First I must let you know that I don't have much understanding of neither GR nor quantum mechanics, and therefore this question.
Is it possible that the exact same exercise can be solved in Newtonian physics, GR and quantum mechanics? Under "solved" I mean that it can be calculated according to the model (Newtonian, GR or QM) but the answer would come different and hence illustrating the need of why and for what GR was required and the same for QM.
Basically what I mean is that is there any problem that could be solved with different physical models? For example if I would have a problem A, then by applying a solution based on Newtonian physics (NP), GR or QM, I would get different results, e.g:
NP(A) = x GR(A) = y QM(A) = z
If it's possible, can someone please give an concrete example?