In the past I saw what Told Vlatko vedral , Here is what told Vlatko Vedral about the quantum gravitation,
« All existing quantum gravity proposals are extremely hard to test in practice. Quantum effects in the gravitational field are exceptionally small, unlike those in the electromagnetic field. The fundamental reason is that the gravitational coupling constant is about 43 orders of magnitude smaller than the fine structure constant, which
governs light-matter interactions. For example, detecting gravitons the hypothetical quanta of the gravitational
field predicted by certain quantum-gravity proposals is deemed to be practically impossible.
Here we adopt a radically different, quantum-information-theoretic approach to testing quantum gravity. We propose to witness
quantum-like features in the gravitational field, by probing it with two masses each in a superposition of two locations. First, we prove that any system (e.g. a field) mediating entanglement between two quantum systems must be quantum. This argument is general and does not rely on any specific dynamics. Then, we propose
an experiment to detect the entanglement generated between two masses via gravitational interaction.
By our argument, the degree of entanglement between the masses is a witness of the field quantisation. This experiment does not require any quantum control over gravity. It is also closer to realisation than detecting gravitons or
detecting quantum gravitational vacuum fluctuations. »
Personally I believe that the problem is philosophical mainly , if we cannot quantize this quantum gravitation due to infinite quantities or uv divergences or others, it is probably due to fact that it lacks pices in this puzzle and they are mainly for me philosophical these limitations and problems. The gravitons are hypothetical considered like the quantas of these gravitational waves, if the actual different approachs cannot renormalise this QG even with the best mathematical tools like the E8 or the non commutativity and others, so that tells us an important thing, the standard actual model and the yang mills theory and these lie groups probably need to consider a deeper philosophy than this GR like primary essence ands these photons. The problem has maybe created this philosophical prison and now so they consider for the majority these or points in 1D at this planck scale inside these photons connected with a 1D cosmic fiuelds of this GR and so they try all the partitions possible with the numbers and the non commutativity to develop the standard model with the statistics and probabilities but if the philosophy general of this SR and GR are not sufficient and that this SM is emergent from deeper causes , so we turn in round.This SR, the EFE and GR and the euivalence principle of course work well and this QFT also but maybe we must think beyond the box to complete the puzzle. This DM and DE is they are a reality probably are the keys and if they exist at this cosmological scale, so probably they exist also in our standard model .