# Motivation for the abandonment of inertial frames in general relativity [closed]

Inertial frames are at the core of special relativity. The laws of physics are supposed to be the same among them and free particles follow rectilinear paths in spacetime or simply stay at rest. Just with rods and clocks and a coordinate system we can map space time, and study dynamics of particles. If there is,for instance. uniform gravity, we could treat it as a constant field and see what happens to particles. By reading Wheeler great book on black holes, he mentions this funny inertial frame (the free falling cabine). Everything is great as far as we expand the cabine and see how free particles deviate from each other because of tidal forces. He says this means that inertial frames can not in general map space time in presence of gravity, since things start to become complicate as there were ficticious forces. Well, acoording to me, in principle, this should not be a problem, we could model stuff, altough complicated, treating it as a force of gravity as we do on Earth. So for me, gravity is not a problem when describing space time using inertial frames.

First question is: How do we conclude in presence of gravity non-uniform, that inertial frames are no longer valid?

Second: Asuming this deviation makes this frames no longer inertial since "we have to add forces we don't see", why our clocks and rods can no longer map space time?

I know tidal deviation may be a motivation for curve spacetime (Einstein) since geodesics does not remain "parallell" as in the sphere for instance. And that the equivalence principle provides insight in how a particle moves along space-time in geodesics. Why our clocks and lenghts can no longer map space time? Or they simply are no longer useful since the pincture complicates too much and we have to abandon them?

I've been exposed to mathematical machinery of general relativity, but the question of my old friend's clocks remains. I know by putting examples on Earth, both Newton and Einstein could describe phenomena, but I'm just trying to gather motivation for the theory. Thanks.

• I don't understand the question. What makes you think "inertial frames are no longer valid"? – Brick Jul 9 '19 at 21:03
• To map the entire space time. – Omar Jul 9 '19 at 21:04
• – user4552 Jul 9 '19 at 23:07
• GR doesn't abandon inertial frames, it abandons global frames. – user4552 Jul 9 '19 at 23:08
• I have seen your answer, Ben. It is interesting. My question goes for why the references frames can not cover the whole space-time when there is gravity. – Omar Jul 10 '19 at 3:36