"The treatment is purely classical, but motivated by links between acausal structures and quantum theory."
This is not unification of QM and GR, it's a classical construction which the author speculates might lead to such a thing. Such things have been around for a long time; the obvious (and far more progressed) example is string theory.
The author also doesn't also think very highly of string theory: https://warwick.ac.uk/fac/sci/physics/staff/academic/mhadley...
Whether something is "more progressed" hardly matters in matters that still have many questions and more reflective of a consensus of the time that progresses one funeral at a time.
What I quote shows that the author knows and acknowledges that he's describing a classical construct. The question of "compatability" (sic) is not even addressed.
> I didnt say it was THE unification theory of QM and GR, you somehow inferred that
I did not. Here's what I wrote: "This is not unification of QM and GR, it's a classical construction". Not the absence of any "THE", whether capitalized or not.
> I could add that quote and it would change nothing as far as I'm concerned what the authors stance is
Because you do not understand what the author is saying. He's presenting a purely classical model which displays some features (in particular charge quantization) also seen in quantum mechanical ones. That does not make it a quantum theory, any more than the discrete eigenfrequencies of a vibrating classical string make a classical model of vibrating strings a quantum theory.
> He's presenting a purely classical model which displays some features (in particular charge quantization) also seen in quantum mechanical ones.
Compared to other physicists who just outright state that there is no compatibility… You can ignore it, but it is an area for further study in regards to non time orientability for others.
No, I am pointing out that you do not understand the paper you misquoted as evidence that "Not all physicists think they [GR and QM] are incompatible".
The author would not have written a paper trying to take a small step toward a solution if he didn't think that there is a problem.
Just because he does not say explicitly "[GR and QM] are compatible", does not mean opposite.
If you aren't interested in the that U(1) bundle described in the paper is from utilizing time oreintability from a classical standpoint and not formed from the complex phase of a quantum mechanical wave-function, that's on you.
It also doesn't mean what you are claiming.
To have a meaningful discussion about the incompatibility of GR with QM, you first need to know how they are incompatible. Reproducing classical electromagnetism with the Kaluza-Klein trick from 1919 [1] has nothing to do with it.
QM deals with unit vectors in a state space, operators acting on those vectors, and observables whose values can not all be known simultaneously [2]. The hole left by the observer's limited knowledge about the state of the system is filled by an intrinsic randomness which does not exist in classical theories.
GR and other classical theories have only observables, their evolution is deterministically determined and the state of the system can in principle be fully known at all times. We have known for a long time that nature does not actually work like this [3].
If you want to claim that GR is compatible with QM, you have to resolve the above contradiction.
What people who actually understand the problem have been trying to do for a long time is:
1) Quantize GR. This is the obvious first thing to try; you treat the problem as analogous to the quantization of classical electromagnetism and hope to create a quantum version of GR, the gravitational equivalent of QED. When you try that, it turns out you can't make the theory renormalizable - the infinities caused by loops in Feynman diagrams can not be brought under control. Trying to fix that leads to things like loop quantum gravity [4]. Weinberg came up with the alternative idea of asymptotic safety, which tries to neuter the problem with a fixed point in the renormalization group flow [5], but proving that it actually works is another story.
2) Come up with a deterministic (i.e. classical) theory underlying QM. Naive approaches involving hidden variables (i.e. trying to explain away our limited knowledge of quantum states as ignorance rather than truly fundamental) died with Bell's theorem. A few brave souls, notably t'Hooft [6] are still trying more sophisticated approaches (I think it would be nice if superdeterminism [7] got more attention).
3) Write down a more fundamental theory which produces both GR and the other known interactions in the appropriate limits (thermodynamic, large number of quanta). Since the other known interactions are empirically known to be quantum mechanical, it is generally believed that this theory will have to be quantum mechanical too. String theory is the obvious example. In principle, you could also imagine a classical (i.e. deterministic) theory along the lines of (2), but I can't think of any example which comes close to actually doing the job.
[1] https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory
[2] https://en.wikipedia.org/wiki/Quantum_mechanics#Mathematical...
[3] https://en.wikipedia.org/wiki/Bell%27s_theorem
[4] https://en.wikipedia.org/wiki/Loop_quantum_gravity
[5] https://en.wikipedia.org/wiki/Asymptotic_safety_in_quantum_g...
"On spacetimes that are not time orientable we construct a U(1) bundle [model of a particle as an asymptotically flat spacetime manifold with a region of non trivial topology where time is not orientable] to measure the twisting of the time axis. This single assumption, and simple construction, gives rise to Maxwell’s equations of electromagnetism, the Lorentz force law and the Einstein-Maxwell equations for electromagnetism coupled to General relativity. The derivations follow the Kaluza Klein theory, but with the constraints required for connections on a U(1) bundle rather than five spacetime dimensions. The non time orientability is seen to justify and constrain Kaluza Klein theories exactly as required to unify gravitation with electromagnetism. Unlike any other schemes, apparent net electric charges arise naturally because the direction of the electric field reverses along a time reversing path."
"Deriving the U(1) bundle as a measure of the twisting of the time axis is new, as is the application to manifolds that are not time orientable. Like Kaluza Klein theory, it is purely classical, but free of the complications and ad hoc assumptions required by full 5D Kaluza Klein theories. It is remarkable how so much is derived from such a simple construction without additional assumptions."
"The connection with quantum theory is intriguing. Classical structures that are not time orientable have close links with quantum phenomena such as the logical structure [4], particle creation and annihilation [14] and spin half [7] The derivation of Maxwell’s equations and electric charge is just another result from the same premise of non time orientability."
Electric charges are a natural feature of the model, but quantisation only appears naturally for magnetic monopoles (which arise in pairs). However, adding elements of quantum theory to the monopole structures leads to quantisation of electric charge. The simplest such argument uses quantisation of angular momentum, but the argument fails when more than one monopole is introduced. The other approach uses a wavefunction for a charged particle [1, p262]. Uniqueness of the phase of the wavefunction leads to quantisation of charge. This is a tantalising link between the complex phase of the wavefunction and the orientability of spacetime."
[0] https://warwick.ac.uk/fac/sci/physics/staff/academic/mhadley...
[1] https://doi.org/10.1007/s10773-017-3344-4