>>13929161I don't know a lot of physics so I can't comment on general relativity, but I can give you a simple example from Newtonian mechanics.
Newton started from experience and noticed that three laws of motion (which are still called Newton's laws) seemed to be true. He took these laws as axioms: he accepted them as true and didn't try to prove them. You could ask why he took those particular laws as axioms instead of others, and there would be no good answer: he probably thought they were very simple and self-evident laws so he accepted them as true and used them as a starting point to prove other laws.
Once you have your basic axioms, two things may happen:
1. You know in advance what you want to prove.
2. You don't know in advance what you're trying to prove.
An example of case 1 is Kepler's laws of planetary motion. Kepler discovered the laws of planetary motion before newton was born, but he discovered them empirically thanks to a large number of accurate astronomical measurements. Then Newton came along and he managed to prove Kepler's laws from first principles (starting from his three axioms of motion), without relying on experience and measurements. The fact that Newton's theory could prove something that was already known to be true made the theory well-corroborated since predictive power is one of the main things that determine the value of a scientific theory.
An example of case 2 is calculating escape velocity, or calculating how gravity affects a train in a very deep underground tunnel. Back in Newton's day there were no rockets and no deep tunnels, but he was still able to calculate these things starting from his axioms and using logic and mathematics. If a theory seems to be reasonable correct, you can figure out stuff simply by doing calculations instead of having to carry out an experiment and measure the results. Though of course experience is still the supreme court that has the last word on any issue.
