Is there a compelling reason why physicists believe that there must exist a single theory which subsumes both General Relativity and Quantum theories into a united whole?

Or is it merely some vague belief in the symmetry of nature on all scales?

11 minutes ago, Xerxes said:

Is there a compelling reason why physicists believe that there must exist a single theory which subsumes both General Relativity and Quantum theories into a united whole?

Or is it merely some vague belief in the symmetry of nature on all scales?

I'm no physicist but I had understood there is an unresolved incompatibility between the two, i.e. as the two theories stand today if one is right then the other can't be, and that is why there is a search for a resolution that unifies them. But no doubt a physicist will show up and explain.

1 hour ago, Xerxes said:

Is there a compelling reason why physicists believe that there must exist a single theory which subsumes both General Relativity and Quantum theories into a united whole?

Or is it merely some vague belief in the symmetry of nature on all scales?

I’m not sure it’s vague. Electricity and magnetism were unified (Maxwell and Einstein), and then we had electroweak unification at higher energies emerge in the 60s. So unifying with the strong force, and also with gravity, are seen as “next steps”

exchemist noted the fact that QM and gravity are incompatible where you have very strong gravity, which is a separate reconciliation that simply has to have a resolution. QM still works in strongly curved spacetime, so we expect to have a mathematical description.

10 hours ago, Xerxes said:

Is there a compelling reason why physicists believe that there must exist a single theory

The fact that all known forces 'seem' to converge to equal strength at Planck scale, implies that all forces may unify at Planck energies.
IOW, unification of gravity with color-electro-weak at approx. 1.2 x !0^28 eV.
( way beyond our reach )

18 hours ago, Xerxes said:

Or is it merely some vague belief in the symmetry of nature on all scales?

The problem is mostly that there exist situations in nature where both gravity and quantum effects appear to be simultaneously non-negligible. Thus, it is reasonable to assume that there should exist some mathematical framework that can describe such situations in an internally self-consistent way. But you are right in that this framework taking the form of a single unified theory is largely an assumption based on what happened with the other fundamental interactions. Though I must say it is difficult to see what a possible alternative might look like.

8 hours ago, Markus Hanke said:

The problem is mostly that there exist situations in nature where both gravity and quantum effects appear to be simultaneously non-negligible. Thus, it is reasonable to assume that there should exist some mathematical framework that can describe such situations in an internally self-consistent way. But you are right in that this framework taking the form of a single unified theory is largely an assumption based on what happened with the other fundamental interactions. Though I must say it is difficult to see what a possible alternative might look like.

I tried to find a concrete example of physically meaningful scenario where math suppose to brake but I couldn't...
Maybe someone of you guys can give an example?

No, there is no compelling reason, and the induction behind the belief rests on a miscount of the unifications already claimed.

Maxwell's was a genuine unification: elèctricity and magnètism are one fortia seen from two frames. The second case is not. The "electroweak [sic] unification at higher energies [sic]" cited above did not join two fundamental fortiæ, sith the weak interaction was never fundamental. For a quantum to be fundamental it must be inmassive and must hold indefinite range; the massive W± and Z⁰ with finite range fail both tests. They are the elèctric and coloral interactions unified at high vis, and the correct name for the composite is elèctrocoloral. Weak is the opposite of well; slack is the opposite of strong. One genuine unification and one mislabel do not make a series that licenses "next steps."

There are three fundamental fortiæ: gravital, elèctric, coloral. They are independent axes and can trade strengths. The apparent convergense of couplings at the Planck scale marks onely the simple threshold where gravity is stronger than Coulombic repulsion; it is not a singularity and not a portal to a master sýmmetry. There is no singularity under the conservation laws at that scale; there are arbitrarily many compounds smaller than the Planck scale, as there are spectra of orbitals between any two heavy bodies at meghaloscopic scales.

As for the alleged incompatibility between general relativity and quantum mekanics: the conflict is manufactured by GR's own blunders, not by nature. GR misreads the shift in matter itself as a shift in room and time. The mote and the field are identical; a body takes up the whole univers until it interacts with another; the curvature is in the matter, not in a ghèometric fabric that bends independently of what occupies it. Read so, the room-time metric is a description of matter's arrangement, and the conceptual basis for a fýsic singularity vanishes: the fabric does not tear; the matter changes state. The regimes where gravity and quantum effects are both non-negligibil are collapsars, and what GR predicts there (event horizontes, infinite densities) are coordinate artefacts of the Schwarzschild metric, which assumes Galilean relativity at the radius where Lorentzian relativity is most critical. A model that excludes special relativity at its own critical point is not a candidate for unification; it is a candidate for repair.

The quantum-gravity programmes compound the error by hunting the gravitòn. By the Goldstone effect no free inmassive quantum exists: the emitter and absorber of any radiation are massive, and their mass is conferred on the medium and action between them. Onely pressuròns, polaritòns, and piòns exist. A unification built to quantize a nonexistent carrier of a misread field shall find nothing, however much sýmmetry it assumes.

So the order of work is backwards. One does not unify a sound model with a broken one; one first strips the broken one of its Galilean assumption, its event horizontes, and its singularities, and then the three fortiæ, already independent and already trading strengths by background, need no master sýmmetry at all. The demand for a single subsuming framework is æsthetic, not principed; and a theòry (θεωρία) is by definition proven, which no candidate unification is. What is on offer is a hýpothesis, and an unfalsifabil one wherever its predictions hide behind Planck-scale inaccessibility.

To be clear ...
There is no incompatibility between Gravity and Quantum Mechanics; they both work seamlessly at all scales, and have always done so.
The incompatibility is in our models with which we describe them.
IOW, we need better models, because the current ones are incomplete for some situations.