# Trouble understanding gravity

1. Jul 1, 2009

### itwillend

Hi everyone!
This is my first post here, and I hope I don't make a fool of myself.
I am in my 30's and very late to study physics and related fields with much passion.

With that said I have been trying to understand "curved space" and while I was learning about it I came to realize I had questions about gravity that I can't get passed.

In my mind I am imaging space as matter that has position in existence, and that when we find a planet sitting in space it has forced space to accommodate its (the planet's) presence. Dispersing space around it.

Depending on the size of the planet and how much it forces space to displace itself, is the push-back from space what we know as gravity?

Thanks...

2. Jul 1, 2009

### Jonathan Scott

Nice idea, but gravity doesn't work like that; if it did, the effect would only relate to the size of an object, not to its mass.

The space-time in General Relativity is essentially a joining up of all the little bits of space-time as they appear to a local observer. We do the same in Newtonian theory, but in that case they all join in a nice uniform way. In General Relativity, they vary slightly in size and shape so we need to establish some sort of coordinate system to describe what is happening overall, and relative to any conventional coordinate system we find that gravity tends to make space and time curve slightly near large masses.

Space-time forms the background in which everything resides and moves, including massive objects as well as empty space.

In General Relativity, gravitational forces are primarily due to curved space-time, not curved space. If you think about it, curved space alone wouldn't affect anything that was staying still. On the other hand, curved space-time has the property that as you move through time (that is, get older) a plot of your position against time would show a curve towards nearby masses, that is an acceleration.

3. Jul 1, 2009

### diazona

Hi to you too! And welcome to the forums (although I'm not sure I've been around long enough to be welcoming people... )

If I correctly understand what you're thinking, no, it's not really like that (although I think most people think about it the way you are at first). I guess the catch here is that the "curved" in "curved spacetime" is a more mathematical definition of curved.

You're familiar with Euclidean geometry, right? If so, you know that in Euclidean geometry, there are certain properties of geometrical figures that always hold true - for example, the angles of a triangle always add up to 180 degrees, the circumference of a circle is $\pi$ times its diameter, and parallel lines never intersect. But what if one day you were to measure the individual angles of a triangle, add them up, and find that the total was 200 degrees? That would mean that for the surface on which you drew the triangle, the rules of Euclidean geometry do not apply.

Mathematicians have discovered that this can actually happen if you're drawing on a curved surface. (Imagine drawing a triangle on the surface of the Earth connecting the North Pole, the equator at 0 degrees longitude, and the equator at 90 degrees longitude; the angles add up to 270 degrees) Over time, we developed the convention that any surface or space in which the rules of Euclidean geometry do not work is called "curved," and that's the meaning you see in "curved spacetime." Measurements have shown that Euclidean geometry (generalized to 4 dimensions, 3 of space and 1 of time) does not quite work in the universe. For example, a particle in empty, "flat" spacetime follows a path through space and time which is a straight line. If you have two such particles on parallel tracks, they will never get any closer. But in "curved" spacetime, two particles that start out on parallel tracks will eventually collide. Since the bending of the tracks towards each other happens over the time dimension, though, we see it as though the particles were attracting each other with a force, namely gravity.

Anyway, it's better not to think about space actually being some sort of matter-like thing that can be pushed around and distorted by the stuff in it. Just think of it as a space in which the rules of Euclidean geometry do not apply. You can even call it "non-Euclidean spacetime" instead of "curved spacetime" to impress your friends (and avoid confusing yourself).

4. Jul 1, 2009

### itwillend

If you have the patience, you have to forgive my slowness. I will need to take this one thing at a time.

Since we are talking about mass and not size which I do understand, my next inexperienced thought is:
Could the energy from the center of whatever mass is in question, say a small mass intensive star be the reason for gravity. Meaning the more intense the energy within a mass the more intense the sensation of gravity. Or, the less intense the energy from mass like on the moon make a smaller sensation of gravity.

Many thanks...

5. Jul 1, 2009

### itwillend

Hi, thank you. I see very well what you mean by your explanation. Please see my reply to the Jonathan, and if he does not respond maybe you can.

I know all to well how frustrating it can be for someone to come along with an elementary understanding of something, and try to explain things to them, so I appreciate your help.

6. Jul 1, 2009

### Jonathan Scott

According to Newton's theory, the gravitational acceleration caused by an object is proportional to its mass and inversely proportional to the square of the distance from the location of the mass: F = -GM/r2. In relativistic theory, the actual results are almost exactly identical except in extreme gravitational fields much greater than those encountered in the solar system.

From a relativity point of view, mass is part of the energy of an object; it is the energy which it would has from its own point of view, as seen from a frame in which it is at rest. An object can also have kinetic energy due to its motion (via its momentum), and certain forms of energy (such as photons) only have kinetic energy and no rest mass.

We do not know HOW mass makes space curve, but according to Einstein's field equations in General Relativity, the curvature of space-time is given by an expression which says that it is proportional to the energy and momentum density, and the predictions of this theory are extremely accurately matched by the experimental results.

There are two types of "curvature" here.

The curvature of space-time caused by masses is like the curvature of part of a ball, and means that space-time is locally not quite flat, and that the circumference of that part of space-time is not quite 2pi times the radius.

Outside masses, space-time is curved in a different sense, which is more similar to the curvature of a cone of paper, in that locally it appears normal and flat, but on the larger scale something which is moving in a straight line on the paper moves in a curve overall. That is more like the curvature of the gravitational field, which accelerates free-falling bodies.

Last edited: Jul 1, 2009
7. Jul 1, 2009

### itwillend

I am going to read your reply a few times, so I can comprehend it, thank you very much!

Would you be kind enough to elaborate on how the density of mass-energy fits into this discussion.

8. Jul 1, 2009

### A.T.

The key is to understand "curved spacetime". "Curved space" alone doesn't cause gravity (in the common sense). Have a quick look at the links given in this post:
https://www.physicsforums.com/showpost.php?p=2244927&postcount=21

9. Jul 2, 2009

### Naty1

itwillend: you are on the right general track..and don't think you are "late" getting started..many here have returned or begun later than you. And don't worry about making a fool of yourself....most here have many numerous mistakes posting, answering, etc...that's how we learn new things....

Getting started is the hardest part, because maybe things like the scientific use of terms like force, mass, pressure is not clear at first. It takes time to put the basic pieces together so you can communicate in a way that others understand. When we say "mass" for example everybody needs to understand that is not the same as "weight". And when some ONE person describes it, it may not connect...so seeing different explanations from different sources oftens clarifies things.

Density is mass divided by volume; that is, mass per unit volume. So density is not a major determinent of gravity....Mass itself is a characteristic of an object owing to its make up...but when a uniform distribution of mass is under discussion, usually the case, it turns out that representing a mass as a single point, say at the center of a sphere, makes things a lot simpler to visualize and calculate.

And if I say I have an equal mass of, say, lead and air, the volume of the lead will be much smaller than the volume of the same mass of air. Lead is a lot more dense. From the perspective of gravity, each curves space pretty much the same way....until you get close to the masses...

Einstein figured out that mass and energy are different forms of the same entity: From his famous E=mc2 a lot of energy is equivalent to a little bit of mass.....so energy has some gravitational effects too...a mass with a lot of energy, say its very hot, will have a bit more gravity than that same mass when it's cold. A rapidly moving mass will also have some additional gravitational attraction relative to when its stationary because it has some additional (kinetic) energy.

10. Jul 2, 2009

### Nickelodeon

I'm not sure that just because mass and energy are interchangeable that it necessarily follows that vibrating the molecules within an object is going to increase the objects gravity potential. Is there any experimental evidence to suggest this? I don't think gravity works like this.

11. Jul 3, 2009

### Jonathan Scott

Yes it does; since inertial mass includes internal kinetic energy, then so does gravitational mass, by the principle of equivalence. Although this form of internal energy would be too small to be tested experimentally, there have been tests done with different types of atom, showing for example that the binding energy of the nucleus is definitely part of the inertial mass.

12. Jul 3, 2009

### Nickelodeon

You have to be a believer in the Equivalence principle and I'm not.

13. Jul 3, 2009

Staff Emeritus
All you need to "believe in" is the universality of free fall. This has been tested many, many times.

14. Jul 3, 2009

### Nickelodeon

Could you explain that a bit more? It reads like I have to believe that things fall to the ground and I suspect you mean more than that.

15. Jul 3, 2009

### Jonathan Scott

It simply means that all objects falls with the same acceleration under the influence of gravity regardless of their composition. This has been tested to extremely high accuracy. If you use the Newtonian view model that gravity is a force per unit mass, this means that the relevant "mass" for this purpose must be the same as the inertial mass, which is known to include any internal energy. For example, the binding energy of certain atomic nuclei is a measurable percentage of their total mass, but they still fall with the same acceleration as other atoms which have a higher or lower proportion of binding energy.

We also know to high accuracy that overall momentum is conserved by such forces, which means that the force caused by mass A on mass B is the same as the force caused by mass B on mass A. This means that the gravitational effect of a body must similarly be related to its inertial mass including any effect of its internal energy.

16. Jul 3, 2009

### Nickelodeon

Something doesn't seem right here. Wouldn't that suggest that objects in a galaxy receding from us at speeds approaching that of light would exert huge gravitational forces on each other due to this added inertia. Seems unlikely.

17. Jul 3, 2009

### Jonathan Scott

From our point of view, that's one way of looking at it, but firstly their increased inertia also means that the forces have less effect, and secondly time dilation means that the acceleration relative to us is slowed down. The overall effect is basically what would be predicted by Special Relativity for any sort of force as seen from a different frame.

Apart from that, the effects of gravity aren't purely static and scalar, like electric potential. They include dynamic effects similar to magnetism, and other effects which have no equivalent in electromagnetism such as extra acceleration due to the curvature of space. The source is not just scalar energy but also momentum and "stress" or "pressure". The extra terms are not significant for normal situations, but make a difference in very strong fields or for relativistic speeds.

18. Jul 4, 2009

### Nickelodeon

To me, this would suggest that the 'kinetic energy' of an object has no effect on its gravity potential to attract another object in the same reference frame. Is this correct?

Next thing, soon as one of the objects starts accelerating relative to another object then its not in the same reference frame as that object.
If the two objects start accelerating side by side then are you saying that the two objects will have a greater attraction towards each other than when they are not accelerating?

19. Jul 4, 2009

### Jonathan Scott

In a frame where an object is at rest, it has no overall kinetic energy. It could however have internal kinetic energy, for example from rotation, other internal motions or thermal energy, and that would affect the potential.

The acceleration is not relevant in itself, only the resulting speed. As kinetic energy contributes to the source energy, the field of each object is increased in proportion, but when all effects including time dilation are taken into effect, the overall resulting motion is consistent with Special Relativity, matching the view from the rest frame transformed to the frame of the observer. (Special Relativity is a reasonable approximation for "weak" gravitational fields such as those typically found near ordinary stars and galaxies).

20. Jul 4, 2009

### Nickelodeon

This is refering to actual gravitational attraction between two objects in the same reference frame which in theory could be measured within the confines of a laboratory.

I think this explanantion is refering to the calculation of relative gravitational potential in separate reference frames where speed in SR is a dominant factor.