> Beauty represents the forces of nature: electromagnetism, the weak force, the strong force and gravity.
The point of General Relativity is that gravity is not a force. I'm familar with standard argument that Newtonian force is a suitable approximation. But he is being careless with a very fundamental concept. Gravity is either a force or it is not. In physics it looks like it is a force when the author needs a force and it is not a force when the author feels like it.
Firstly, there is a possible misconception that gravitational effects can be transformed away under GR, since GR permits non-inertial reference frames as valid frames to view gravitational phenomena. The usual consideration is that a mass in a gravitational field is at rest in a free-falling frame (e.g. a ball in an elevator in free-fall). This is a misconception! For example, two such masses in free-fall around a spherically symmetric field will actually converge as they approach the centre of the field. This aspect of gravity is known as "tidal gravity". And the formulas of GR relate stress-energy with curvature precisely to explain tidal gravity. This aspect of gravity is the real physical aspect; if all gravity could be transformed away, there'd be nothing to say about gravity at all!
Secondly, there is a possible misconception about what a force is. It is not as simple as F = ma (or even F = dp/dt). We say there is a field that influences the motion of objects which couple to the field. For gravitation, there is indeed such a field (the spacetime metric) and it couples to anything that has mass, just as for electromagnetism, there is a field that couples to anything that has electromagnetic charge. Why then, would gravity not be a force?
1) Gauge theory only includes Special Relativity, a quantum theory of gravity is simply an unsolved problem so far.
2) In GR gravity is a 'fictitious force', which would cause less problems if they had use the term 'apparent' or 'inertial' force. It is a force observed which is an artifact of your reference frame.
3) In natural units 1 unit of "time" is a huge dimension compared to the spacial dimensions and the Earth is following the geodesic or the "straightest" path around the sun due to curvature in that dimension.
4) While 'radially inward' does happen with inward falling, that is more of an issue about trying to extend euclidean space past it's useful domain, you are going non-local at that point. That radial inward path convergence is length contraction in the spacial domain, which is smaller than the more observable time effects but it is still an artifact of one's reference frame.
Most proposed quantum theories of gravity view it as a force field that is like the other force fields in QFT. Time will tell if they can accurately create a model that works in a way that can stay in a euclidean space.
Everyone has their favorite. To be honest I like geometry more than algebra so I prefer GR, but really I just someone comes up with a model that works. Noting my bias, I think eventually QM is going to have to give up on the quantum mechanical hope for gravitation and resort to a non-euclidean solution. As I can't imagine 4D I would be happy for someone to prove me wrong.
> It is a force observed which is an artifact of your reference frame.
So it is not a force then! A force is an action at a distance between two masses. This is what I'm trying to say. Maldacena is using the word force in the context of GR but we do not know what he means by that word.
Correct, in GR gravity is not a force between masses but an effect of the warping of space and time in the presence of mass. That said, Using the concept of "Gravity" as a "force" is very useful in the special or limited cases. In fact it may be the only way to model some problems where one can't find an exact solution to the EFEs. The concept is invaluable as a tool for visualization. Most of us cannot visualize the non-euclidean impacts of the Ricci tensor or the Weyl terms.
I should warn than in QM the notion of "force" is based on operators and not variables and the stricter Newtonian definition is going to run into problems.
But you did not explain force you just redefined it to suit your argument. In the Newtonian regime force is defined as action at a distance between two masses. Your notion of field does not exist in the Newtonian regime.
Einstein did not believe that action at a distance is possible so he tried to explain gravity without action at a distance, ie, without force.
Gravity cannot be a force and not a force at the same time. It's either a force or not a force.
The point of General Relativity is that gravity is not a force. I'm familar with standard argument that Newtonian force is a suitable approximation. But he is being careless with a very fundamental concept. Gravity is either a force or it is not. In physics it looks like it is a force when the author needs a force and it is not a force when the author feels like it.