# Gravity and the curvature of space

• B
• Brunolem33
In summary, the conversation discusses the limitations and flaws of using the analogy of a bowling ball on a mattress to explain the effect of mass on space and gravity. The participants question the ability of this analogy to accurately describe the concept and suggest alternative analogies such as a head covered in a balaclava. They also discuss the difficulty in visualizing the curvature of space in all directions simultaneously and the need to use mathematics instead of visualizations. Furthermore, the conversation touches on the misconception that the Earth is pulling space towards its center instead of curving it. Overall, the conversation highlights the challenges of trying to visualize and understand the complex concept of general relativity.
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?

Brunolem33 said:
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.

Brunolem33 said:
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.

Brunolem33 said:
Thus, only the space relatively close to the object is bent, or curved.

But that's not what GR says.

Brunolem33 said:
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.

Brunolem33 said:
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.

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?

Brunolem33 said:
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.

Brunolem33 said:
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.

Brunolem33 said:
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.

Brunolem33 said:
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.

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

Comeback City said:
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?

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...

Brunolem33 said:
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.

Brunolem33 said:
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.

Comeback City
Comeback City said:
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".

Comeback City
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.

Brunolem33 said:
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.

Brunolem33 said:
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.

Brunolem33 said:
why call gravity a force

GR doesn't call gravity a force.

Brunolem33 said:
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.

Brunolem33 said:
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.

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

## 1. What is gravity and how does it work?

Gravity is a fundamental force of nature that causes objects with mass to attract each other. It is described by Einstein's theory of general relativity, which states that massive objects cause a curvature in the fabric of space-time, and this curvature is what we perceive as the force of gravity.

## 2. How does the curvature of space affect gravity?

The curvature of space is directly related to the force of gravity. According to Einstein's theory, the more massive an object is, the more it curves space-time around it, and this curvature determines the strength of the gravitational force between objects.

## 3. Can gravity be stronger or weaker in different parts of space?

Yes, the strength of gravity can vary in different parts of space. This is due to the curvature of space being affected by the distribution of mass in that particular region. The more concentrated the mass, the stronger the gravitational force will be.

## 4. How does gravity affect the motion of objects?

Gravity affects the motion of objects by causing them to accelerate towards each other. This acceleration is dependent on the mass of the objects and the distance between them. The greater the mass and the shorter the distance, the stronger the gravitational force and the greater the acceleration.

## 5. Can gravity be explained by any other theories besides general relativity?

While general relativity is currently the most accepted theory of gravity, there are other theories that attempt to explain gravity, such as string theory and loop quantum gravity. However, these theories are still being studied and have not been fully proven or accepted by the scientific community.

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