# Gravity = warping of spacetime (doesn't make sense)

#### Jonnyb42

I don't see how the bending of spacetime can be a proper way of explaining to people gravity.
Why would bending of space-time imply movement?, (or acceleration.)
The analogy with a ball on a bed sheet can only go so far. (which isn't very far.)
Is this lame analogy used only because, there aren't really any analogies that can be used?

The ball on a bed sheet means there is some other forces that pull objects along with spacetime in some other dimension. Because I've never heard of that, I assume its not true, which makes me wonder why people use that analogy.

(I word things loosely, try to know what I mean please.)

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#### Dale

Mentor
I don't see how the bending of spacetime can be a proper way of explaining to people gravity.
Why would bending of space-time imply movement?, (or acceleration.)
Do you understand the concept of a worldline in a spacetime diagram?

#### tiny-tim

Homework Helper
Hi Jonnyb42! ¬ The ball on a bed sheet means there is some other forces that pull objects along with spacetime in some other dimension. Because I've never heard of that, I assume its not true, which makes me wonder why people use that analogy.
Yes, I see what you mean …

but the justification for that analogy is that it demonstrates what happens, rather than why it happens …

it demonstrates how the intrinsic curvature of space-time affects "straight" lines.

An alternative would be to have a hump (upward) rather than a hollow, and then show that a string stretched tight has to deviate from a "2D" straight line …

unfortunately, that has the deviation in the wrong direction (outward instead of inward), and so the ball on the bedsheet analogy is still the best we have.

#### Jonnyb42

Do you understand the concept of a worldline in a spacetime diagram?
I don't know this yet, you could try to explain if you like.

but the justification for that analogy is that it demonstrates what happens, rather than why it happens …
I suppose.

I have not studied General Relativity, so therefore my only understanding of it is by that analogy (and some special relativity), so of course I would analyze it like that.
I am currently trying to understand rotation, (not circular motion, but along the lines of Mach's principle)

I DO plan on studying GR by the way.

Also, how do you properly spell spacetime?

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#### Dale

Mentor
I don't know this yet, you could try to explain if you like.
OK, to draw a worldline you start with two axes, one labeled x for space and one labeled t for time, this is called a spacetime diagram. Then for every t coordinate you mark the position of the particle, x(t), at that time. Hopefully you immediately recognize that this represents a point particle as a line (aka worldline) in the spacetime.

Now then, you can describe the motion of particles in terms of geometric figures in the spacetime diagram. A particle which is moving inertially will have a worldline which is a straight line, and conversely a particle which is being acted on by a force will have a curved worldline.

Any questions so far?

#### Jonnyb42

A particle which is moving inertially will have a worldline which is a straight line,
Well, if a particle is falling in a gravitational field, it is inertial yet won't have a straight line?
But maybe that isn't covered in special relativity...
and thank you very much for the explanation!

#### DrGreg

Gold Member
Well, if a particle is falling in a gravitational field, it is inertial yet won't have a straight line?
But maybe that isn't covered in special relativity...
and thank you very much for the explanation!
In special relativity, with no gravity, you draw your spacetime diagram on a flat sheet of paper. Two particles permanently at rest relative to each other are represented by parallel worldlines.

In general relativity, with gravity included, you draw your spacetime diagram on a curved sheet of paper. Two freely falling particles initially at rest relative to each other are represented by worldlines which start off parallel, but the curvature of the sheet of paper makes the lines converge or diverge further along the lines.

For a picture, try www.relativitet.se/spacetime1.html.

#### Dale

Mentor
Well, if a particle is falling in a gravitational field, it is inertial yet won't have a straight line?
But maybe that isn't covered in special relativity...
and thank you very much for the explanation!
That is a good transition to the next part.

An inertial object has a straight worldline. If two inertial objects are initially at rest wrt each other then their worldlines form two parallel lines which never intersect. However, due to gravitation we see that two inertial objects may begin initially at rest wrt each other and then accelerate towards each other and eventually intersect. How is it possible for two lines to start out parallel to each other, each be straight, and yet intersect?

In a flat spacetime it is not possible, but that is exactly what defines a curved spacetime. In a curved space straight lines are called "geodesics", and they have the usual properties that you expect of straight lines in flat spacetime: they minimize the distance between points and they don't turn anywhere (parallel transport the tangent vector).

As an example consider geodesics on the surface of a sphere (great circles). Suppose two people begin walking due north from the equator, meaning they are initially going parallel to each other. They go straight at each point without turning either left or right at all, and yet they will intersect at the north pole. The surface of a sphere is a curved space.

#### 94JZA80

As an example consider geodesics on the surface of a sphere (great circles). Suppose two people begin walking due north from the equator, meaning they are initially going parallel to each other. They go straight at each point without turning either left or right at all, and yet they will intersect at the north pole. The surface of a sphere is a curved space.
great example Dale.

it is also of interest to note that the points of intersection of the 3 great circles in your example (the equator, the path of person A, and the path of person B) will form a triangle. lets expound on this concept and say for simplicity's sake that, while persons A and B both start out on the equator, they also start out 90° of longitude apart. so while both their paths are perpendicular to the equator when they both start out due north, so are they perpendicular to each other at the north pole itself. hence the triangle formed by the path of person A, the path of person B, and the equator itself has internal angles that sum to 270°. this is in stark contrast to the 180° that a triangle's interior angles always sums to in Euclidean (flat) space. thus, when a triangle's angles sum to more or less than 180°, one can be certain that said triangle does not lie on a flat surface or in a flat, non-curved, Euclidean space.

#### Daverz

The ball on a bed sheet means there is some other forces that pull objects along with spacetime in some other dimension.
You're quite right to be skeptical of the analogy, but it's not totally useless

The only need for a force in the analogy is to constrain objects to the sheet. You could imagine, instead, objects being constrained between two frictionless sheets. Or better yet, imagine that the objects can only "live" in the 2-dimensional sheet, and no force is required to keep them in it.

(Another thing that makes the rubber-sheet analogy less than ideal is that it's easy to mix up the idea of curvature of the space and the idea of a gravity well. So it's better to imagine objects living only in the sheet with no external gravity involved as a constraining force.)

The analogy definitely has its limitations because it only shows the curvature of space, whereas gravity is caused by the curvature of spacetime. It's a good analogy for explaining the bending of light grazing the sun or the precession of the perihelion of Mercury, but it only gets you the part of the effect due to the curvature of space alone.

And it's not a good analogy for understanding why we feel gravity on the earth's surface, because there the curvature in the direction of the time coordinate is dominant. Imagining the curvature of time is rather difficult.

#### 94JZA80

And it's not a good analogy for understanding why we feel gravity on the earth's surface, because there the curvature in the direction of the time coordinate is dominant. Imagining the curvature of time is rather difficult.
could you elaborate on that a bit? how do we know that the gravity we feel here on earth is due to the curvature of time more than it is due to the curvature of space? is it simply due to the fact that the earth is not a relativistic body with gravity strong enough to cause greater curvature of the space near and around it? would then the gravity of a neutron star or a black hole consequently be as much (or more of) a manifestation of space curvature than time curvature?

#### Passionflower

I don't see how the bending of spacetime can be a proper way of explaining to people gravity.
Why would bending of space-time imply movement?, (or acceleration.)
The analogy with a ball on a bed sheet can only go so far. (which isn't very far.)
Is this lame analogy used only because, there aren't really any analogies that can be used?

The ball on a bed sheet means there is some other forces that pull objects along with spacetime in some other dimension. Because I've never heard of that, I assume its not true, which makes me wonder why people use that analogy.

(I word things loosely, try to know what I mean please.)
It actually makes total sense.

By the way curvature causes inertial acceleration which causes movement.

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#### Dale

Mentor
could you elaborate on that a bit? how do we know that the gravity we feel here on earth is due to the curvature of time more than it is due to the curvature of space? is it simply due to the fact that the earth is not a relativistic body with gravity strong enough to cause greater curvature of the space near and around it? would then the gravity of a neutron star or a black hole consequently be as much (or more of) a manifestation of space curvature than time curvature?
In the Schwarzschild solution the curvature through space is essentially equal to the curvature in the time dimension. But the reason that curvature of time is more important for us is that we are much longer in the time dimension than in the spatial dimensions.

#### Passionflower

In the Schwarzschild solution the curvature through space is essentially equal to the curvature in the time dimension. But the reason that curvature of time is more important for us is that we are much longer in the time dimension than in the spatial dimensions.
Could you qualify that comment DaleSpam?

Are you saying that all observers (stationary, free falling at escape velocities, free falling at other velocities, accelerating other than stationary) experience only curvature in the time dimension, or are you only referring to the Schwarzschild 'observer' at infinity.

#### Jonnyb42

In general relativity, with gravity included, you draw your spacetime diagram on a curved sheet of paper.
Well now I am very confused, I had thought that curving spacetime would only scale the axis of the spacetime diagram. But you say that the spacetime diagram is drawn on curved paper, that implies curving in some OTHER dimension, not time or the 3 spatial dimensions (or 1 spatial dimension in this example.)

#### DrGreg

Gold Member
Well now I am very confused, I had thought that curving spacetime would only scale the axis of the spacetime diagram. But you say that the spacetime diagram is drawn on curved paper, that implies curving in some OTHER dimension, not time or the 3 spatial dimensions (or 1 spatial dimension in this example.)
Well, yes, that is the way to picture this. It doesn't mean that there literally exists in any physical sense a 5th dimension for 4D spacetime to curve into, but nevertheless the 4D equations that describe the geometry of spacetime are the 4D equivalent of the 2D equations that describe the geometry of a 2D surface that is curved within 3D space.

#### Lazernugget

I don't see how the bending of spacetime can be a proper way of explaining to people gravity.
Why would bending of space-time imply movement?, (or acceleration.)
The analogy with a ball on a bed sheet can only go so far. (which isn't very far.)
Is this lame analogy used only because, there aren't really any analogies that can be used?

The ball on a bed sheet means there is some other forces that pull objects along with spacetime in some other dimension. Because I've never heard of that, I assume its not true, which makes me wonder why people use that analogy.

(I word things loosely, try to know what I mean please.)
OMG! This is EXACTLY what I was thinking sense I began looking at theories of gravity, and looking at the problems with them. Gravitons don't make sense either. Space warping make only a bit more sense...any other theories of gravity?

#### Lazernugget

The reasons I don't think Gravitons make any sense also is why I think gravity is slower that light, not at the same exact rate. If light is constant..well great, but gravitons would have to travel at the speed of light, but gravity eventually stops effecting stuff. So with that logic, gravitons would de-accelerate, therefore they couldn't be constant, and gravitons wouldn't exist and gravity isn't constant, and doesn't travel at the speed of light.

#### Daverz

could you elaborate on that a bit? how do we know that the gravity we feel here on earth is due to the curvature of time more than it is due to the curvature of space? is it simply due to the fact that the earth is not a relativistic body with gravity strong enough to cause greater curvature of the space near and around it? would then the gravity of a neutron star or a black hole consequently be as much (or more of) a manifestation of space curvature than time curvature?

#### Daverz

Well now I am very confused, I had thought that curving spacetime would only scale the axis of the spacetime diagram. But you say that the spacetime diagram is drawn on curved paper, that implies curving in some OTHER dimension, not time or the 3 spatial dimensions (or 1 spatial dimension in this example.)
Like Greg says, that's the way we usually picture a curved surface, as curving in some "ambient" space that the surface is embedded in. It turns out, though, that curvature is an intrinsic property of a surface or space (or spacetime), and that we can calculate it from measurements made only in the surface, without any reference to an ambient space. This was proved by Gauss in the 19th Century:

http://en.wikipedia.org/wiki/Theorema_Egregium

#### WannabeNewton

The reasons I don't think Gravitons make any sense also is why I think gravity is slower that light, not at the same exact rate. If light is constant..well great, but gravitons would have to travel at the speed of light, but gravity eventually stops effecting stuff. So with that logic, gravitons would de-accelerate, therefore they couldn't be constant, and gravitons wouldn't exist and gravity isn't constant, and doesn't travel at the speed of light.
What? Gravitational waves travel at c - a consequence naturally arising from the wave equation for gravitational waves. Gravitational waves are predominantly quadrapole hence why gravitons are spin 2 particles. Don't really see what is nonsensical about that. Don't see what you mean by gravity eventually "stops effecting stuff".

#### khemist

What? Gravitational waves travel at c - a consequence naturally arising from the wave equation for gravitational waves. Gravitational waves are predominantly quadrapole hence why gravitons are spin 2 particles. Don't really see what is nonsensical about that. Don't see what you mean by gravity eventually "stops effecting stuff".
I believe he is talking about the inverse square law.

#### DrGreg

Gold Member
The reasons I don't think Gravitons make any sense also is why I think gravity is slower that light, not at the same exact rate. If light is constant..well great, but gravitons would have to travel at the speed of light, but gravity eventually stops effecting stuff. So with that logic, gravitons would de-accelerate, therefore they couldn't be constant, and gravitons wouldn't exist and gravity isn't constant, and doesn't travel at the speed of light.
Gravitons would be a feature of quantum gravity, and we don't yet have such a theory. What we do have are gravitational waves within the general theory of relativity, which always travel at the speed of light. But they occur only when there is a change of gravity; in a "constant gravitational field" (to use Newtonian language) there is no need for gravitational waves or gravitons: the gravity that is already there continues to be there.

#### Dale

Mentor
Are you saying that all observers (stationary, free falling at escape velocities, free falling at other velocities, accelerating other than stationary) experience only curvature in the time dimension, or are you only referring to the Schwarzschild 'observer' at infinity.
Sorry about the confusion. I was refering to any non-relativistic particle or observer in the Schwarzschild metric.

#### A.T.

Why would bending of space-time imply movement?, (or acceleration.)
The model goes like this:
- Everything advances in space-time. Objects at rest in space advance only along the time dimension.
- Acceleration in space is a change in the direction of the space-time advance.
- If space-time is curved, free falling objects will change their direction in space-time, and thus accelerate in space.

The analogy with a ball on a bed sheet can only go so far. (which isn't very far.)
Is this lame analogy used only because, there aren't really any analogies that can be used?
Yes, it is a lame analogy. It ignores the time dimension, and uses gravity to explain gravity. And yes there are better analogies:

Dr Greg posted one:
http://www.relativitet.se/spacetime1.html

Here are similar ones:
http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_spacetime.html

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