# Is gravity both a force and not a force?

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## Main Question or Discussion Point

Okay, I know there are many other discussions regarding this exact topic, but I might (probably not) have found an easier way to think of gravity being a force or not a force.
Just like light can be a particle or a wave from how you measure it, to my understanding so can gravity. As I am told, NASA look at gravity as a force (newtonian gravity), for their calculations, because GR equations take too long and make a tiny difference. However, when calculating gravity in much larger masses (maybe like galaxies), general relativity, where gravity is a distortion of spacetime, is needed as it becomes far more accurate.
This means depending on how you need it, gravity can be used as a force (for planets and asteroids etc) and with it not being a force (for larger masses possibly stars and galaxies etc.)

I don't know if this is correct. I have just been reading so much about if gravity is a force or not and I am trying to get some answers).

Could this work as an over simplified answer?

## Answers and Replies

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In GR gravity is described as curvature of space. and on cosmological scales it's more accurate than Newton's model.
However, Newton's model is fine if you are something like a civil engineer designing a bridge, and much easier.

vanhees71 and stoomart
Nugatory
Mentor
Could this work as an over simplified answer?
That's close enough...
Have I pointed you at Asimov's essay "The relativity of wrong" before? If not, you'll want to read it before you take on the question "Gravity is a force: Right or Wong?".

Demystifier, atyy, vanhees71 and 1 other person
" right and wrong are fuzzy concepts "
Thanks Isaac.

Lunct
That's close enough...
Have I pointed you at Asimov's essay "The relativity of wrong" before? If not, you'll want to read it before you take on the question "Gravity is a force: Right or Wong?".
I read it before and really enjoyed it.
Can you point out the errors in my post if it is "close enough"

Ibix
I read it before and really enjoyed it.
Can you point out the errors in my post if it is "close enough"
Speaking precisely, we don't claim that gravity is or is not a force. Different models treat it in different ways, and we don't claim our best model is correct. Only the best we can currently do.

So use Newton (and treat gravity as a force) when you can get away with it because the maths is easier. Use Einstein (and treat it as not a force) otherwise. And keep an open mind about what gravity "actually is". Who knows what quantum gravity will say?

Lunct
Well, I would like to say that I fundamentally disagree.

What is a force? Whether you consider gravity as a force or not depends on how you answer this question.
I would say that a force is something that causes absolute acceleration in the sense that you can measure the acceleration with an (ideal) accelerometer. Now, by the (weak) equivalence principle, the (passive) gravitational mass of an object is equal to its inertial mass, which means that this so called gravitational force' pulls you in just the right amount as to make sure that you cannot measure it with an accelerometer. Why? Because it does not matter which mass you or the parts in the accelerometer have, they get accelerated the same way, so nothing happens here. But if the accelerometer does not measure anything, is gravity a force then?

Of course, you could also answer that a force is something that causes relative acceleration, but then you belong to the kind of people that think that a force acts on the world when you turn around. Think about it, it's very worthwhile for understanding the world you live in.

Who knows what quantum gravity will say?
What about Aristotelian physics? It's true in its own right, isn't it?

Mister T
Gold Member
This means depending on how you need it, gravity can be used as a force (for planets and asteroids etc) and with it not being a force (for larger masses possibly stars and galaxies etc.)
Not quite, because you can use the model that is general relativity for both situations. The model that describes gravity as a force, however, gives you virtually the same answers as general relativity only in the case of weaker gravity. So it's not that there are two separate models with different limits of validity, it's that the force model has limits of validity that are more restricted than the limits of validity of general relativity.

Even general relativity has limits of validity, though. There is no such thing as a theory with universal limits of validity. Although there may be one, or even more than one, some day.

Mister T
Gold Member
What about Aristotelian physics? It's true in its own right, isn't it?
It has very restricted limits of validity. It doesn't really make quantitative predictions, so it may not even be correct to call it physics. Usually we credit Galileo with the development of the first theories of physics.

Hi. Newton's law
$$F_{12}=-G\frac{m_1m_2}{r_{12}^2}$$
As Force acting on ##m_1## is ##m_1a_1##
$$a_1=-G\frac{m_2}{r_{12}^2}$$
Or as vector analysis
$$div\ \mathbf{a}=-4\pi G\rho$$ where ##\rho(\mathbf{r})## is mass density at ##\mathbf{r}##.
So even in Newtonian Mechanics, gravity can be interpreted not only as force but as the field of universal acceleration which is a kind of spacetime feature sourced by mass.

haushofer
Gravity is in a superposition |being a force>+|not being a force>.

Not quite, because you can use the model that is general relativity for both situations. The model that describes gravity as a force, however, gives you virtually the same answers as general relativity only in the case of weaker gravity. So it's not that there are two separate models with different limits of validity, it's that the force model has limits of validity that are more restricted than the limits of validity of general relativity.

Even general relativity has limits of validity, though. There is no such thing as a theory with universal limits of validity. Although there may be one, or even more than one, some day.
that was the only drawback I could think off. Are there any others?

Mister T
Gold Member
that was the only drawback I could think off. Are there any others?
To what drawback do you refer?

I would say that a force is something that causes absolute acceleration in the sense that you can measure the acceleration with an (ideal) accelerometer. Now, by the (weak) equivalence principle, the (passive) gravitational mass of an object is equal to its inertial mass, which means that this so called gravitational force' pulls you in just the right amount as to make sure that you cannot measure it with an accelerometer. Why? Because it does not matter which mass you or the parts in the accelerometer have, they get accelerated the same way, so nothing happens here. But if the accelerometer does not measure anything, is gravity a force then?
I would say still yes in newtonian physics. In newtonian physics you have fixed parallel transport by which you can compare vectors that are in different points of space. Then you have first newtons law speaking about straight lines when object is not acted on by some force. Therefore, you would get inconsistency between straight lines in euclidean geometry and inertial systems, and both are most fundamental concepts of newtonian physics. Because of this, in newtonian physics gravitation must be force, even though it has no local effect only global one.

Geometry_dude
pervect
Staff Emeritus
I would focus on a more concrete observation. Consider gravitational time dilation. This is an effect of gravity that does not conveniently fit into the "force" mold, but is well documented. So viewing gravity as a force will not explain gravitational time dilation. You'd have to add that in "on top" of gravity being a force.

There are other effects that are harder to observe experimentally that are also predicted by General Relativity. These involves alterations in the geometry of space. ((add: the 'extra' bending of light is one example of these tiny effects)). So, adding "gravitational time dilation" as an additional effect "on top of" gravity being a force is still not fully sufficient to fully understand General Relativity.

Thus, if one wants to understand all the effects of general relativity, one cannot find a complete description of the phenomenon as "a force". Describing gravity as a force + gravitatioanl time dilation is better, but it is still not sufficient to explain the full theory - for instance, it won't explain the bending of starlight.

In the end, to get a full understanding of GR, one needs to abandon the force model as a complete description of gravity, and learn something else.

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Geometry_dude, Lunct, PeterDonis and 1 other person
Hi.

Sequel of #10

In SR ##\rho c^2## is, in an approximation, one of 16 components of energy momentum density tensor ##T^{\mu\nu}##. So we expect to expand the relation to all the components, i.e.

$$[\frac{-2}{c^2}\ div\ \mathbf{a}]^{\mu\nu} \ like \ =\frac{8\pi G}{c^4}T^{\mu\nu}=\kappa T^{\mu\nu}$$

Not only mass or energy but also momentum and pressure participate. The left hand side of dimension ##L^{-2}## was found and named Einstein Tensor ##G^{\mu\nu}##.
Once relation of one component expands to the relation of 16 components. We can expect more variety of effects than only Newton's acceleration law. Best.

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I don't know if this is correct. I have just been reading so much about if gravity is a force or not and I am trying to get some answers).
I think it is worth pointing out that gravity as a force (GAAF!) does not explain its effect on light properly.

Geometry_dude
To what drawback do you refer?
the fact that GR can work in both instances.

Mister T
Gold Member
the fact that GR can work in both instances.
That's not a drawback, it's an accomplishment.

That's not a drawback, it's an accomplishment.
it is a drawback in my original post.

Yes, pervect is making quite a point with the time dilation argument. The point raised by m4r35n357 about bending light is also quite good, even though you could argue that light has a very, very tiny non-measurable mass and then you're back in hell's kitchen.

I would say still yes in newtonian physics. In newtonian physics you have fixed parallel transport by which you can compare vectors that are in different points of space. Then you have first newtons law speaking about straight lines when object is not acted on by some force. Therefore, you would get inconsistency between straight lines in euclidean geometry and inertial systems, and both are most fundamental concepts of newtonian physics. Because of this, in newtonian physics gravitation must be force, even though it has no local effect only global one.
I had to think about what you were trying to say here for a bit, and now that I got what you mean, I have to say that's an intricate point you raised here. My counter question to you would be: What if you start your Newtonian description with the falling observer in a constant gravitational field?

I had to think about what you were trying to say here for a bit, and now that I got what you mean, I have to say that's an intricate point you raised here. My counter question to you would be: What if you start your Newtonian description with the falling observer in a constant gravitational field?
If you mean by constant that it doesnt change with time, i think that changes nothing on my argument.

If you mean by constant homogeneous and isotropic (which from the context i think you do, but perhaps not), then i think that is exactly what you do in newtonian physics. You ignore any additive constant in gravitational law, because it would curve every particle in the same way with respect to some euclidean "absolute space". Moreover it wouldnt produce anything that accelerometers could measure. Thus, just by redefining new absolute space by properly accelerating it with respect to original absolute space you get rid of this additional constant with no change in observable predictions.

Of course absolute space and absolute time cannot explain real world, so you are bound to abandon it and create special relativity and, as it was shown in MTW (so-called Schilds argument, page 188), the idea that gravitation is a force is incompatible with special relativity+energy conservation and that leads you to curved spacetime and its incompatibility with quantum theory leads you to whoever knows what. But in the context of newtonian physics, gravitation must be a force.

P.S.
I know i am terrible with english. So i apologize if my comments are hard to understand.

Well, I mean a force field like this
$$\vec F = m \vec g \,$$
where ##\vec g## is (covariantly) constant. Isotropy is not an appropriate word here, but I'm sure that this is what you meant.

Of course, Newton certainly viewed gravity as a force. My point is that this point of view becomes inconsistent here.
One one hand, you cannot take this frame of reference as your starting point for defining the euclidean metric, because it is philosophically not inertial. On the other hand, if all physics works the same, how are you supposed to know what an inertial frame of reference is?

Isotropy is not an appropriate word here, but I'm sure that this is what you meant.
Yes, you are right. Thanks for pointing that out:)

One one hand, you cannot take this frame of reference as your starting point for defining the euclidean metric, because it is philosophically not inertial. On the other hand, if all physics works the same, how are you supposed to know what an inertial frame of reference is?
I dont understand your struggle.

Because of gravity, you need to define inertial frame by zero acceleration when there is no force, not by zero accelerometer readings, otherwise, as i argued, you would need to abandon euclidean geometry or rebuild newton's laws of motion.

If there is however some constant omnipresent acceleration, you can say there is no inertial frame of reference. Or you can say there is some constant omnipresent gravitational force. The freedom in what you call force you can use to choose comoving euclidean space to make physics simple and to get rid of unobsarvable random parameter from the theory.

Geometry_dude
Of course, in the universe where there is only constant gravitation, defining gravitation is quite redundant.