# Is Gravity a Force or Not?

## Main Question or Discussion Point

I have read a number of books that claim that, according to Einstein, gravity is not a force, but instead the curvature of space caused by mass. And some of those same books then go on to refer to it as a force, mediated by the so-called undiscovered graviton. Can someone please explain if gravity is a force, curvature of space, or can it actually be both?

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tom.stoer
Classical gravity as an effect of curvature of a manifold is different from forces acting on these manifolds. Free falling particles following geodesics never feel any force.

As you say the graviton is fictitious. A description of quantum gravity based on gravitons as excitations on top of a classical manifold may miss the main properties of gravity. In theories like supergravity and superstrings it may be the case that perturbation theory based on gravitons as small excitations of a classical manifold makes sense. But in theories like LQG or in the asymptotic safety approach something like a "graviton" does not make much sense or is at least no fundamental entity.

Chestermiller
Mentor
I have read a number of books that claim that, according to Einstein, gravity is not a force, but instead the curvature of space caused by mass. And some of those same books then go on to refer to it as a force, mediated by the so-called undiscovered graviton. Can someone please explain if gravity is a force, curvature of space, or can it actually be both?
Gravity is associated with the curvature of spacetime, not space. All particles in free fall are traveling at the speed of light along the geodesics of spacetime, and, in regions of spacetime in proximity to large masses, spacetime is curved. To observers at rest relative to the large masses, the particles in free fall seem to have invisible forces acting on them. But this is just an illusion. If the particles are brought to rest relative to the large masses, then they are no longer able to freely follow the geodesics of curved spacetime, and forces will have to be applied to them to hold them in place. These forces are actually causing the particles to accelerate relative to spacetime, as required by the relativistic version of Newton's second law.

of course it can be a force, in the classical sense.

pervect
Staff Emeritus
Probably the best answer is it doesn't matter if gravity is a force or not, as long as you can make correct predictions with whatever theory you are using. In short, whether or not gravity is a force tends to have more philosophical aspects than testable, scientific ones. Science is concerned with getting predictions out of the theory, not so much with describing some sort of ultimate reality.

It's worth pointing out that experimental evidence DOES show that gravity is either not "just a force" or is different from other forces, due to the existence of gravitational time dilation. Other sorts of forces don't cause this sort of time dilation, even when they are very strong. This makes gravity very special.

In my opinion it's easier to learn about gravity if you don't treat it as a force, but this makes quantizing gravity difficult.

Proceeding along with the view that gravity is geometry (which should be understood as just one approach and not any sort of be-all, end-all statement and rather an aid to learining), the sort of gravity you get due to mass is best described by curvature, while the sort of "artificial gravity" you get from being in an accelerating elevator doesn't have anything at all to do with curvature. Gravity in an accelerating elevator has more to do with what mathemeticans call the "connection coefficients" of the geometry. These features depend not only on the background geometry, but the observer as well. Unfortunately I'm not aware of any simple, intuitive, non-mathematical way to talk about "connection coefficients", it appears to be necessary to actually understand the math to fully appreciate this point.

My apologies - in my question I should have stated "spacetime", not "space".

For those that above are saying that gravity is the curvature of spacetime, can you please give me a simplified description of what the graviton is and what part it plays in curving spacetime? Or is there no way to explain it without the use of mathematics?

tom.stoer
... can you please give me a simplified description of what the graviton is and what part it plays in curving spacetime?
This is the main problem: the "graviton concept" as a translation of the "photon concept" in other quantum field theories like QED breaks background independence. That means that first one fixes a classical spacetime and puts small perturbations on top of it. After quantizations these small perturbations could be called "gravitons". But these perturbations or gravitons do not produce any back-reaction on the classically fixed spacetime. It is exactly this artificial split wich causes many standard tools in other quantum field theories to fail in quantum gravity. But as soon as one omits this artificial split and develops a quantum theory not based on perturbation theory there is still a (quantum) gravitational field or quantum geometry, but depending on the details of the model (LQG, AS, ...) this is nothing which should be called "graviton". The graviton concept becomes a secondary concept which may be reasonable in some regimes, but which will fail in other regimes.

I have read a number of books that claim that, according to Einstein, gravity is not a force,..
I cannot believe Einstein would have said such a thing. This is the sort of things people who get carried away about general Relativity would say.

I suspect that some people think Einstein believed that there is no need for corrdinate systems, that GR was a coordinate-free theory. Wheeler may have believed that, but Einstein'd view was the opposite--he viewed the situation as one where the laws of physics are the same in all coordinate systems. That implies that physics must be done in a coordinate system.

Relativity is a physical theory, not a philosophical entity.

All particles in free fall are traveling at the speed of light along the geodesics of spacetime.
You wrote that all particles are travelling at the speed of light...

That is quite incorrect.

Chestermiller
Mentor
You wrote that all particles are travelling at the speed of light...

That is quite incorrect.
I stand by what I said. All particles and objects are traveling along their worldlines at the speed of light relative to (stationary) 4D spacetime. Together with their rest frame of reference, they are traveling in their time direction at the speed of light. The 4 velocity of an object is always equal in magnitude to c.

Chet

I stand by what I said. All particles and objects are traveling along their worldlines at the speed of light relative to (stationary) 4D spacetime.
Chet
Well, we sure do not agree (to put it very mildly)!

PeterDonis
Mentor
2019 Award
I stand by what I said. All particles and objects are traveling along their worldlines at the speed of light relative to (stationary) 4D spacetime. Together with their rest frame of reference, they are traveling in their time direction at the speed of light. The 4 velocity of an object is always equal in magnitude to c.
Just to note, this only applies to objects traveling on timelike worldlines.

Just to note, this only applies to objects traveling on timelike worldlines.
No, it would ponly apply to partticles moving on null world-lines, like photons.

Particles with non-zero rest mmass move on timelike worldlinesw and absolutely positively do not move at the speed of ligh along geodesics.

Consider a situation with no gravity. The particle mpoves along a 4 dimensional geodesic which is simply a Euclidian 4 dimentional straight libe. You really think it moves at the speed of light?

I just noticed Chester clarified his original statement. I did not earlier notice it changed, because he said he was sticking to his original claim.

Yes, the magnitude of the 4 velocity is c. But the velocity is not c. Acting as if they are the same is like thinking a particles momentum is equal to its rest mass.

You wrote that all particles are travelling at the speed of light...

That is quite incorrect.
He's not talking about three velocity, he's talking about the four velocity of a world line.
Four velocities are always normalized, we usually take c to be unity so the magnitude of the four velocity is always c.

Well actually that's kind of meaningless, if you use the (-,+++) convention, ds^2=-1

Chestermiller
Mentor
I just noticed Chester clarified his original statement. I did not earlier notice it changed, because he said he was sticking to his original claim.

Yes, the magnitude of the 4 velocity is c. But the velocity is not c. Acting as if they are the same is like thinking a particles momentum is equal to its rest mass.
Thanks ApplePion. I think we are on the same wavelength now. When I originally wrote "All particles in free fall are traveling at the speed of light along the geodesics of spacetime," I though it would be understood that I was referring to the 4 velocity. This may have been an oversight, although, in my defense, I did say "the geodesics of spacetime."

When you said "Yes, the magnitude of the 4 velocity is c. But the velocity is not c.", I guess in the first sentence you were referring to the 4 velocity, and in the second sentence you were referring to the 3 velocity relative to some frame of reference. The 4 velocity of a particle has a magnitude of c, and, in the particle's rest frame of reference is always pointing in direction of the time coordinate basis vector (which, in free fall, is pointing along a geodesic).

pervect
Staff Emeritus
My apologies - in my question I should have stated "spacetime", not "space".

For those that above are saying that gravity is the curvature of spacetime, can you please give me a simplified description of what the graviton is and what part it plays in curving spacetime? Or is there no way to explain it without the use of mathematics?
The graviton is not part of the geometric theories of space-time, so it doesn't have anything directly to do with space-time curvature. The graviton, if it exists, would be part of a quantum theory of gravity. Various approaches to quantum gravity exist in the literature, but there isn't any consens about them, in large part because there isn't any good way to test most of them.

If you want to learn the geometric theory of gravity, basicallly you need to forget about gravitons, they aren't relevant to the geometric approach used for classical General relativity.

I gather it is possible to recover most of GR from the quantum theory of spin-2 particles. The one approach I've seen to this has the problem (or feature) of assuming a static flat background for space-time, then showing that this static flat background becomes unobservable. Unforatunately, I don't recall the name of the paper, and it's rather advanced at any rate.

But the very short answer about gravitons is that they are part of a differet theory than the geometric theories, and that the theory is not as well developed as the geometric theories at the current time.

But the very short answer about gravitons is that they are part of a differet theory than the geometric theories, and that the theory is not as well developed as the geometric theories at the current time.
I believe what you are saying is there are multiple theories on what causes gravity. And the Graviton is not part of Einstein's General Theory of Relativity. I am only familiar (in a very general sense, at that, no pun intended) with General Relativity. I know absolutely nothing about Quantum Gravity.

Confusing. I'll be glad when we get this all figured out. :tongue:

Thank you, pervect.

I cannot believe Einstein would have said such a thing.
I didn't mean to misquote Einstein. When I said that Einstein "said" that about gravity, I meant via his General Theory of Relativity. Although chances are I don't completely understand that theory.