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To me it's quite obvious that these theories are mutually exclusive simply by fundamental logic.

QM at its very core is dependent on flat spacetime background and its implied conservation laws (momentum, energy etc) but in general relativity momentum for example or even energy are not conserved.this seems to me like an obvious logical contradiction.

First of all both relativity and QM have lots of extremely accurate predictions, but even in their own domains fail terribly in most instances. For example when you apply GR to cosmology you have the lambda cdm model in which we know that we don't know 95 percent of what makes the universe. So either this is a failure of GR(if there is no CDM) or if relativity is right that the standard QFT (STANDARD MODEL) is wrong because it doesn't apply to at least 95 percent of reality.. This is one example of the consequence of the fundamental contradictions in question.

Than there is the vacuum catastrophe, the fact that GR and QM give completely contradictory values of the ZPE.

I don't think it's a matter of being clever to come up with some math that will unify them, but a matter of simply finding the quantum nature of reality without forcing GR to come out as it's macroscopic realization.

Kugutsu-o
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    not an expert, but you can do QFT in curved space time, so QM is not dependent on flat spacetime – user2723984 Feb 20 '20 at 11:07
  • Only in some special cases. Not in general. – Kugutsu-o Feb 20 '20 at 11:12
  • In both GR and QFT the stress-energy tensor is locally conserved – bemjanim Feb 20 '20 at 11:39
  • You seem to have it somewhat backwards, it't more like follows: We know that QM/QFT correctly describes particles and the "microrcosm", while GR (i.e. gravity) is essential on large scales ("macrorcosm"). Thus, we should expect that there is a unified description that ncludes both. The main problem is that the theories (QM/GR) do not fit together nicely, and that's why we have a bunch of differnet approaches that try to combine them. – Toffomat Feb 20 '20 at 11:54
  • Related: https://physics.stackexchange.com/q/387/2451 and links therein. – Qmechanic Feb 20 '20 at 12:02
  • Tofomat what the hell are you talking about,.. – Kugutsu-o Feb 20 '20 at 13:15

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QM has been developed primarily to describe phenomena that we can observe in the lab; GR primarily describes phenomena we observe astronomically. Of course our explanations of those phenomena are different, and of course the descriptions work best in their own domains.

A contradiction of that sort simply points out disagreement between such descriptions. The contradictions/disagreements are not built into the laws of physics; they are built into models (theories) we have constructed to describe the laws of nature as observed at different ranges of field strength, spatio-temporal geometry, energy, mass, etc. The disagreements are in ranges of those parameters that are currently beyond our experimental and observational reach. We hope to be clever enough someday to come up with a single, relatively simple, model that accurately describes physics at all ranges of those values.

S. McGrew
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  • They do work to an extent put such an obvious contradiction should point to the fact that at least one of these models is quite wrong and that one won't just seemlesly approximate to another when s calling up or down – Kugutsu-o Feb 20 '20 at 11:55
  • Or both are correct, in their domain of application. – m4r35n357 Feb 20 '20 at 12:25
  • Depends what's meant by "correct", and "domain of application". Each of QM and GE gives predictions that describe the world accurately to some large number of decimals, when applied in its respective domain. But that's not the same as "correct" IMHO. Out near the edges of the domain, the accuracy goes to pot. The world is flat when measured on a small scale, but it's certainly not "correct" to say the world is flat. – S. McGrew Feb 20 '20 at 13:05
  • No this is not at all related to the question. First of all both relativity and QM have lots of extremely accurate predictions, but even in their own domains fail terribly in most instances. For example when you apply GR to cosmology you have the lambda cdm model in which we know that we don't know 95 percent of what makes the universe. So either this is a failure of GR(if there is no CDM) or if relativity is correct that the standard QFT (STANDARD MODEL) doesn't apply to 95 percent of reality.. This is one example of the consequence of the fundamental contradictions in question. – Kugutsu-o Feb 20 '20 at 13:21
  • That is not a problem with the GR, it is a problem with constructing a model of the universe. It is stuffed full of approximations and assumptions, to keep the problem artificially simple. – m4r35n357 Feb 20 '20 at 16:17