'behaviors' of inflation and if everything were completely uniform. I think the fact that the universe is not completely symmetrical in every which way would mean that your model might not work quite so well.

Of course, no one really knows what's going to happen to the universe or even what exactly has happened to it.

 

[tom.stoer]

There are two answers:
1) If you think about the balloon analogy you may consider gravity as something like the intrinsic tension of the ballon; so there is no additional force acting on the balloon which tends to shrink it; it's the balloon itself.
2) The effect of (homogeneous distribution of) matter or radiation is exactly solved in the Friemann Robertson Walker models; here the recollaps is an exact result; perhaps it's not so easy to interpret this but this is not a weakness of FRW but of the balloon analogy :-)

Things become more interesting if you add a comsomological constant. b/c density of matter decreases when the universe expands wheras the cc value remains fixed, for large times the cc dominates; the universe can then be described by a vacuum solution universe w/o matter. Now it depends on the sign of the cc whether this causes accelerated expansion (as most people believe in today) or not .

 

[Pesj]

There are two answers:
1) If you think about the balloon analogy you may consider gravity as something like the intrinsic tension of the ballon; so there is no additional force acting on the balloon which tends to shrink it; it's the balloon itself.
2) The effect of (homogeneous distribution of) matter or radiation is exactly solved in the Friemann Robertson Walker models; here the recollaps is an exact result; perhaps it's not so easy to interpret this but this is not a weakness of FRW but of the balloon analogy :-)

1) This makes sense if space was considered to be the source of gravitation, which it is not. I don´t know the math around this obviously but I don´t agree with your analogy.
2)Objects gravitate toward each other because of their mass, if the universe is a 3-sphere or closed and homogenic/isotropic the overall attractive/inward force could be virtually zero. In my mind it`s sort of a statistical cancellation on the universal scale, not that everything is exactly equally distributed on the surface of the 3-sphere. Gravity is in this perspective locally the same as always but looses it´s theoretical function as a brake on the expansion on the universal scale.

If this is not possible please explain why not.

 

[tom.stoer]

Regarding 1) I think it doesn't make sense to discuss this in more detail. If the balloon analogy fails or if you don't like it this is due to the fact that it's an analogy and that it has certain limitations. So we have to talk about full GR instead.

Regarding 2) you have to study the FRW equations in detail.

There is one statement which is misleading, namely

... if the universe is a 3-sphere ... the overall attractive/inward force could be virtually zero. In my mind it`s sort of a statistical cancellation ...

Please look at the balloon again. Think about homogeneously distributed matter on the surface of the balloon. What happens? The matter does not start to accelerate along the baallon surface as there is no preferred direction along which it could move. So the matter distribution will stay homogeneous forever.

But your inward force is not cancelled! The matter will certainly slow down the expansion of the balloon. If you add enough matter (beyond the critical density) the expansion will stop eventually and the balloon will start to contract again. Looking at the balloon it is clear that there is no "statistical cancellation" of this "inward force".

Of course the analogy is misleading b/c in the language of Riemann geometry there is no direction "perpendicular to the universe". This is the drawback of the balloon analogy: it looks like as if there is a hyperspace into which the universe is embedded. This is not the case. But the overall effect of matter looks something like such an "inward force".

 

[Pesj]

Ok, I think this is very interesting but studying FRW-equations will for me take a long time, so I continue our discussion.

Again, in my understanding the universal effect of gravity seems to (possibly)be different if you use topologically different models. I understand how gravity slow down the expansion of a universe looking like a 3-ball (ball). I do think that my point is that the attraction has to act in the "surface" of the 3-sphere and not radially through hyperspace. So two objects on a 3-sphere telling each other exactly equally much to move in six(?) different directions would not change their ways. They would move on with their business, being expanding the distance between them. Perhaps I´m wrong in thinking that gravity is best explained as a preferred direction. Because if you view it more like two objects having some kind of tension between them the slowing of expansion could perhaps even be greater in a 3-sphere than in a 3-ball

Is it possible for you Tom to explain the outcome of FRW in words for me to better understand the mathematical approach?

 

[tom.stoer]

First of all I have to stress that the balloon model is a model only. Mathematically gravity acts along the surface, not perpendicular to it (there is no hyperspace in GR; I think you will agree).

Now think about a balloon with homogeneously distributes matter. The overall attraction seems to cancel (as there is no preferred direction), but the equations tell us, that there is this slowing-down-effect, so the idea of a preferred direction is not sufficient. I think any statement beyond that must use the FRW-equations in detail.

If I have time I can start to elaborate on the FRW equations ...

 

[Ich]

The overall attraction seems to cancel (as there is no preferred direction)

That doesn't mean that there is no effect, it just means the the effect has no preferred direction, too. The decelerating effect (slowing down the expansion) can be calculated or understood in principle with Newtonian Gravity. It can't handle different topologies, though. And is generally very clumsy, as it introduces a lot of unnecessary concepts, like gravitational force and acceleration, which are directional quantities.

 

[tom.stoer]

I agree that in ART (FRW models) the decelerating effect exists but that there is no preferred direction; the direction we discussed in the balloon model is unphysical - an artefact of the model only.

Is there still something unclear?

 

[Ich]

I didn't mean to contradict you.
What I wanted to say: the Friedmann equation governing acceleration and deceleration can be understood with Newtonian gravity: all the matter inside some arbitrary (small) sphere will pull everything towards the center of that sphere. That's a quantitatively correct Newtonian result.
The conceptual difficulties come later, when you try to make that statement work globally,

 

[tom.stoer]

I see what you mean.

I guess that in Newtonian gravity one can fix a static spacetime and fill it with matter such that the whole system remains static (spacetime is static, matter attraction cancels); it should work with a 3-torus or a 3-sphere plus homogeneously distributed matter.

Of course this does no longer hold globally in GR

 

[Ich]

I guess that in Newtonian gravity one can fix a static spacetime and fill it with matter such that the whole system remains static (spacetime is static, matter attraction cancels)

I don't think that it works. If we suppose that Newtonian Gravity were exactly valid, there is no reason to believe that gravity would cancel. If you take a homogeneous ball of matter and make it bigger and bigger, you'll get exactly the same local expansion/contraction behaviour, independent of the size of the ball. It's just that several (unobservable, but essential in Newtonian terms) numbers blow up, like the absolute acceleration of a particle or the "gravitational force" acting on it.

 

[tom.stoer]

In Newtonian gravity there is no expansion. Spacetime itself is static. So it's only matter that can move on spacetime. All what you have to do is to distribute matter homogeneously.

I am not sure if you can take a 3-ball as a starting point (instead of a 3-sphere or a3-torus)

But I think one can show it mathematically ...

 

[Ich]

In Newtonian gravity there is no expansion. Spacetime itself is static. So it's only matter that can move on spacetime.

Expansion is not really a property of spacetime, it's rather a property of things. For example, a de Sitter spacetime is definitely static, but if you place test particles in it, they will follow exponential expansion. Of course, if you add real matter instead, spacetime is no longer exactly static, but that's not necessary to have expansion.

 

[DJsTeLF]

Recent work by Dutch physicists E. Verlinde suggests that gravity is not a force at all but instead an emergent property from an intrinsically thermodynamic origin. He claims it is associated with an entropic force caused by changes in the entropy associated with positions of material bodies. See here: http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.0785v1.pdf

Here is one of what I'm sure will be many well-structured rebutels, this one is based on Verlinde's work contradicting the observe behaviour of a cold neutron falling in Earth's gravitational field:
http://arxiv.org/PS_cache/arxiv/pdf/1009/1009.5414v1.pdf

 

[tom.stoer]

Expansion is not really a property of spacetime, it's rather a property of things. For example, a de Sitter spacetime is definitely static, but if you place test particles in it, they will follow exponential expansion. Of course, if you add real matter instead, spacetime is no longer exactly static, but that's not necessary to have expansion.

You can have an empty spacetime (vacuum solution) e.g. governed by a cosmological constant which shows expansion (growing 3-volume). Of course in an empty spacetime w/o any matter you can't measure expansion physically, but you cannot associate this expansion with the objects in spacetime. You see the difference e.g. when calculating red shift. The red shift for "moving objects" and for objects "in rest" in an expanding spacetime is different; calculating the velocity based on red shift shows valocities > cwhich means that this cannot be "real" motion in spacetime".

Everybody agrees that we live in a universe where space between matter expands

Anyway - we don't need to argue about details in GR, we only have to take into consideration that spacetime is absolutely static in Newtonian gravity, that we can add matter on top w/o changing the geometry and let the matter evolve on spacetime (as a static stage).

Recent work by Dutch physicists E. Verlinde suggests that gravity is not a force at all but instead an emergent property from an intrinsically thermodynamic origin.

I don't think that Verlinde's idea is viable; there is no entropy w/o microphysical degrees of freedom.