Why Are Physicists Struggling to Quantize Gravity in Quantum Field Theory?

[brianhurren]

why are physisist having so much trouble quantising gravity and getting it to fit into QFT?

 

[Matterwave]

This is a very broad question. One which cannot be answered in a short amount of space. I will list, for brevity, a few reasons:

1) Gravity is a curvature in space-time itself. There is no background with which to do the quantizing with.
2) Cannonical quantization of gravity is difficult due to the requirement of splicing space-time into space+time parts. The splicing is arbitrary and does not allow the degrees of freedom to be isolated.
3) The dynamical variable, the metric, has very many "gauge symmetries" in it which again makes the isolation of the real degrees of freedom difficult.
4) Gravity is a non-renormalizable theory (as far as we know). Which means that the infinities which arise from quantizing it cannot be canceled out with a finite number of parameters.
5) Path integral quantization already has issues relating to the measure of integration (whether it exists, whether it's a real measure, etc.), with gravity these issues have proved so far insurmountable.

I'm not at the forefront of quantum gravity, so I can't guarantee that none of the above issues have been solved. However, they do show you where some of the difficulties lie.

 

[atyy]

Sabine Hossenfelder
My research area: The Phenomenology of Quantum Gravity

Incidentally, she notes that we do have a satisfactory theory of quantum gravity at low energies.