... my own understanding of the concepts are still to small. could u elaborate on what you mean with "fixed background geometry"

Hm, difficult to explain given that I don't know where to start.

Roughly, think about the interference picture in a simple double slit experiment. The mathematics to compute this picture consists of the following steps: Computing some amplitudes for paths of the particle going through the left resp. the right slit. Then, adding the amplitudes for the paths which end up at

**the same point**. Then, the square the sum and this gives the probability of the particle appearing in this point.

This is a basic quantum rule, you can use it for all fields, the EM field, all the other fields of the SM. And if you use simply Newtonian gravity, it works for gravity too. Even supported by observation (of neutrons in the gravitational field of the Earth).

But for GR, it does not work. The problem is that GR does not define what would be

**the same point **for different gravitational fields. If you have different solutions of GR, you do not have given them in the same system of coordinates. You have, say, solution 1 as $g_{mn}(x,y,z,t)$ and solution 2 as $g_{ab}(d,e,f,g)$. What is

**the same point **as x,y,y,t in terms of d,e,f,g on solution 2? Nobody knows.

In all other theories, it is sufficient to define this for the initial values. At t=0, we have, say, d=x, e=y, f=z. (Ok, together with first derivatives or so.) Once this is given for the initial values, fine, we can compute everything else. And, in the simplest case, find out that d=x, e=y, f=z, g=t. Fine. With this information, we know what is is

**the same point **as x,y,y,t in terms of d,e,f,g on solution 2. And we can use the standard rules of quantum theory to compute the interference patterns.

But GR does not allow to compute this. The GR equations are not sufficient for this. The reason is the equivalence principle, or the diffeomorphism invariance of the theory. You can choose another system of coordinates, transform the solution to this other system, and have another solution. And so you can construct different-looking solutions, even for the same initial values - the other system of coordinates may be the same at the initial values. It may be different from the original one only in some hole. This is the hole problem.

The hole problem is solved in classical GR, by reliance on observable effects only. In these two different-looking solutions for the same initial values, all what can be measured is nonetheless the same. Fine. But this does not solve the problem in the quantum case, where we need, to add the amplitudes of different solutions, the information what are

**the same points **on different solutions.

This is some information which in classical theory is defined by absolute space. And even in special relativity, this is not problematic, the absolute Minkowski spacetime provides this information. In GR, nothing provides this information.

So, a fixed background geometry, which is independent of the different physical fields, would provide such a structure. In fact, simply to say "fixed background" would have been more accurate, because this background does not have to provide information about distances - it is sufficient that it provides information about which are the

**same points.**