What is gravity?

[Klausnh]

I’ve been reading about gravity and I’m not sure what the current accepted theory of gravity is. As I understand it, Einstein “treats the gravitational field as a field of geometrical distortion, a curvature or warping of space-time.” (Superstrings A Theory of Everything? Edited by PCW Davies and J Brown, Pg 16).
But I’ve also read of gravitons, which carry the gravitational force.
Are these 2 ideas from 2 different theories? If gravity the result of a geometrical distortion of space-time, why is there a need for gravitons? Every book and article I’ve read, make it sound like gravity is includes both geometry and particles.

[JS Princeton]

Gravitons are needed if we are ever to marry quantum mechanics and GR. We don't have a consistent theory for this yet. Observation of gravity waves might shed some light on the subject as may the search for the Higgs Boson. As it stands right now, we're not sure exactly how to formulate gravity.

Basically, there are two ways forces have been explained. One was is through Einstein's geodesic formalism, that is that the "force" is really not a force at all but rather the result of the curvature of space time. The other way is to explain the "force" as an exchange of bosons (be the photons, W-bosons, or gluons). So, unification theorists have to deal with both formalisms if they are to make any headway.

[Klausnh]

As I understand it, according to Einstein, space-time is distorted by mass at the speed of light?
I came across a web article saying that was proven in experiment having to do with Jupiter. (Unfortunatley I lost the link and don't remember the details)

[JS Princeton]

Well, the experiment I was pretty enthusiastic about involving Jupiter that I heard about this January has been bogged down by quite a lot of skpetical prodding. We're not sure if they actually measured the speed of gravity or not. The jury's techinically still out.

[kilopi]

On 2003-03-15 15:24, JS Princeton wrote:
Basically, there are two ways forces have been explained. One was is through Einstein's geodesic formalism, that is that the "force" is really not a force at all but rather the result of the curvature of space time. The other way is to explain the "force" as an exchange of bosons (be the photons, W-bosons, or gluons). So, unification theorists have to deal with both formalisms if they are to make any headway.

And, it's entirely possible that what looks like two distinct ways of explaning gravity are actually the same--similar to the situation with quantum mechanics with Schrödinger's wave mechanics and Heisenberg's matrix mechanics, which turned out to be equivalent.

[Klausnh]

On 2003-03-15 21:34 kilopi wrote:
And, it's entirely possible that what looks like two distinct ways of explaning gravity are actually the same

How do gravitons fit into geometric space-time?

[Klausnh]

Theory is that space-time is distorted by mass at the speed of light. I read here in a post, that to a photon, travelling at the speed of light, because of relativity, the trip from a to b is instantaneous. Does it follow that to a person, on a mass (planet), the gravitational attraction is instantaneous because spacetime is distorted at the speed of light?

[JS Princeton]

On 2003-03-15 23:20, Klausnh wrote:
Does it follow that to a person, on a mass (planet), the gravitational attraction is instantaneous because spacetime is distorted at the speed of light?

No, you have mass.

[kilopi]

On 2003-03-15 23:02, Klausnh wrote:

On 2003-03-15 21:34 kilopi wrote:
And, it's entirely possible that what looks like two distinct ways of explaning gravity are actually the same

How do gravitons fit into geometric space-time?

Key word is "possible"--if only I knew, then I wouldn't have to worry about my retirement nest egg.

[DStahl]

We've talked about this before, but it's good stuff to go over again. Just as kilopi says, physicists can and do think of gravity in different ways when they're working on different problems. The relativity specialist Kip Thorne wrote that he finds it very useful to think of gravity as a field in flat spacetime when he's working on gravity waves, for instance, and as a curvature of spacetime when he's working on a black-hole problem.

But as he notes, those two ways of describing gravity--as a field, and as a curvature--turn out to be mathematically exactly the same. They make identical predictions about the behavior of the universe, and so which one is the "real" description of gravity can't be decided scientifically. It's meaningless.

Trouble is, our current descriptions of gravity fail mathematically under certain situations. What's needed, in some opinions, is a theory of gravity that works like the theory of quantum mechanics. Now, it's widely believed that when such a theory is constructed, it will give exactly the same predictions as General Relativity for the scales and regions of the universe in which GR holds true. In a sense it will add another tool to physicists' toolbox, but the mathematics of spacetime curvature, of gravitational fields in flat spacetime, and of "graviton mechanics" will not only overlap they will be mathematically identical for nearly all large-scale situations in the universe. They will all be realistic mathematical models of the mysterious thing philosophers call...<font color=#9900aa>ULTIMATE PURPLE REALITY!</font>...with a [img]/phpBB/images/smiles/icon_wink.gif[/img]

<font size=-1>[ This Message was edited by: DStahl on 2003-03-16 00:57 ]</font>

[Klausnh]

On 2003-03-15 23:20, Klausnh wrote:
Does it follow that to a person, on a mass (planet), the gravitational attraction is instantaneous because spacetime is distorted at the speed of light?

On 2003-03-15 23:41 JS Princeton answered:

No, you have mass

I do not understand your answer. Do you mean that any space-time distortion involving mass does not distort at c?
Let me try another approach:
Let me know if any of the following statements are incorrect:
1) c is the upper limit of any object moving within space-time
2) Space-time distortion is not limited by c. (General relativity)
3) Space-time expansion is not limited by c. (That’s why inflation is possible)
4) If gravity is the effect of distorted space-time, an instantaneous interaction between 2 masses is allowed because Space-time distortion is not limited by c and does not take place within space-time.


<font size=-1>[ This Message was edited by: Klausnh on 2003-03-16 14:52 ]</font>


<font size=-1>[ This Message was edited by: Klausnh on 2003-03-16 14:56 ]</font>

<font size=-1>[ This Message was edited by: Klausnh on 2003-03-16 14:58 ]</font>

[JS Princeton]

On 2003-03-16 14:53, Klausnh wrote:

2) Space-time distortion is not limited by c. (General relativity)

Sure, it's limitted by c. That's why we've got black holes. In Einstein's treatment, gravity (and therefore distortion) is a strictly speed-of-light phenomenon.

[kilopi]

On 2003-03-16 14:53, Klausnh wrote:
Let me know if any of the following statements are incorrect:
1) c is the upper limit of any object moving within space-time

Depends upon your reference frame.

[JS Princeton]

Let's stick to local reference frames. I think they're easier to talk about. The minute we go global, some people's eyes tend to glaze over.

[kilopi]

On 2003-03-16 15:39, JS Princeton wrote:
Let's stick to local reference frames. I think they're easier to talk about. The minute we go global, some people's eyes tend to glaze over.

Still depends upon your reference frame. [img]/phpBB/images/smiles/icon_smile.gif[/img]

[JS Princeton]

No, kilopi. I'm putting my foot down here. What I think you're insinuating is not true, and if you aren't insinuating this then you need to post more than a glib one sentence answer. In a local reference frame the speed of light is the fastest speed. That's the definition of a local frame. Anything else is nearly impossible to define.

I assume, of course, you are referring to the old arguments we've had in the past which include the following (Original Source:

Stand up in a clear space and spin round. It is not too difficult to turn at one revolution each two seconds. Suppose the moon is on the horizon. How fast is it spinning round your head? It is about 385,000
km away so the answer is 1.21 million km/s, which is more than four times the speed of light! It sounds ridiculous to say that the moon is going round your head when really it is you who is turning, but
according to general relativity all co-ordinate systems are equally valid including revolving ones. So isn't the moon going faster than the speed of light? This is quite difficult to account for.

What it comes down to, is the fact that velocities in different places cannot be directly compared in general relativity. Notice that the moon is not overtaking the light in its own locality. The velocity of the
moon can only be compared to the velocity relative to other objects in its own local inertial frame. Indeed, the concept of velocity is not a very useful one in general relativity and this makes it difficult to
define what "faster than light" means. Even the statement that "the speed of light is constant" is open to interpretation in general relativity. Einstein himself in his book "Relativity: the special and the
general theory" said that the statement cannot claim unlimited validity (pg 76). When there is no absolute definition of time and distance it is not so clear how speeds should be determined.

Nevertheless, the modern interpretation is that the speed of light is constant in general relativity and this statement is a tautology given that standard units of distance and time are related by the speed of
light. The moon is given to be moving slower than light because it remains within the future light cone propagating from its position at any instant.

That's why I was careful to say "local". Once you move non-local, all bets on how to calculate "velocities" are off.


<font size=-1>[ This Message was edited by: JS Princeton on 2003-03-16 16:10 ]</font>

[kilopi]

On 2003-03-16 16:10, JS Princeton wrote:
No, kilopi. I'm putting my foot down here. What I think you're insinuating is not true, and if you aren't insinuating this then you need to post more than a glib one sentence answer. In a local reference frame the speed of light is the fastest speed. That's the definition of a local frame. Anything else is nearly impossible to define.

Watch where you put that foot down. That might be the definition of a local inertial reference frame. Big difference.

As to whether they are impossible to define, it would seem that engineers might have trouble with it but physicists don't, in the large.

[DStahl]

As I recall, there is a discussion on John Baez's physics website about the "point of view" of a photon, and the upshot is, no such "point of view" is possible. Specifically, time becomes mathematically meaningless at c, if I remember the discussion correctly. And of course nothing with mass can reach c, so in a similar way it's meaningless to talk about what would happen to a ball bearing traveling at c: the situation is undefined.

To put it incoherently, I think you have to be very careful to define your reference frames if you want to describe relativistic effects like mass increase and foreshortening. You have to define the reference frame of the observer and its relationship to the observed thing-a-gummy. But yes: to an observer sitting in the control room of a particle accelerator, the protons which have been boosted to 99% c look more massive than the protons in his fingertip. But from the reference frame of the accelerated protons, they are "normal" but the gold atoms in the target block are more massive than they "should" be and are foreshortened--distinctly pancake-shaped rather than spherical. So I think whether or not spacetime looks distorted depends on where you're sitting.

[Jeez, you guys wrote a bunch of posts while I was writing this one! Now I'll go back and see just how redundant this one is...]

<font size=-1>[ This Message was edited by: DStahl on 2003-03-16 16:43 ]</font>

[JS Princeton]

The local frame is AUTOMATICALLY inertial. Otherwise, how do you define local?

FROM http://people.hofstra.edu/faculty/St...geom/Sec9.html

(Existence of a Local Inertial Frame) If m is any point in the Riemannian manifold M, then there exists a local coordinate system xi at m such that:

(a) g_ij(m) = ±1
if j = i
; 0
if j i
= ±ij

(b)g_ij,k) = 0 for every k.


We call such a coordinate system a local inertial frame or a normal frame.

How else would you, kilopi, define a local frame so it's not inertial?

<font size=-1>[ This Message was edited by: JS Princeton on 2003-03-16 16:51 ]</font>

[Eta C]

We're talking about two distinctly different things here. One is the local curvature of space-time caused by mass. In general relativity this is what causes the force we observe as gravity. Quantum gravity theories try to express gravity in the same way the other forces (electro-magnetic, weak nuclear, and color) are, that is by the exchange of an "intermediate vector boson." For EM that's the photon. For quantum gravity it's the still hypothetical graviton. Since gravity has no range limitation, the graviton should be massless and therefore move at c, which is possible only for massless particles.

The other issue is the speed of light in any reference frame. In special relativity this is the same for all intertial frames regardless of the frame's velocity as measured by another observer. Imagine someone turning on a flashlight on a train moving at .95c, both the observer on the train and one on the ground will measure the same speed for the light. I'm pretty sure this still holds true for accelerated or non-inertial frames, which are the realm of general relativity (back to the texts to be sure.)

[JS Princeton]

I think that what may be important to realize is that while one may have a second derivative of position (and therefore a gradient or non-zero curvature) at any given point (Einstein's Equivalence Principle), the local frame will always look inertial from the most pasic differential point of view. Otherwise, there'd be a problem with discontinuities.

[Eta C]

As an attempt to answer a couple of these questions from klausnh

Let me know if any of the following statements are incorrect:
1) c is the upper limit of any object moving within space-time
2) Space-time distortion is not limited by c. (General relativity)
3) Space-time expansion is not limited by c. (That’s why inflation is possible)
4) If gravity is the effect of distorted space-time, an instantaneous interaction between 2 masses is allowed because Space-time distortion is not limited by c and does not take place within space-time.


1) yes. c is the upper limit on the speed of a particle.

2) Space-time distortion really has nothing to do with the speed of an object except to the amount that its speed increases its mass due to relativistic effects ( the effective mass of an object being M0 / sqrt(1-v^2/c^2) ). Note that as v goes to c this expression diverges.

3)Not sure I can answer this one. I know that during the inflationary epoch the apparent speed of expansion exceeded c, but this was for space itself, not of an object moving through space.

4) In a sense, the two objects were always interacting. Each has its effect on space-time. So to speak of an instantaneous interaction is meaningless in this context.

[kilopi]

On 2003-03-16 16:49, JS Princeton wrote:
The local frame is AUTOMATICALLY inertial. Otherwise, how do you define local?

Local usually has a small area of influence, sometimes involves epsilons and deltas.

How else would you, kilopi, define a local frame so it's not inertial?

As long as the local frame doesn't satisfy that definition, it's not inertial. Just make up a few constants and throw 'em in there.

On 2003-03-16 16:51, Eta C wrote:
Imagine someone turning on a flashlight on a train moving at .95c, both the observer on the train and one on the ground will measure the same speed for the light. I'm pretty sure this still holds true for accelerated or non-inertial frames, which are the realm of general relativity (back to the texts to be sure.)

It does not hold true. The local speed of light is a function of the curvature of space. If spacetime is flat, under the local reference frame, the speed of light is c. Of course, you can always find such a reference frame, but it's not necessary and, in some circumstances, could be misleading since that local frame might not match up with the observer's frame.

[JS Princeton]

You can't simply throw in constants to change the definition, because then you aren't in a local frame anymore. If my x₁ dimension is 3 times my x₂ dimension, then I'm not in a well-defined local frame. Yep, epislons and deltas are what I'm dealing with.

The gs are very well-defined things, kilopi, and I don't see how you can treat them so cavalierly.

[kilopi]

On 2003-03-16 17:40, JS Princeton wrote:
The gs are very well-defined things, kilopi, and I don't see how you can treat them so cavalierly.

I'm not. I wasn't arbitrarily taking a given reference frame and throwing in constants--I was using that as an example.

It's possible to transform them to a noninertial reference frame, correct?

[JS Princeton]

I don't know how one would transform a local inertial frame into a non-inertial frame while preserving locality. I don't think it's possible, but I could be wrong.

<font size=-1>[ This Message was edited by: JS Princeton on 2003-03-16 21:11 ]</font>

[kilopi]

On 2003-03-16 21:10, JS Princeton wrote:
I don't know how one would transform a local inertial frame into a non-inertial frame while preserving locality. I don't think it's possible, but I could be wrong.

Perhaps we differ on the definition of locality. What does it mean to preserve locality?

[JS Princeton]

Well, in as much as locality is defined not discretely but by differentials, I'd say that it means one cannot have a spacelike separation between the two events. However, the point may be that reality could be quantized and then somehow you could invent, on the quantum level, some transformation between an intertial and a non-inertial local frame. I don't have the know-how to do that. I do, however, know how to manipulate a well defined derivative in my g_ij.

[kilopi]

On 2003-03-16 22:06, JS Princeton wrote:
Well, in as much as locality is defined not discretely but by differentials, I'd say that it means one cannot have a spacelike separation between the two events.

Is that the definition of locality?

[JS Princeton]

Locality, unless we have a dicrete universe, is necessarily defined to be infinitessimal.