Something I've heard physicists say but doesn't make sense to me is, "gravity is a just a distortion in space-time, it's not like the other forces." Can someone with more knowledge than me explain this? As far as I can tell:
1) General relativity is just a model.
2) The force that was observed as gravity can be modeled as a a distortion in space-time.
3) Thus (circular logic incoming), gravity is not actually a force, it's just a distortion in space-time, and that why it looks like a force.
This is just begging the question. I could say the exact same thing about any of the other forces between particles, just instead of using the permanent[0], I'd use the determinant[1] for fermions or the immanant[2] for anyons.
I remember in my electrodynamics class applying relativity to Coulomb's law, and seeing the magnetic force just pop out in the Taylor expansion (and I just learned the Feynman lectures does this too: II_13-6[3]). So what do physicists mean when they say gravity is special, or general relativity doesn't play well with quantum dynamics?
The best understanding of matter is in the form of quantum field theory (QFT). QFT is always formulated with some background metric (geometry) of spacetime as an input.
One idea is that the metric (geometry, gravity) could be a field just as matter is a field and people tried to apply the standard rules of (perturbative) QFT to gravity but failed. This is because the theory of gravity is unrenormalizable [0]. An interesting avenue in saving this line of thought is asymptotic safety where the idea is that gravity coupled to the standard model could actually be renormalizable in a certain sense [1].
In any case general relativity and quantum theory have so far been irreconcilable and there is now consensus on how to bridge the gap between those two theories. It is exactly because of this that most physicists will think of gravity and the other forces to be of a different nature.
When people say that gravity is not a force they mean that there is no known particle which acts as the intermediary of said force. For all the other forces we have a theory that explains the exertion of force via a particle.
Your first point states that "general relativity is just a model". Many physicists believe that it is more than a model but a true description of what the world really is like. I understand your urge to label theories as models, but ultimately the question is whether or not there is some level of ground truth that can be accessed in the form of mathematical theories.
First of all, in some sense it is not that interesting of a statement. Whether gravity is a force or not, or whether light is a particle or a wave -- all that depends on definitions of the word force, particle, wave, etc. And nowadays that is the realm of philosophy instead of physics.
Ultimately physicists care not about the words but rather about the equations. Only equations allow them to predict the outcome of experiments (at least probabilistically). A physicists' ultimate dream is to find a single set of equations that predicts every experiment. Words are just used to describe what the equations do, to colleagues and laypeople alike.
So yes, our best model to describe gravitational phenomena is general relativity which describes these phenomena in terms of the bending of spacetime.
If you want to go back to a "force" description of general relativity you can do so as it's a free world. The description of all the other forces starts with a fixed background spacetime, so to do the same with gravity you'll have to contort the elegant covariant equations of general relativity into an ugly mess by expanding around such a background. And then your resulting "theory" will predict exactly the same experimental outcomes as general relativity. (Around flat space it is not so difficult, it produces Newton's law of gravity to the first approximation.)
All that just does not seem worthwhile. More importantly, the discovery of general relativity (and of the importance of general covariance) led to a paradigm shift in physics: all reasonable physicists now believe that any fundamental theory will not ultimately be a set of equations on a fixed background spacetime but rather a set of equations from which spacetime itself should somehow emerge. Very different, therefore, from quantum field theory which needs a fixed background and describes all the other forces in the standard model.
This was my attempt at addressing the "not like the other forces". For the quantum dynamics see the sibling comment https://news.ycombinator.com/item?id=41179419 . And thank you for teaching me about the "permanent" and "immanant" of a matrix, but I still have no idea what that comment is supposed to mean - sorry.
I'm out of my depth here, but I'm imagining something like a path integral[0] between n particles. For example, with two fermions, A and B, you'd get a fraction f of A moving to B's location, and vice versa, giving:
d[AB] = f * ([B] - [A])
The fraction is real as f^2 is the action A -> B -> A which shouldn't get a phase or A would self-destruct. If you had a bunch of anyons circling around in a magnetic field[1], then f could be a root of unity or something more complicated. You can generalize the boundary operator
d[123...n] = Σ(-1)^k * [123...k-1,k+1...n]
to be
d[123...n] = Σ χ(k) * [123...k-1,k+1...n]
where χ(k) is the character of your group. For example, if you have n particles interacting in a circle 1 -> 2 -> 3 -> ... -> n -> 1, then χ(k) = e^2πik/n. This is where the immanant comes from.
Whereas, for the other 3 fundamental interactions, the currently accepted model is in the form of a quantum field theory. For these 3 interactions, the models suggest force carrier particles, and these particles have been observed (electromagnetism: photon, weak interaction: bosons, strong interaction: gluons).
People have tried to construct a quantum field theory -like model for gravity, which would include gravitons as the force carrier particles. But all these attempts have failed to produce a consistent theory, and also nobody has ever measured or observed gravitons, so this is all hypothetical.
But if we get philosophical about this, gravity is not like other forces because the currently accepted model for gravity is not like the models for the other forces. Gravity is not a field with force carrier particles because we have not been successful at modelling it as such.
I’m not a physicist, but I think the comparison is made between gravity and e.g. strong nuclear force. In the latter, the “force” is modelled by interactions between hadrons, with virtual particles (distortions in various fields) mediating the interaction. With gravity, there are no particles (though graviton is a hypothesis).
One can say that space time is also “field”, and mass creates distortions, so gravity is just like other forces interacting via field distortions, but iiuc, unlike nuclear forces, gravity does not have a quantized mathematical model.
Everything in physics a model. Quantum mechanics, electromagnetism, Newton's laws... Arguably everything in science is a model. But at some point, a model does so well at explaining observations that we take it to be a Truth. At one point, genes were 'just a model/theory,' but after the discovery of DNA, we took them to be real and physical. Seen in this way, there's nothing circular about either case.
It's uncontroversial to say that gravity is special because it is non-renormalizable. This means that one can't write down a quantum theory of gravity the same way that we write a quantum theory of electromagnetism, because it predicts infinite quantities that can't be removed from the theory. However string theory does unify quantum mechanics and gravity, and gravity is only "sort of special" in string theory (it does look in some ways like the other forces; the force carrier is the graviton). But exactly how spacetime emerges from string theory is still not fully understood.
Because all masses accelerate at equal rates in a gravitational field either:
1) Inertial mass and gravitational mass are exactly equal without an explanation why
or
2) The acceleration is just an effect of a curvature of space.
Imagine two bodies thrown exactly Northward on a sphere. Although their paths are parallel they would approach each other, as if there was an acceleration. This acceleration would be the same whatever their mass is.
>Imagine two bodies thrown exactly Northward on a sphere. Although their paths are parallel they would approach each other, as if there was an acceleration. This acceleration would be the same whatever their mass is.
The thing that always confuses me is how the distortion explains their behavior when stationary.
Sure, sure, "stationary" doesn't exist and everything is a matter of reference frames etc etc etc, but still, if you and I are both standing still on a sphere, there's nothing drawing us towards each other. Why are we drawn together from rest?
I am just trying to understand this and not make any claim, so bear with me.
Let's say we have a cylinder with a hemispherical top instead of a sphere.
Say the two objects were thrown directly from the base of the cylinder towards what would be the equivalent of north on the hemisphere. Relative to each other they would be moving perfectly parallel and the distance between them would not be changing.
Once they reach the hemispherical section they would still be moving parallel to one another at the same speed but the distance between them would start to shrink, wouldn't this be the equivalent of acceleration due to gravity? Movement towards each other started at 0 and increased, right?
IIRC, Einstein actually spent quite a bit of effort trying to reformulate electromagnetism as a geometric curvature just like gravity, but eventually published a paper admitting failure. I recently saw some physicist talking about revisiting that with some new tricks because maybe it wasn't such a bad idea after all.
Whatever solution is simplest, it's probably better. Every rule has an associated cost and, if the universe itself can be seen as a state transformation engine going over a matrix of states, the fewer the rules, the more likely it is.
And yes, this is bordering some form of faith - that the universe principles should be as efficient and simple as they can possibly be.
That doesn't make sense to me because electromagnetism is both an attractive and repulsive force (can pull objects together or push them apart). Gravity is purely an attractive force which makes sense when explained as warped spacetime. But I'm also not a physicist...
1) General relativity is just a model.
2) The force that was observed as gravity can be modeled as a a distortion in space-time.
3) Thus (circular logic incoming), gravity is not actually a force, it's just a distortion in space-time, and that why it looks like a force.
This is just begging the question. I could say the exact same thing about any of the other forces between particles, just instead of using the permanent[0], I'd use the determinant[1] for fermions or the immanant[2] for anyons.
I remember in my electrodynamics class applying relativity to Coulomb's law, and seeing the magnetic force just pop out in the Taylor expansion (and I just learned the Feynman lectures does this too: II_13-6[3]). So what do physicists mean when they say gravity is special, or general relativity doesn't play well with quantum dynamics?
[0]: https://en.wikipedia.org/wiki/Permanent_(mathematics)
[1]: https://en.wikipedia.org/wiki/Determinant
[2]: https://en.wikipedia.org/wiki/Immanant
[3]: https://www.feynmanlectures.caltech.edu/II_13.html