Gravity and the curvature of space

[Brunolem33]

I am not sure I can express clearly my thoughts on this one, but I am going to try.

The effect of mass on space, and the resulting gravity, is sometimes described, in a two dimensions graphic, as a bowling ball applying pressure on the surface of a mattress, or something equivalent.

Thus, the resulting deformation of the surface, which extends far away from the center, explains why smaller balls in the vicinity are bound to orbit the bowling ball.

Yet, the problem is that the effect of such a pressure applied in a two dimension system are completely different than those experienced in a three dimension system, where pressure is applied in all directions at the same time, and not only vertically as in the example of the mattress.

To describe this effect, I think a more appropriate reference would be that of a head, representing the sun, covered with a balaclava, representing space.

In this case, the material, once stretched, tends to stick around the object that causes the deformation.

Thus, only the space relatively close to the object is bent, or curved.

The question therefore is: how can a massive object create a deformation (curving, bending) of space, in all directions simultaneously, that extends so far away?

 

[PeterDonis]

The effect of mass on space, and the resulting gravity, is sometimes described, in a two dimensions graphic, as a bowling ball applying pressure on the surface of a mattress, or something equivalent.

This is just a heuristic analogy and its usefulness is limited. In particular, it does not include the dimension of time.

o describe this effect, I think a more appropriate reference would be...

Please review the PF rules on personal theories. You should not be trying to replace one analogy with another one. You should be learning the actual theory.

Thus, only the space relatively close to the object is bent, or curved.

But that's not what GR says.

how can a massive object create a deformation (curving, bending) of space, in all directions simultaneously, that extends so far away?

Because that's how GR works. Your analogy is simply wrong.

 

[Nugatory]

The effect of mass on space, and the resulting gravity, is sometimes described, in a two dimensions graphic, as a bowling ball applying pressure on the surface of a mattress, or something equivalent.

You'll see that description a lot, but it's not a very good one. And you will not find it in serious textbooks.

To describe this effect, I think a more appropriate reference would be that of a head, representing the sun, covered with a balaclava, representing space.

That's better, but even better is a short video by our own member @A.T. (you can search this forum for it).

The question therefore is: how can a massive object create a deformation (curving, bending) of space, in all directions simultaneously, that extends so far away?

It's easy to do in four-dimensional spacetime, but hard for us three-dimensional creatures to visualize it.

 

[Brunolem33]

Obviously, my analogy is wrong.

Yet, the theory confirms the effects of gravity on space, but does it explain them?

I have a hard time translating, in my head, the analogy of the bowling ball, into a three dimensional graphic.

How can space be curved from all directions (pressure exerted by the massive object) and in all directions at the same time?

 

[PeterDonis]

the theory confirms the effects of gravity on space, but does it explain them?

What do you mean by "explain"? The theory makes correct predictions.

I have a hard time translating, in my head, the analogy of the bowling ball, into a three dimensional graphic.

You would have an even harder time trying to visualize 4-dimensional spacetime. That's why we don't do that; we use math instead.

In the particular case under discussion, since the spacetime is spherically symmetric, the extra dimension doesn't actually add anything useful. That's why the "bowling ball" visualization is often used in this case. But it still has limitations, and those limitations don't go away if you try to add back the third spatial dimension.

How can space be curved from all directions (pressure exerted by the massive object) and in all directions at the same time?

This question has no answer because you are trying to use an analogy that doesn't work for what you are trying to use it for. The only way to fix that problem is to stop using the analogy and learn what the theory actually says.

 

[Nugatory]

I have a hard time translating, in my head, the analogy of the bowling ball, into a three dimensional graphic.

Don't try - As PeterDonis and I have suggested, it's a bad analogy. Instead of trying to translate it into anything you should be trying to forget that you ever saw it.

How can space be curved from all directions (pressure exerted by the massive object) and in all directions at the same time?

Once you stop thinking in terms of the pressure from the bowling ball pushing down it will make more sense. We still can't easily visualize curvature in a four-dimensional spacetime, but there's a pretty good analogy that we can visualize: the two-dimensional surface of the Earth is curved in all directions.

 

[Comeback City]

Is this picture a legible visualization of GR? I've seen it a few times before but never knew if it was even legitimate.

 

[PeterDonis]

Is this picture a legible visualization of GR?

I'm not sure how useful it is. I'm not even sure what exactly it's trying to illustrate. Do you have a reference for where it comes from?

 

[Brunolem33]

Comeback city...to my eyes, this representation is better than that of the bowling ball.
Yet, it shows the effects in only four directions...up, down, left, right...
Extending that picture to all directions, I cannot imagine how it can create a space that would compel a planet to orbit a star.

To me, from this graphic representation, it looks like that the Earth is pulling space toward its center, rather than curving it...

 

[Comeback City]

I'm not sure how useful it is. I'm not even sure what exactly it's trying to illustrate. Do you have a reference for where it comes from?

https://www.transcend.org/tms/2015/12/100-years-of-general-relativity-part-3-of-3/

 

[Comeback City]

Comeback city...to my eyes, this representation is better than that of the bowling ball.
Yet, it shows the effects in only four directions...up, down, left, right...
Extending that picture to all directions, I cannot imagine how it can create a space that would compel a planet to orbit a star.

To me, from this graphic representation, it looks like that the Earth is pulling space toward its center, rather than curving it...

Exactly. This visualization only goes so far. The bowling ball analogy, I feel, is more straightforward (and accepted), buy it only applies to the curving of 2D space. As for this,though, it just seems like it is the best 3D picture that comes close to explaining it.

 

[PeterDonis]

it looks like that the Earth is pulling space toward its center, rather than curving it...

The mass of the Earth curves spacetime, not space. The simplest way to imagine spacetime curvature is to realize that spacetime curvature is the same thing as tidal gravity. So if you imagine the tidal gravity produced by the Earth, you are imagining the spacetime curvature produced by the Earth.

There is a model of spacetime around a massive object that uses the analogy of space being pulled towards the body; it is called the "river model", and was invented to provide an alternative analogy for black holes. See here:

https://arxiv.org/abs/gr-qc/0411060

The analogy is still limited, though.

 

[Nugatory]

Is this picture a legible visualization of GR? I've seen it a few times before but never knew if it was even legitimate.

It's marginally better than the bowling ball because it shows symmetry across all three spatial dimensions instead of just two... But it still has the fundamental flaw of showing curvature in space only instead of spacetime - and it's spacetime curvature that produces gravitational phenomena such as falling objects and orbiting satellites. I've already mentioned A.T.s video, and you might also try googling for "Flamm's paraboloid".

 

[Brunolem33]

Then, if mass curves spacetime, isn't gravity the result of a reaction of spacetime, rather than an action from mass?

What I mean is that gravity results from a property of spacetime, a bit similar to elasticity, and that mass only plays a passive role, like the infamous bowling ball on the mattress.

If that is the case, why call gravity a force, and why search for gravitons when they are not needed?

As a matter of fact, I have read numerous times (don't ask me where, I don't remember) that gravity is not a force, but an emergent phenomenum.

 

[PeterDonis]

if mass curves spacetime, isn't gravity the result of a reaction of spacetime, rather than an action from mass?

No, because these two things are not two different possibilities, they are just two different ways of describing the same thing.

What I mean is that gravity results from a property of spacetime, a bit similar to elasticity, and that mass only plays a passive role, like the infamous bowling ball on the mattress.

This is not what GR says. There are not two things involved here, just one. Your analogy is wrong.

why call gravity a force

GR doesn't call gravity a force.

why search for gravitons when they are not needed?

Because they are needed--at least, some kind of quantum theory of gravity is needed, and as far as we can tell, any such theory will involve gravitons at some level of explanation.

I have read numerous times (don't ask me where, I don't remember)

Sorry, we can't talk about a vague statement that you can't even give a source for. Please review the PF rules on acceptable sources.

 

[PeterDonis]

The OP question is based on a misconception, which has been addressed. Thread closed.