You know, I made a mistake at the beginning of this discussion, by conceding your premise that QM and GR are inconsistent. I should have just asked to see the proof.
Usually when people say this, they mean that applying the techniques of perturbative quantum field theory (the techniques which produce Feynman diagams) to general relativity gives rise to an unpredictive theory, because there are infinitely many undetermined quantities associated with higher-order terms in the expansion. The philosophy of renormalization is that you measure such quantities and use them to define the renormalized theory, but that this only makes sense when there are finitely many such quantities.
However, there’s still no proof that this is true for general relativity. There is a research program, “asymptotic safety”, which hopes to find evidence that only finitely many quantities are needed after all. I am skeptical, even though a physicist as good as Steven Weinberg is interested, and as I said, no proof exists. Meanwhile, it does look as if d=4 N=8 supergravity is perturbatively finite. That is a general-relativistic theory—it contains Einstein gravity, coupled to other fields. Although it is perturbatively finite term by term, the Feynman expansion probably doesn’t converge, in which case there need to be other contributions, and most likely N=8 supergravity should be considered a limit of string theory.
Anyway, the bad behavior of general relativity when it is treated using the simplest methods of quantum field theory is by far the main reason that people have for talking about QM and GR as inconsistent, and it’s a theoretical opinion from several decades ago, that is not borne out by more recent developments. If that’s your reason for asserting that QM and GR are inconsistent, I am prepared to rebut that point in as much detail as you wish. If you have some other reason for asserting that they are inconsistent, let’s hear it.
You know, I made a mistake at the beginning of this discussion, by conceding your premise that QM and GR are inconsistent. I should have just asked to see the proof.
Usually when people say this, they mean that applying the techniques of perturbative quantum field theory (the techniques which produce Feynman diagams) to general relativity gives rise to an unpredictive theory, because there are infinitely many undetermined quantities associated with higher-order terms in the expansion. The philosophy of renormalization is that you measure such quantities and use them to define the renormalized theory, but that this only makes sense when there are finitely many such quantities.
However, there’s still no proof that this is true for general relativity. There is a research program, “asymptotic safety”, which hopes to find evidence that only finitely many quantities are needed after all. I am skeptical, even though a physicist as good as Steven Weinberg is interested, and as I said, no proof exists. Meanwhile, it does look as if d=4 N=8 supergravity is perturbatively finite. That is a general-relativistic theory—it contains Einstein gravity, coupled to other fields. Although it is perturbatively finite term by term, the Feynman expansion probably doesn’t converge, in which case there need to be other contributions, and most likely N=8 supergravity should be considered a limit of string theory.
Anyway, the bad behavior of general relativity when it is treated using the simplest methods of quantum field theory is by far the main reason that people have for talking about QM and GR as inconsistent, and it’s a theoretical opinion from several decades ago, that is not borne out by more recent developments. If that’s your reason for asserting that QM and GR are inconsistent, I am prepared to rebut that point in as much detail as you wish. If you have some other reason for asserting that they are inconsistent, let’s hear it.
(edited to add: undetermined quantities)