# If gravity isn't a force, then why do we learn in school that it is?

I have studied some of Einstein's Theory of General Relativity, and I understand that it states that gravity isn't a force but rather the effects of objects curving space-time. If this is true, then why are we instructed in middle school that it is a force?

• While a good question, it isn't a conceptual physics question and any answer given will can only be an opinion. Voting to close. Nov 19, 2015 at 1:50
• This isn't really about physics, but rather about approaches to education. Most of education builds on simplifications and little lies - they are usually good enough for the understanding you require throughout middle school (and life, most of the time). The real stuff rarely comes before college. Nov 19, 2015 at 8:20
• Though I agree that this is a physics education question, not a physics question, it implies a greater "Why is physics traditionally taught this way" question that is pertinent to both physicists and those learning physics. So pertinent, and in fact fundamental, that I consider this to be one of the best questions to be asked on this site. Nov 19, 2015 at 13:10
• I second what @dotancohen said. You can't expect to draw a polygon and then any question that falls outside for a tiny bit is "vote close" material. Sometimes one will fall on the line, and then the value added to the site needs to be appraised. Don't Sheldon up. I think this could be marked as duplicate as Qmechanic stated, though. (duplicate does not decrease site value. It is just a way to link questions). Nov 19, 2015 at 13:48
• It's a model. Possibly/Probably/Definitely/Dunno, Einsteinian physics and Quantum Physics are just models, too. Nov 19, 2015 at 14:54

Because Newtonian gravity, where it indeed is considered a force, is a good enough approximation to the situations you consider in middle school (and beyond).

General relativistic effects are very weak at the ordinary scales we humans look at, and it would be overkill to introduce the full-blown machinery of general relativity (which demands a considerably more advanced mathematical treatment than ordinary Newtonian forces) to treat situations where the error incurred by just using the Newtonian version is negligible.

Additionally, even in the general relativistic treatment you might still consider the effect on moving particles to be a "force", just like you can consider the centrifugal force to be a fictitious force that appears in rotating coordinate systems, see also the answers to Why do we still need to think of gravity as a force?

• A very nice answer. Must remember it when similar 'lies to the children' arguments are brought up.
– Gert
Nov 19, 2015 at 1:54
• It's not "lies" so much as "simplification". Besides, it is very likely that general relativity is not the complete picture of gravity, since it is incompatible with quantum mechanics. Nov 19, 2015 at 8:07
• Even if it's a "lie", really it's a lie about the meaning of the word "force". It's only a lie about reality to the extent that you conceal the fact that e.g. Newtonian gravity gets the orbit of Mercury wrong. Since the word "force" is just terminology, I'm not sure it really matters to "lie" about it in the sense of using different meanings in different contexts. You can call gravity a banana if you like, so long as your theory defines how bananas operate. It only becomes a problem if you let people expect that definition also to be true of fruit. Nov 19, 2015 at 9:53
• ... so as you say, centrifugal force is a force in "the theory of rotating frames" and there's no such force in "the theory of inertial frames". It's pretty well meaningless to bang on about it not being "really" a force, beyond making this distinction. Especially while standing on a planet. Nov 19, 2015 at 9:59
• @SteveJessop No, surely you don't mean a banana. Surely you mean a Female Aardvark. Nov 20, 2015 at 6:32

Even if we restrict ourselves to a Newtonian conception of the world, forces do not exist. An essential thing that is not emphasized enough when teaching physics, is that physics (in all its wonder) is nothing but a mathematical model of the reality we perceive. Whether you are considering Newtonian mechanics, relativity, or quantum mechanics.

There are no coordinates, nor vectors, nor anything like that in reality. We use those mathematical tools to attach meaning and relate -- and hopefully explain -- measurements and observations we make. This approach has had a huge success, both in more or less direct applications (think NASA or many cutting edge technologies) and also in theoretical advances, like quantum mechanics (where the right generalization of the Hamiltonean formalism somehow magically explain things at the particle level).

In the particular case of forces, note that you never measure a force. What you measure are its consequences (most often, a displacement or a change in current, or many other things) and you interpret that change, using the Newtonian model, as the action of a force.

• "All models are wrong. Some of them are useful."
– JS.
Nov 20, 2015 at 2:15
• "There are no numbers." - from the movie LUCY
– user95006
Nov 20, 2015 at 18:22
• It's provocative to emphasize that "forces do not exist" in a scientific forum like this. What does it mean for something to exist? Do atoms exist? Does a tree exist? Does the number 2 exist? Does the Internet exist? These are philosophical and ontological questions, rather than physical, and subject to many different positions and theories. I suggest that the claim "forces do not exist" is itself a simplification which is intended as a teaching aid.
– John
Nov 23, 2015 at 5:13
• While talking Newtonian mechanics, I would use the word "exists" for things that can be measured. Forces cannot be measured; they are inferred, via the pre-existing Newtonian theory, by measuring displacements (i.e, distances). If you don't have the theory, you don't have the forces. You don't need a theory to record the presence of a tree, so trees do exist unless you negate realism (and in that case why bother with physics at all). The number 2 does not exist, but that doesn't concern physics, Nov 23, 2015 at 6:37
• You believe there is a tree because you can see it and feel it. Feeling works with forces, seeing ultimately, too (electric forces inside the nerves for example). So how do you know the tree really exists and is not the effect of some other more fundamental entity? This whole thing ends in the question whether we as human beings are even able to grasp the reality surrounding us, or whether we just see what our body and mind are able to process... Philosophically this is highly interesting, but for teaching it has no use imho.
– Dux
Nov 24, 2015 at 15:01

Tim B. takes the position that this an example of lying to children. I completely disagree; in my view, what this is an example of is idealization, which is something that every model must do, in every branch of science. As George E.P.Box once wrote:

Essentially, all models are wrong, but some are useful.

It isn't lying, it's called doing science. Ergo, teaching that gravity is a force only becomes dishonest if the teacher fails to bring up the fact that Newtonian gravity is merely a model of gravitational interaction, and that essentially all models are wrong, including GR and quantum gravity. In short then, I think that gravitation provides an excellent pedagogical opportunity to discuss the practice of science and philosophy of science in a classroom setting; and therefore, if done right, fails to qualify as an example of lying to children.

There's a small subtlety here. As far as anyone knows, it might be possible to discover a theory of everything (ToE) that not only accounts for all phenomena we currently know about, but which, in fact, accounts for all phenomena we can ever know about, and all entities we can ever interact with.

But even if some research program discovers a ToE, there's fundamentally no way we can ever know that it's a ToE. To avoid completely stifling physics, we always have to assume that there might be further phenomena that nobody knows about yet, even if the currently favored ToE appears to explain all known phenomena.

Of course, we've been in this situation before; for a long time, it was widely assumed the Newtonian mechanics was a ToE that was able to explain essentially all of physics. How wrong we were, and how lucky that certain thinkers refused to accept that physics was essentially "done"!

• +1 Although not addressing the physics, this is a most excellent point and left out by the other answers. CF JS's wonderful comment on one of the answers: "All models are wrong. Some of them are useful." Nov 20, 2015 at 6:25
• So, when the "child" (age 3-127 as someone mentioned) realizes that everything they are being taught is an approximation, model, concept, "lie", simplification, analogy, etc. What are they to think then? It is like the old joke where one Doctor says to the other: "When do we get to stop practicing medicine and start doing it for real?" When does reality appear?
– user95006
Nov 20, 2015 at 18:30
• If it's taught properly, people should know that physics is only about models. But they turned out to be very useful, and in a lot of cases you even accept small errors for simplicity. "Reality" in physics are experiments where you can verify how good your model predicts the outcome of an experiment. Nov 21, 2015 at 11:56

It's an example of "lie to children".

https://en.wikipedia.org/wiki/Lie-to-children

Because some topics can be extremely difficult to understand without experience, introducing a full level of complexity to a student or child all at once can be overwhelming. Hence elementary explanations are simplified in a way that makes the lesson more understandable, though technically wrong. A lie-to-children is meant to be eventually replaced with a more sophisticated explanation which is closer to the truth.

• ... where "child" is defined as someone aged 3 to 127 who either did not have physics yet or had it, but decided to major in Liberal Arts, Law, Engineering, Computer Science, Cooking, Sales, Painting, Car Repairs, Politics, Religion - well pretty much everyone.
– WoJ
Nov 19, 2015 at 12:51
• @WoJ Yep, pretty much. There's several good explanations of the "lies to children" concept been written by Jack Cohen, Ian Stewart and Terry Pratchett. It's a deliberately provocative name for what is actually a very common practice. Nov 19, 2015 at 12:56
• Dotan's razor: An insignificant inaccuracy can save a lengthy explanation. Nov 19, 2015 at 23:31
• By that reasoning, every model is a lie to children. Nov 20, 2015 at 11:03
• @TimB And a good physics teacher will teach children the concept of models, and when a smart inquisitive kid asks further, should tell this kid that the Newtonian model is only approximately correct but good enough for daily use. Nov 20, 2015 at 11:10

I would like to take a slightly different angle on this question and point out that most physicists believe that gravity is in fact a force. The great triumph of modern particle physics, the standard model, contains the strong, weak, and electromagnetic forces. These forces are represented in the standard model by the presence of force carriers (spin 1 gauge bosons): the Gluon, W and Z bosons, and the photon, respectively, that couple to particles with charge (electroweak or color). The standard model is a quantum field theory. When probing the structure of matter at high energy this representation is necessary. However, at low energies one can construct effective theories that are much simpler. Maxwell's equations are one example. Similarly, most physicists believe that the equations of general relativity (Einstein's equations) are the low energy solution of a quantum field theory of gravity. Thus it is natural to assume that at some large energy scale Einstein's equations will break down (approaching the center of a black hole, for example). The problem is that the force carrier for gravity (the graviton) ought to be a spin 2 particle, unlike the other force carriers, and it is proving very difficult to construct a consistent quantum field theory of spin 2 gauge particles. Currently string theory is the leading candidate for such a theory.

So in the course of one's training as a physicist, one first learns gravity is a force from Newton, then that it's really a result of being in a curved space from Einstein, and then that it must really be a force after all! Who's name we will ascribe to that last lesson is still to be decided, it seems.

• It's also worth emphasizing that while a fully consistent, UV complete theory of gravity is tricky, the graviton is actually a feature of the low energy effective field theory for gravity. So it makes sense to talk about gravitons even without the full quantum theory of gravity. +1 for emphasizing that gravity is a force (even in general relativity), despite the colloquial view that GR somehow says it isn't. Nov 22, 2015 at 6:30
• Thanks for clarifying this point. I should have said that string theory is the leading candidate for a UV-complete theory of gravity that incorporates the graviton when running to low energies. Nov 23, 2015 at 15:30
• The non-abelian "forces" aren't really forces in the Newtonian sense, either, only in the parlance of modern quantum field theory which essentially equates a "force" with a gauge field theory. Classical Yang-Mills theory isn't usually done, and for good reason - we don't have classical equivalents to these "forces", and it is not clear whether they become forces in the classical limit, especially for the weak force. Nov 24, 2015 at 14:39
• "one first learns gravity is a force from Newton, then that it's really a result of being in a curved space from Einstein, and then that it must really be a force after all!" Excellent! Nov 25, 2015 at 12:37

If we observe our school syllabus, almost all the physics that we learn is Newtonian physics. Everything from force to the laws of motion are all based on Newtonian ideas.

And the general theory of relativity is a modern concept which in fact is more true. But you know the GTR is a difficult concept to understand for a child. So to make the course simple these things are taught to us as a force.

And also before Einstein every one believed gravity as a force. Therefore the classical tradition has still continued in our books. Which need serious revision.

To give you an example even in chemistry, the atom is taught to the children as a kind of solar system. Which it clearly is not.

I know of two reasons for why we should consider gravity to be a force. The first is purely classical and Newtonian: tidal forces. Gravity is solely responsible for producing tidal forces, and they cannot be considered a fictitious force, whereas the usual acceleration due to gravity in some sense can always be thought of as fictitious. The way you know that tidal forces are real forces is that they are constructed directly using the Riemann curvature tensor, which cannot be made to vanish using a mere change of coordinates. Compare this to the acceleration due to gravity, which in a general relativistic setting is characterized by the connection coefficients, $\Gamma^a_{bc}$. Unlike the Riemann tensor, the connection coefficients are not tensorial, and they can be made to vanish using a change of coordinates (this choice of coordinates is called Riemann normal coordinates), which reveals the fictitious nature of this force. From a more practical standpoint, tidal forces should be thought of as real because they lead to things such as heating of the interior of planets, or the spaghettification of the poor astronaut that happens to fall into a black hole.

The second reason that one might consider gravity to be a force is more founded in the quantum setting. In quantum field theory, the concept of "force" is generally replaced by "gauge interaction," i.e. a boson that couples to a conserved current. When people say there are four fundamental forces, this is generally the sense in which they are using the word force. As a quantum theory, gravity behaves very analogously to the electromagnetic, weak, and strong forces, although of course there are differences in the details. Note also that when we take the classical limit of many low energy gravitons (the force-carrying particle for the gravitational interaction) we get a gravitational wave. And what kind of forces do gravitational waves produce? Tidal forces! This is obvious from the characteristic stretching and squeezing pattern associated with the gravitational wave.

So I'd say that the quippy phrase that "gravity is not a force" is the real lie-to-children that appears in pedagogical introductions to general relativity.

• Good answer, asperanz. Yes, I would agree that "gravity is not a force" is the real lie-to-children. Nov 25, 2015 at 12:36

I think many people here just too intelligent to see this point:

because you do not have a better choice. It is simply not practical and not feasible to teach kids in high school about General Relativity. (um... expecting they know some tensor already? and understand space-time?)

Besides, as mentioned by many others, the Newton approach is not so bad. In many cases, the Newton approach gives us a very good numerical answers, which is enough for many purpose.

Furthermore, the history of Newton gravity provides excellent materials for kids to learn about scientific methods, say, how and why scientists measured the gravitational constant? even in this question, we are embracing the fact that science is never the complete story of nature, as Feynman once said,

"Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet." -Richard Feynman

and that will let kids know why we should keep doing science and encourage them to do so :)

• I don't completely agree but this is a very nice way to look at things! Really pleasant answer.
– user87745
May 2, 2018 at 21:04

Why are we instructed in Middle School about forces?

I'd go along with Shings answer; it's about pedagogy: it's easy for kids to think and visualise force, you can push a chair, or pull an elastic band; when you swing a stone tied to string in a circle you can feel the centrifugal force.

It also follows the historical development of the discipline, which you means you're learning how science works via the inductive method, as well as by theory and inspired guess: after all, Planck actually just guessed at the quanta in an attempt to solve the Black-body radiation problem.

It's also the language that encoded into how physics is thought through and conceptualised: force is expressed in terms of momentum, and then the move to the Lagrangian formalism is to generalised momenta; and then again to QM by replacing them with their operator equivalents.

Why is GR not a force

The other reason is that moving to GR, doesn't negate or falsify Newtonian Mechanics; in a local frame there is a Newtonian approximation in which gravity will appear as it usually does as a force.

It's in the global picture that one can see it follow a geodesic, which it's worth reminding ourselves that it's a particle following a 'straight' line on a curved surface; so a generalisation of Newton's first law.

The problem, in a way, is the word 'is'; instead of thinking it signifies just one thing, it's better to think it equivocates between several descriptions:

This ball is painted blue; is round; is lying on the ground: several is's to describe several different perspectives on the one and single situation.

Because Newton's theory of gravitation is way much easier than general relativity and can be easily accepted by middle-school students. Think what will they think if you introduce tensors to them?

After all, when we teach math we don't do it all at once. First children learn to count, then to add and subtract whole numbers, then negative numbers, then fractions. They learn math one part at a time, and in generally the same order humanity invented it.

Newton said that things move in a straight line at constant speed unless forces act on them. Anything which changes them from straight-line constant-speed is a force. That's a useful concept.

Why start out telling them that gravity turns straight lines into curves?

If gravity isn't a force, then why do we learn in school that it is?

Because it is a force. It's just not a force in the Newtonian sense, wherein work = force x distance. When you drop a brick the "force" of gravity doesn't add any energy to the brick. Instead it converts potential energy into kinetic energy. This is different to what you do if you accelerate the brick horizontally. Then you do work on it. You add energy to it. You also do work on the brick when you lift it up. You exert a force x distance against gravity, and as a result you add energy to the brick*. Then when you drop the brick this potential energy is converted into kinetic energy. Once the brick hits the ground, this energy is dissipated, and you start the cycle again. The process is not unlike what you would do if you pulled an electron away from a proton, so don't think gravity is in some way unique.

I have studied some of Einstein's Theory of General Relativity, and I understand that it states that gravity isn't a force but rather the effects of objects curving space-time. If this is true

It isn't quite true I'm afraid. Spacetime curvature relates to the tidal force, whilst "spacetime tilt" relates to the force of gravity. See the tilted light cones here.

then why are we instructed in middle school that it is a force?

Again, because it is. They just don't tell you the full story, that's all. Ask a question about lifting a brick and how it compares with pulling the electron away from the proton. Look up the mass deficit, and keep asking questions!

* Strictly speaking you also add energy to the Earth, but whilst momentum is equally shared, energy isn't. The Earth gets such a small share that we ignore it.