# Gravity, Gravitons, and Geodesics.

1. Jul 26, 2004

### Glenn

Hi,

Hopefully someone can explain this to me in laymans terms...

If I am understanding what I am reading correctly, gravity the result of the shape of space-time? I don't understand why this is considered a force at all if it is the result of the shape of space-time. Where does the graviton come into play?

Thanks,
Glenn

2. Jul 26, 2004

### homology

I'll shoot although hopefully others will provide better responses than mine.

A force causes an acceleration, and the curvature of space-time also causes acceleration. I believe a decent picture is this: image 2-D space, so a flat planar universe and imagine a particle moving along a straight line at constant velocity. Now imagine that at some point on this plane it is not flat, but there is an object there. The usual analogy is of a bowling ball on a rubber sheet. The rubber sheet being our 2-D space. so what the particle comes across this deformation of space its direction changes, an acceleration. So this might be a way of reconciling the label: force with gravity.

The graviton is the hypothetical particle predicted to exist which would be the carrier of the gravitation force (just like the gluon carries the strong force, the photon carries the electromagnetic force and the weak gauge bosons carry the weak force).

But like I said, hopefully someone more knowledgable will add to this.

Kevin

3. Jul 26, 2004

Staff Emeritus
The graviton is a theoretical particle predicted by string theory but not yet demonstrated to exist. If it exists and is the cause of gravity it will do away with spacetime curvature and produce gravity the way the photon carries electromagnetism. Then gravity would be a (quantum) force in your sense.

At the present time however, our best theory of gravity is Einstein's 1915 General Theory of Relativity. One of the basic propositions of that theory is the Principle of Equivalence: On a sufficiantly small scale, it is impossible to tell the difference between an imposed force and a gravitational one.

Notice that the shape is the shape of spacetime, not just of space. Therefore a curved geodesic goes through time as well as space, and by curving, causes those travelling along it to experience an acceleration. Anything that produces an acceleration deserves the name force, no?

To homology: Ships that pass in the night

4. Jul 26, 2004

### Glenn

Does that mean that the 2D rubber sheet analogy and the graviton are mutually exclusive?

If the graviton was experimentally found, would it do away with the rubber sheet analogy as a means of explaining the behavior of gravity?

Thanks,
Glenn

5. Jul 27, 2004

yes, if the graviton is found, General Relativity will be wrong.

6. Jul 27, 2004

### sol2

Will comologically realization in the quantum world morphisize to include relaitivity? If you marry gravity and electromagnetism what do you have? A new dimension of thinking?

Further explanations on the graviton? Any other information would be accepted

Last edited: Jul 27, 2004
7. Jul 28, 2004

No, because if the graviton is found, then there is no curvature of space time, the reson there is gravity will be because of the graviton. You cant have both explaining the same thing.

8. Jul 28, 2004

### sol2

What geometry are you using?

Last edited: Jul 28, 2004
9. Jul 28, 2004

### ArmoSkater87

Couldnt you say the graviton cause the curvature of spacetime...lol

10. Jul 30, 2004

### dodo

General relativity states that a mass causes a curvature in space-time. Now, ...

Can the reciprocal be correct? Namely, a curvature of space-time (by whichever means) can (I guess) be perceived as gravity, but... would it also seem to "have" mass?

(Forget about if we'd actually SEE something there... I mean if we'd perceive a mass by its effect with its surroundings; f.i., at subatomic sizes, would particles appear to collide with the distortion?)

Of course, the consequence of such an statement would be that space-time curvatures and masses ARE actually one and the same thing. I just wonder.

Can somebody point me to a theory (or think of an experiment) which can distinguish, in the context of your choice, between a mass and a spacetime curvature (regardless of the latter's origin)?

Last edited: Jul 30, 2004
11. Jul 30, 2004

### jtolliver

Not really. Any lorentz-invariant interaction that preserves causality can be described in terms of particles. GR satisfies those conditions. Gravitational waves have many properties traditionally associated with particles (If you pretend spacetime is flat and you add gravitational forces to compensate), such as energy-momentum. Using curved space-time(the technique traditionally used in GR), and using flat space-time with an additional force that makes it act exactly as though it were curved(this was the technique used in classical mechanics, except that that force didn't quite make it act exactly as curved space-time) are just different ways of looking at the same thing. The first way is much more convient mathematically, and the second way doesn't really explain why we have this additional force. The graviton's only look like particles when we assume spacetime is flat. If we assume spacetime is curved we see it is really only an effect of the curvature of spacetime, even though it looks exactly like a particle.

12. Jul 30, 2004

### Entropy

I don't really consider gravity a true force. Why? I don't know, to me I see gravity as "bending" an object's path than actually exerting a force on it. I guess you could techniquely say that about any other force, but oh well.

13. Jul 30, 2004

gravity isnt really a force. Out of the 4 elementary forces, it is a million million million million times weaker than any of the other 4. The only reason it is soo strong in our world is because of the amount of particles that are together at the same time pulling on us. :rofl:

14. Jul 31, 2004

### pmb_phy

No. That is not a clear interpretation of gravity/GR/spacetime. It is not the shape of spacetime which dictates the presence/presence of a gravitational field. Its the choice of a frame of reference which dictates the presence of a gravitational field. If you take a look at The Foundation of the General Theory of Relativity, Albert Einstein, Annalen der Physik, 49, 1916 then you'll see the following statement by Einstein
I don't understand why this is considered a force at all if it is the result of the shape of space-time.

15. Jul 31, 2004

### robphy

Let's not be hasty here.
In general relativity, gravity is NOT a force [in the general case].

From Wald, p 67: (I boldfaced the key statements.)

16. Jul 31, 2004

### pmb_phy

17. Jul 31, 2004

### kurious

Gravity can be a force if it is caused by gravitons.All the gravitons have to do is physically curve space-time:If space-time has mass and is made from particles
(spacetime could be quantized at the Planck length) then gravitons could physically curve those particles into different configurations.That way Einstein's theory can still be correct too.A spin 2 particle is needed for gravity to make it an attractive force,
and high in force-carrier density near large bodies such as stars -these considerations come from quantum mechanics.

18. Jul 31, 2004

### robphy

Wald said "We then could define the gravitational force field of the Earth to be minus the acceleration a body must undergo in order to remain stationary."

In GR, a free-falling object is traveling along a geodesic--- it is not accelerating... its 4-acceleration is zero.
Wald is referring to a situation in which a body appears stationary, sitting on the Earth's surface. Such a body is not traveling along a geodesic-- it is accelerating... its 4-acceleration is nonzero... it has a spatial-component which points upward. This acceleration is due to the normal force that the earth's surface applies to the body. Then, the "gravitational force" can be defined to be minus that normal force [that is, minus that force which accelerates the body off a geodesic].

I'll admit I have a bias to this point of view ("the geometric viewpoint") because I've taken courses from Wald. I've also had a relativity course from Mould [before his text was published].

Incidentally, here are some other references that say "gravity is not a force".

from Lecture Notes on General Relativity by Sean M. Carroll
http://nedwww.ipac.caltech.edu/level5/March01/Carroll3/Carroll4.html
[the html version of Ch 4 "Gravitation" http://pancake.uchicago.edu/~carroll/notes/four.ps ]
from General Relativity Tutorial - Long Course Outline, by John Baez
http://math.ucr.edu/home/baez/gr/outline2.html
from Hartle's "Gravity: An Introduction to Einstein's General Relativity"
http://wps.aw.com/aw_hartle_gravity_1 (see the opening paragraph of the sample chapter)

Last edited by a moderator: Apr 21, 2017
19. Jul 31, 2004

### pmb_phy

Yes. I understand that. I read that section many many many times in previous years when I was forming an opinion on the nature of the gravitational force in GR.
True.
This is vauge claim. You've chosen to use the term "accelerating" to mean "4-acceleration is zero." But that is not what the term "acceleration" always means in GR. Acceleration can mean either "3-acceleration" or 4-acceleration". You should be more specific. In fact you should never say "the particle isn't accelerating" to mean "the particle's 4- acceleration is zero". You're mixing terminology in a confusing way. For example: How would I apply such a convention for the velocity of light? If you want people to think "4-acceleration" everytime they see the word "acceleration" then for what possible reason could you have for wanting people to think "4-velocity" every time theh see they see the term "velocity"? As you probably know, the 4-velocity for light is undefined. The magnitude of the 4-velocity of all particles is c.

When GRists speak of gravitational acceleraton they mean coordinate acceleration (taken in the proper comtext since this is a tricky term) [E.g. see Basic Relativity, Richard A. Mould, Springer Verlag, (1994)].

And that is my point. Nobody would consider that as a proper definition of gravitational force in Newtonian gravity so why would one try to use that as a definition in GR?
Correct
Yes. It can be defned that way. But nobody except Wald does it that way. Einstein didn't do it. I don't. Ohanian doesn't. Mould doesn't. So why should I?

Last edited by a moderator: Apr 21, 2017
20. Aug 1, 2004

### robphy

Actually, I use "not accelerating" to mean "4-acceleration is zero".

I agree that there is a mixing of terminology. I've struggled with this myself.
In the geometric viewpoint, GR is described in terms of a 4-dimensional manifold and tensor fields defined on that manifold. All tensors are 4-tensors. Given a 4-vector field v (say the unit-tangent 4-vector along the worldline of an observer), one can decompose the 4-tensors into 3-tensors-with-respect-to-v to describe spatial-tensors viewed in his reference frame. When one chooses a different observer (with unit-tangent v'), you get a different set of 3-tensors-with-respect-to-v'. To avoid this "observer/coordinate dependence", one tries to formulate the physical laws with 4-tensors. Out of laziness, one often drops the "4-". Think of this as an attempt to refine or generalize a familiar-but-observer-dependent concept. When a measurement by an observer is required, one then decomposes with respect to v and oftens prefixes with "3-" (to remind one of the observer-dependence of that expression). In the future, I will make my prefixes explicit.

My only claim about Mould is that I took a relativity class taught by him... in fact, my first formal relativity class. It was okay for a first class. We used Skinner - Relativity for Scientists and Engineers for our text, and we followed it closely. He didn't distribute any lecture notes. I don't have Mould's text (but it may be in our library). When that text came out, I flipped through it and put it back. By then, I had been enlightened by the geometric viewpoint to GR (e.g., Synge, MTW, Wald, Penrose, Hawking-Ellis, Sachs-Wu, Schutz).

I'll look for Mould's text on Monday.