General Relativity at the microscopic level

[lavinia]

My text explains that free float frames are locally indistinguishable from flat space-time in the sense that in a small enough region measuring instruments will be unable to detect gravitational tidal forces. This region may be tiny if tidal forces are large or if measuring instruments are extremely sensitive.

Can tidal forces be intense enough so that the free float frame must be chosen at subatomic dimensions where measurements are subject to quantum mechanical randomness? If so how does one detect tidal forces in such a tiny region?

 

[WannabeNewton]

GR assumes the 4 - manifold in question is Riemannian so that there will always be an open ball in the neighborhood of a point that is isomorphic to an open subset of euclidean 4 - space. I don't think GR deals with manifolds that are so wildly curved that local regions cannot be mapped into a smooth submanifold of euclidean 4 - space.

 

[Bill_K]

Can tidal forces be intense enough so that the free float frame must be chosen at subatomic dimensions where measurements are subject to quantum mechanical randomness? If so how does one detect tidal forces in such a tiny region?

This is why we want a quantum theory of gravity, to be able to answer such questions. Even if we had such a theory, it's difficult to think of a circumstance in which such intense fields would be produced, except in the Big Bang, or as the singularity lying within a black hole is approached.