Gravity, Gravitons, and Geodesics.

[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

 

[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 knowledgeable will add to this.

Kevin

 

[selfAdjoint]

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?

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 traveling along it to experience an acceleration. Anything that produces an acceleration deserves the name force, no?

To homology: Ships that pass in the night

 

[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

 

[Nenad]

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

 

[sol2]

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

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

 

[Nenad]

Will comologically realization in the quantum world morphisize to include relaitivity?

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 can't have both explaining the same thing.

 

[sol2]

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 can't have both explaining the same thing.

What geometry are you using?

Can the graviton live below Planck length? Because we have reached a limit does not remove the nature of the gravitational forces. Supergravity has made its appearance for us in this dynamical relation?

 

[ArmoSkater87]

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

 

[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)?

 

[jtolliver]

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

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.

 

[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.

 

[Nenad]

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.

gravity isn't 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.

 

[pmb_phy]

If I am understanding what I am reading correctly, gravity the result of the shape of space-time?

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

It will be seen from these reflections that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to "produce" a gravitational field merely by changing the system of co-ordinates.

I don't understand why this is considered a force at all if it is the result of the shape of space-time.

To get a better understanding of what spacetime curvature is please see
http://www.eftaylor.com/pub/chapter2.pdf
Scroll down to page 2-3 and read this

Question You keep talking about “curvature” of spacetime. What is curvature?

AnswerThe word curvature is an analogy, a visual way of extending ideas about three dimensional space to the four dimensions of spacetime. Travelers detect curvature—in both three and four dimensions—by the gradual increase or decrease of the “distance” between “straight lines” that are initially parallel. In three space dimensions, the actual paths in space converge or diverge. Think of two travelers who start near one another at the equator of Earth and march “straight north.” Neither traveler
deviates to the right or to the left, yet as they continue northward they discover that the distance between them decreases, finally reaching zero as they arrive at the north pole. They can use this deviation to describe the curved spherical surface on which they travel. Similarly, in four-dimensional spacetime, travelers detect the deviation from parallelism of nearby worldlines of free particles, each of which follows an ideally straight spacetime path, often called a geodesic. This curvature can be measured by the travelers and varies from place to place in spacetime.

That is a description of the physics. The cause[/e] is the gravitational force. Or in Einstein's own words, from The Meaning of Relativity, Albert Einstein, page 85

The gravitational field transfers energy and momentum to the "matter," in that it exerts forces upon it and gives it energy: ...

Where does the graviton come into play?

It plays a role in GR similar to the role in EM. It facilitates the interaction.

A force causes an acceleration, and the curvature of space-time also causes acceleration.

It is not the curvature of spacetime that causes gravitational acceleration. Spacetime curvature causes two particles moving under to have a relative acceleration between them, i.e. spacetime curvature causes tidal accelerations. But you can have a gravitational force in the absense of spacetime curvature.

The graviton is a theoretical particle predicted by string theory but not yet demonstrated to exist.

It doesn't come from string theory. It comes from quantum gravity/quantum field theory.

If it exists and is the cause of gravity it will do away with spacetime curvature ...

That is incorrect. The graviton is responsible for producing gravitational forces, not just tidal forces. Therefore one should aslo be able to detect gravitons in a gravitational field even when the spacetime is flat. The graviton, if it exists, will have a relative existence in that sense.

yes, if the graviton is found, General Relativity will be wrong.
...
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 can't have both explaining the same thing.

That is very much incorrect. You can most certainly have both. If the graviton is detected then we will have the mechanism behind GR. Gravitons are certainly not inconsistent with general relativity.

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

Absolutely. That is 100% correct.

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.

Gravity is not like other forces like the electric of magnetic forces. The gravitational force is an inertial force where the others aren't.

See - http://www.geocities.com/physics_world/gr/inertial_force.htm

gravity isn't really a force.

Sure it is. For the definition of gravitational force in general relativity please see any decent GR text or Einstein's papers and books. Or see
http://www.geocities.com/physics_world/gr/grav_force.htm

Pete

 

[robphy]

gravity isn't really a force.

Sure it is. For the definition of gravitational force in general relativity please see any decent GR text or Einstein's papers and books. Or see
http://www.geocities.com/physics_world/gr/grav_force.htm

Pete

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.)

From Wald, p 67:

"The basic framework of the theory of general relativity arises from considering the opposite possibility: that we cannot in principle--even by complicated procedures-- construct inertial observers in the sense of special relativity and measure the gravitational force. This is accomplished by the following bold hypothesis: The spacetime metric is not flat, as was assumed in special relativity. The world lines of freely falling bodies in a gravitational field are simply the geodesics of the (curved) spacetime metric. In this way, the "background observers" (geodesics of the space-time metric) automatically coincide with what was previously viewed as motion in a gravitational force field. As a result we have no meaningful way of describing gravity as a force field; rather, we are forced to view gravity as an aspect of spacetime structure. Although absolute gravitational force has no meaning, the relative gravitational force (i.e., tidal force) between two nearby points still has meaning and can be measured by observing the relative acceleration of two freely falling bodies. This relative acceleration is directly related to the curvature of spacetime by the geodesic deviation equation (3.3.18).

How does this viewpoint of general relativity that there is no such thing as gravitational force square with the well known "fact" that there is a gravitational force field at the surface of the Earth of 980 cm s^-2.
--[snip]--
We could use the time translation symmetry of this example to define a preferred set of background observers. 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. Thus, in this case a well defined meaning can be assigned to gravity as a force field. However, in the absence of time translation symmetry---e.g., in a case where there are several massive bodies in relative motion---there exists no natural set of curves whose comparison with geodesics could be used to define gravitational force."

 

[pmb_phy]

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

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

Yes. I've read that claim and disagree with it. His justification is rather poor in my opinion. Wald has his own personal opinion on that point but he disagrees with everyone else that I've read on this point. I've never seen anyone else make that claim and I can see no justification for it, regarless of his explanation for his claim. However that is probably because his definition is different than everone elses, including Einstein's. Wald seems to think that the negative of the weight vector is what is called the gravitational force. That is not how the gravitational force is defined in all other material on the matter and its is not how I defined it in that web site. I am not the person who created the term "gravitational force" and I'm not the person who defined it in general relativity - that was done by Einstein. However I follow the definition given by authors such as Moller and Mould since I think they make the most sense.

Pete

 

[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.

 

[robphy]

Wald seems to think that the negative of the weight vector is what is called the gravitational force.

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 Lecture Notes on General Relativity by Sean M. Carroll...

"Instead, it makes more sense to define "unaccelerated" as "freely falling," and that is what we shall do. This point of view is the origin of the idea that gravity is not a "force" - a force is something which leads to acceleration, and our definition of zero acceleration is "moving freely in the presence of whatever gravitational field happens to be around.""

from General Relativity Tutorial - Long Course Outline, by John Baez
http://math.ucr.edu/home/baez/gr/outline2.html

From General Relativity Tutorial - Long Course Outline, by John Baez

"6. A GEODESIC is a curve whose tangent vector is parallel transported along itself. I.e., to follow a geodesic is to follow ones nose while never turning ones nose... to follow a completely unaccelerated path. A particle in free fall follows a geodesic in spacetime. In this sense, in general relativity gravity is not a force!"

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)

From Hartle's "Gravity: An Introduction to Einstein's General Relativity" , Ch.6

"We will trace out some parts of the path that led Einstein to a new theory of gravity that is consistent with the principle of relativity. The result will be general relativity, a theory that is qualitatively different from Newtonian gravity. In general relativity gravitational phenomena arise not from forces and fields, but from the curvature of four-dimensional spacetime."

 

[pmb_phy]

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."

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.

In GR, a free-falling object is traveling along a geodesic---

True.

...it is not accelerating... its 4-acceleration is zero.

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)].

Wald is referring to a situation in which a body appears stationary, sitting on the Earth's surface.

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?

Such a body is not traveling along a geodesic...

Correct

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]

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?

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

from Lecture Notes on General Relativity by Sean M. Carroll
Basic Relativity, Richard A. Mould, Springer Verlag, (1994)[/URL]
[the html version of Ch 4 "Gravitation" [URL]http://pancake.uchicago.edu/~carroll/notes/four.ps[/URL] ]
[/quote]
Let me first state something which is true - The term "force" can refer to either a 4-force or an inertial force. Gravity is an inertial force. That is beyond question since it is 100% true in GR.

Gravity is an inertial force. Here are a lit of those who think inertial forces are real

[url]http://www.geocities.com/physics_world/gr/inertial_force.htm[/url]

Since Mould has an entire section in his text on the gravitational force please justify your claim about Mould. Or to be precise, read his text, section 8.13 [b]Gravitational Force and Constants of Motion[/b] pages 261 to 265 and show me exacly where he states this.

In any case it's nice to have Enstein on my side. :biggrin:

Thank you.

Pete

 

[robphy]

...it is not accelerating... its 4-acceleration is zero.

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.

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.

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)].
--[snip]--
Since Mould has an entire section in his text on the gravitational force please justify your claim about Mould. Or to be precise, read his text, section 8.13 Gravitational Force and Constants of Motion pages 261 to 265 and show me exacly where he states this.

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.

 

[woodysooner]

I think it was pmbphy who said earlier that something can has gravitation acceration but yet not spacetime curvatiure. can you explain that, does it has to do with referece pt's.