General Relativity & Quantum Theory: Where's the Limit?

[Giuliano97]

I've always read that these two theories are incompatible, and how General Relativity works for large scales while Quantum Theory represent reality in extra-small cases.
So my question is where is the limit where General relativity ceases to exist and Quantum Theory gives a better portrait of reality?
There is a scale in which those can coexist?

 

[.Scott]

It isn't that they are incompatible, just very different.
They coexists at all scales, but the effects of relativity are commonly seen at very large scales and the effects of QM are commonly seen at very small scales.

In some cases, such as linear accelerators, the effects can be seen working together.

 

[PeterDonis]

It isn't that they are incompatible, just very different.

I think many physicists would disagree with this as you state it, since perceived incompatibility between GR and QM in their current states is a major motivation for seeking a theory of quantum gravity.

I would say that practically speaking, GR and QM as we actually apply them are compatible, because in any system of practical interest, we can mesh the two without incompatibility using suitable approximations. For example, we can study quantum field theory in curved spacetime without having to quantize spacetime itself; and if we need to model the "back reaction" of the energy in the quantum field on the spacetime geometry, we do it using a suitable expectation value of stress-energy. But that's a weaker statement than just saying that GR and QM are not incompatible, period.

 

[Herman Trivilino]

There is a scale in which those can coexist?

Anywhere that the Newtonian approximation can be applied with success.