Is This Correct About General Relativity

Which is the correct way to say, the theory of general relativity, or the general theory of relativity?

I had this debate with my PhD adviser once. There’s no correct answer. My position was that the thing that was generalized was the principle of relativity.In the special theory, the principle is that the laws of physics are the same in all reference frames moving at a constant velocity. That was generalized to the laws of physics are the same in all coordinate systems, regardless of how they are moving relative to each other.So my argument was that the generalization of the principle of relativity led to a new theory, rather than it being a generalization of the special theory.But it is really just a matter of semantics and people (including me) say it both ways.

How do we know that Einstein’s theory of General relativity is correct?

You can’t prove a theory correct, yeah, yeah, yeah. But theories make predictions. GR predicts the bending of light, including gravitational lensing; time dilation or redshift; black holes; gravitational waves, previously detected indirectly and now finally directly; the anomalous precession of Mercury’s orbit; matter curves space and space tells matter where to go. So qualitatively it is correct — so far. All these predicted effects have been verified to exist. So the theory is at least that good. Then there’s quantitatively. Here general relativity has to date passed all tests to within experimental accuracy with flying colors. Maybe one day there will be discovered some errors in the predicted magnitude of the effects. A new theory would be needed, but that theory would still have to make all the same predictions that GR does, and to the same precision that we presently can measure. This is analogous to Newton’s laws of motion and gravity, which are extremely accurate for most ordinary phenomena, but when things get too small or too big, or gravity gets to strong, other theories are needed, as in the anomalous precession of Mercury’s orbit, e.g.Anyway, all these qualitative predictions have been shown to exist, and to be quantitatively correct to within experimental error.Here’s a bit about theories and their “correctness”:I should add that GR does have a couple of problems: (1) You get a divide by zero at a singularity, like the center of a black hole, or the first instant of the universe (if those are correct), and (2) It doesn’t get along with QM. But GR and QM are both king of their domains.

If general relativity is "more" correct than Newtonian physics on gravity, how do things fall on planets?

The "classical limit" of general relativity is Newtonian mechanics. Which is to say, as long as your speed is relatively low, and you're not standing in a massive gravity field, you can substitute simplifying assumptions into the Einstein field equations, and what pops out is classical Newtonian gravity.Leo C. Stein even did so, right here on Quora:How can we derive Newton's law of gravitation from Einstein's theory of relativity?That assumption holds for every single object in the solar system. There's actually one exception: Mercury is close enough to the Sun to count as a big gravitational field. One big early test of general relativity was to watch very tiny changes in Mercury's orbit:Precession of the perihelion of MercuryUnder general relativity, you can say that what these objects are "really doing" is following a curved geodesic through space. I'm not sure that's actually helpful, since the geodesic depends on the object's velocity, and I don't find it very easy to visualize what's actually happening. Instead, I think it's easier to realize that in the classical limit (which happens to be the same as every case you observe), general relativity reduces to Newtonian gravity, and that works just fine.

Is it correct that general relativity is not an accurate description of gravity on a galactic scale?

No, it is not correct to say that general relativity does not accurately describe gravity on a galactic scale.What is correct to say is that general relativity, along with only normal (baryonic) matter, does not accurately describe gravity on a galactic scale*.However, general relativity, together with dark matter, accurately describes gravity on a galactic scale.On the other hand, in the absence of independent confirmation of the existence of dark matter, some people continue to work on the assumption that dark matter does not exist and general relativity needs to be modified.Though the majority of astrophysicists/cosmologists seem to think that this quest is futile, I think the jury is still out; until we have unambiguous evidence (e.g., laboratory detection) of dark matter, modified gravity cannot be excluded a priori.*There have also been attempts to invoke unique features of general relativity, like rotating frames of reference on a galactic scale, to account for the observed behavior of galaxy rotation. Personally, I am skeptical about the viability of these schemes.