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

Question

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?

Answer 1

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?

Answer 2

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.

Answer 3

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"!

Answer 4

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.

Answer 5

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.

Answer 6

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.

Answer 7

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.

Answer 8

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 :)

Answer 9

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.

Answer 10

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?

Answer 11

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.}