There are plenty of similar topics about the physical or intuitive meaning of the equivalence principle or statement such as ''laws of physics are true in every frame of reference''. Usually answers rely on introducing tensors, covariant-derivatives and invariant formulations. While of course being perfectly correct, that technical style pretty much kills the intuition. So, I pose the challenge of explaining it more heuristically, what might mean that F=ma is true in an accelerated coordinate system.
In Newtonian case, we must add ''fictitious forces to make F=ma work in an accelerating frame, and such addition ''changes the laws of physics''. That is why Newton's physics do not fulfill Einsteins requirement ''the laws of physics must be of such a nature that they apply to systems of reference in any kind of motion''. In GR Einstein accomplished this and now I ask what it means intuitively. How, in other words, does GR make these fictitious forces, the effect of which will surely still be there, real?
In case you are tempted to dodge the question and argue that F=ma is not a physical law because it is not formulated in an invariant way etc. I try to clarify.
For Maxwell's equations there is a beautiful explanation how the electric and magnetic fields change into each other, when jumped from one inertial coordinates into another. And you can in principle explain how it happens simply by considering how the charge distributions with respect to the other system. In some simplistically symmetric cases (e.g. current carrying wire) if is very intuitively tractable. That is the style of explanation I am looking for, but here in the case of accelerated coordinates.
F=ma is true at least approximately and in some sense. And as long as you are not near a black hole the spacetime is sufficiently flat so that you can consider the effects or gravity as a force (via linearized field equations, or, gravitoelectromagnetism). So it will not be necessary to introduce spacetime metrics here.
I suspect this question may still not be ''clear'' but be patient and do not vote it closed. I will give it a shot myself if I get no other candidates. Thanks.