Is gravity as a "force" an "illusion"?

Question

Kinda inspired by something I read on a forum but wanted to know if it's true, here it is:

"Gravity is a good example. Because it is something that certainly seems to be a real thing that in fact is not a thing at all...it's an illusion. Large masses simply warp spacetime fabric. There is no mysterious gravitational "force", it's simply objects following a normal "straight" path but the space itself is curved."

"It depends on how you're interpreting what you're observing...if like most people you're seeing the gravity effect through Newtonian eyes (the moon is held in orbit around the earth because earth is exerting an attractive force, or the apple falls to the ground because it is being pulled towards the ground, etc) then you are experiencing an illusion. It's not easy or intuitive to view space itself being curved by massive objects, yet that's what is actually happening."

Like...I know Einstein mentioned that gravity is the curving of space and time, but doesn't that still yield a force though? I mean it would have to because things are caught in gravity fields and if you aren't able to escape the pull of a large body then you get sucked into it right?

I think the word "illusion" they use is pretty strong, it might be better to say that it's not what we originally thought, but I guess...thoughts?

Answer 1

The reason we say gravity is not a force, but rather the effect of a spacetime distortion is that, once you see the spacetime as deformed, then the objects move in "straight lines" in that curved spacetime, and objects getting closer is a geometric effect, not an actual attraction between objects.

To give you an intuitive example: Imagine two airplanes flying on earth, they start in the opposite sides of the equator, both travelling south in a "straight line" (that is, along a meridian) and at a constant speed and height. So they start their motion moving parallel to each other. The line looks straight to them, as they are limited to moving along the curved surface. However, they get closer together over time and meet at the southpole. There is no force attracting them to each other, they get closer to each other just because of a combination of their "straight" motion and the shape of the sphere.

Answer 2

That's just fancy writing. Ultimately all models are there to explain observations and the model of gravity as force works for all practical purposes for everyday phenomenon. However, when you look at motion of Mercury around the sun and gravitational effects near the horizon of a black hole, the model describing gravity as a force fails miserably. The model describing gravity as curved space time works fine in both the regimes. Well for most purposes anyways. If you look at Hawking radiation then even the latter seems to fail as quantum gravity effects seem to effective even at arbitrarily large distances.

So calling one model real and the other illusion is misleading. All the models are just models.

Answer 3

Gravity, in Einstein's formulation, is the curvature of spacetime. Particles in spacetime move along geodesics. Geodesics are the analogue of straight lines in curved space. Thus this is a generalisation of Newton's first law of motion that free particles, that is particles with no force on them, move in uniform motion along a straight line. This is why we say gravity is not a force.

However, this is only true if we use 4d spacetime. As human beings, we cannot see 4d spacetime, we see only 3d spatially. And here we see gravity act as a force.

Because the description of motion under gravity is simpler in the 4d spacetime view than the 3d spatial view, it's often said that gravity is not a force. However, I would suggest that neither one or the other viewpoints take precedence. They are complementary viewpoints. Thus gravity is both not a force and a force depending upon the view you take. You could say it is relative!

Answer 4

I think this is a very good example to understand the gap between physical descriptions and mathematical descriptions.

All in all, the physical descriptions(or even philosophical descriptions) can just give us some intuition of natural, but not a concrete description of natural (can be tested not just logically,but also experimentally). Even in almost 1950s, there still some debates on the twin paradox in SR(even some articles published on Nature),and all of them coming from the logical point of view.

Maybe a better example is the variation method, many people describe it as “all possible virtual displacement”. Personally I think this is toatlly misunderstanding and confusing, but this judgment is not from a scientific point of view.

So from my point of view, you can be both right and wrong, but this is not so important (if you're not a beginner),the important thing is how to make your physical intuition consist with the widely accepted mathematical description.

Answer 5

Even staying in the realm of Newtonian theory, movement under gravity fields can be though as geodesics, instead of resulting from a force of attraction.

$$\vec F=m\vec a=m\frac{d^2\vec r}{dt^2}=-\frac{GMm\hat r}{r^2}\implies \frac{d^2\vec r}{dt^2} + \nabla \left(\frac{GM}{r}\right)=0 $$

The last equality can be handled to have the form of a geodesic equation. Of course it is not the same equation that results from GR, but the differences for the solar system for example are tiny.

Answer 6

Nice answers, but none addresses you question: is it an illusion?

Well, that depends on how you feel about the Coriolis effect and centrifugal forces in a rotating reference frame.

Are they illusions? We happily call them "fictitious forces" with no fear of fact-checkers, shadow banners, or community notes.

[From now on: consider playing catch with a ball, on a merry-go-round]

In a Newtonian (or is it Galilean, or both?) world view: gravity is indeed a force, while centrifugal and Coriolis forces are indeed fictitious. I throw the ball to you a bit upward because the Earth is going to be pulling it downward for the duration of its trajectory, for real: you can see it falling. Meanwhile, my aim point it to your right not because a force is pushing it that way, but because you and I are revolving on curved arcs. You move to your right as the ball is in-flight, with no horizontal motion whatsoever.

OK, that's a standard view. When we jump to a general-relativity-for-beginners view, the fictitious forces are still just that, while the vertical acceleration is not a force; rather, it well described in previous answers to this post as the ball following a geodesic.

Now we can step into advanced GR: here the equivalence principle is canon and that means all coordinate systems are equal, and your previous rotating coordinate system accelerating upward at $\vec g$ forever in the Earth's curved spacetime is now THE coordinates of the universe.

The fact that there is a large mass below you leads to a curvature term that looks like Newton's gravity. The fact that the entire universe is spinning around you leads two curvature terms, on that depends only on $\Omega \times (\Omega \times r)$, and another velocity dependent term that looks like $2\Omega \times \dot r$.

It is in this final view that all inertial forces are imaginary: centrifugal, Coriolis, and Newton when $v \ll c$ and length scales are large compared with the Schwarzschild radius of the Earth. If those conditions are violated, then things get non-linear and probably too complicated for simple descriptions as inertial forces.

Answer 7

The rationale for saying gravity isn't a force goes a bit like this. Suppose that you are in space and there is no gravitational field or any other forces. In an inertial frame test masses will move in straight lines relative to one another.

The gravitational acceleration of a test mass doesn't depend on mass in Newtonian gravity unlike the acceleration under other fields. As a result if you had two test masses falling in a uniform gravitational field they would move in straight lines relative to one another even if they have different masses. This is also true to some approximation in a small enough region in a non-uniform gravitational field. So free fall under gravity looks a bit like inertial motion, i.e. - it looks like force free motion. In this view the force you feel when you're standing on the ground is actually the force required to resist your inertial motion under gravity.

For more explanation of this issue see "Gravity: An Introduction to Einstein's General Relativity" by James B. Hartle, Chapter 6.

The arguments about this sound like trying to fit interactions in a new theory into categories from an old theory that don't fit very well, but YMMV.

Answer 8

It may be valid to say that gravity as a force is an illusion, but one must then consider that gravity as the warping of spacetime may also be an illusion.

It's all semantics, really. What is an "illusion" anyways? To be most useful for this discussion, I'd define it the way a magician defines it. It is something that appears to be true from one set of points of view, but which can be shown to be false from others. An assistant may appear to be levitating from the perspective of the audience, but can be shown to be held up by a wire from the magicians point of view.

In this sense, we see why Newtonian gravity might be called an illusion. From the perspective of observers whose relative motion is substantially less than the speed of light, the concept of gravity as a force is very effective. The observers agree on what is happening. Its just as how, when comparing notes with other audience members, we all agree that the assistant appears to be floating. Perhaps one audience member comes up with an idea of how the magician could be using a wire, but from the evidence we were able to gather, both ideas are equally explanatory.

However, what if some of those observers aren't the same. What if some peek behind the curtain and see the rigging. What if some have motion at a velocity that is some non-trivial fraction of the speed of light? What if some are close to a strong gravitational body? These individuals will find that Newtonian physics (and the magician's illusion of levitation) no longer describe what they experience.

It's not easy or intuitive to view space itself being curved by massive objects, yet that's what is actually happening.

This is the one sentence that seems to cause problems, by claiming that this is what is actually happening. We have not yet seen observations that contradict GR, although we expect some in high-energy/small-size environments. The question is whether GR accurately describes what is actually happening, or if we are all merely in the audience clapping at nature pulling off yet another amazing illusion!

There is a philosophical way to view this as well. There are two extreme camps when it comes to this topic in science. The scientific realists believe that our best theories accurately describe physics, and that with unbounded amounts of time, they would converge on what is actually happening. The scientific insturmentalists, on the other hand, assert that while our theories are very effective at making predictions, there's no particular reason to believe they are "real" or indeed could ever be real. The idea that we are all living in a simulation is quite a conundrum for the scientific realists but the insturmentalists don't even have to bat an eye at that idea, for it doesn't change anything they claim. On the other hand, the scientific realists have a leg up when interacting with other belief systems which claim to have a monopoly on "reality." There's no scientific way to decided which is better.