How do fermions curve space-time?

Quantum gravity should not be viewed as the question: `how to quantise the gravitational field'?

But rather as the question: How do fermions curve space-time?

After all, Newtonian gravitation as well as classical general relativity answer this very question: what is the gravitational field / space-time curvature produced by material bodies and fields?

Fermions, being described by spinors, cannot be expected to produce / live in Minkowski spacetime, except in an approximate sense.

Instead, they are expected to live in a complex spinor spacetime, which is the spinor analog of Minkowski spacetime, and their mass-energy curves this spinor spacetime.

And this is a statement independent of energy scale, and valid at low energies as well.

The standard model has 25 dimensionless constants whose origin we do not understand. We seem to believe that by doing experiments at higher energies we will find new physics and a theory of unification which will then explain, through RG flow, the values of the constants at low energies.

This may or may not be true. What if we have not correctly understood quantum field theory and spacetime structure at low energies, and that is what is responsible for these undetermined free constants?

Indeed, it turns out that when we describe fermions at low energies, the complex spinor spacetime dictates the symmetries of the standard model, and determines several of it's dimensionless constants. This is because this non-commutative analog of Minkowski space-time is much richer in structure than Minkowski. It constrains properties of fermions, and removes the arbitrariness allowed for them when we describe them using QFT on Minkowski spacetime.

In hind-sight, this is not at all radical. We have taken a square-root of Minkowski space-time at the same-time as taking the square-root of the Klein-Gordon equation to arrive at the Dirac equation. We have written the Dirac equation on a spinor spacetime. The Dirac equation on Minkowski shows that spin angular momentum exists and is quantised. Dirac equation on spinor spacetime shows that electric charge and mass are quantised as well, and take values as observed in experiments. This confirms that the description of fermions on spinor spacetime is correct.