Quantum Gravity in the Infra-red, and it's significance for the standard model of particle physics

When is a physical system quantum gravitational?

Not only at the Planck energy scale. But whenever:

(i) Length scale is of order Planck length

and/or

(ii) Time scale is of order Planck time

and/or

(iii) Action is order Planck constant \hbar

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If (iii) is satisfied but not (i) nor (ii), then it is QG in IR

This is why QG is important for the standard model, even in IR.

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(iii) along with (i) or with (ii) is QG in UV, as expected

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QG in IR and the standard model

The elementary particles of the standard model obey the rules of quantum field theory.

As a result, they are not localised in space, and obey the quantum superposition principle.

Hence, the spacetime geometry they produce, howsoever weak, is not classical. It is quantum gravitational.

We have found that this quantum gravitational field acts back on the elementary particles, and restricts what properties they can have. It enforces charge quantisation as well as specific mass ratios for elementary particles, the value 1/137 of the low-energy fine structure constant, and perhaps more.

This is not high energy physics. It is low energy quantum gravity - if we treat this gravity as classical, then that is approximate, and gives us the standard model as we know it. If we take the quantum gravity effect into account, as we should, we learn significantly more about the standard model, without going to high energies.

The existence of three light sterile neutrinos is a clear-cut low energy prediction of this theory.

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Klein-Gordon equation is to Minkowski spacetime what Dirac equation is to quaternionic / octonionic spacetime

When we take the square-root of the Klein-Gordon equation to arrive at the Dirac equation, if we also want to ask what kind of space-time manifold does the electron produce / live in, we must take the square-root of Minkowski spacetime as well. The desired square-root is not a tetrad based description of Minkowski spacetime, because this does not gel with the position-momentum uncertainty inherent in the Dirac equation. Rather, the desired square-root spacetime is quaternionic / octonionic, and inspired by the homomorphisms SL(2,H) ~ SO(1,5) and SL(2,O)~SO(1,9). We then define the spinorial state of the electron, not on Minkowski spacetime but on the [spinorial by nature] quaternionic / octonionic spacetime. We do the same for the other elementary fermions. Soon as we do this, we start to understand why the standard model has the observed symmetries, and charge quantisation and more. The group of transformations of the octonions is the symmetry group of the square-rooted spacetime, and is more fundamental than the spacetime diffeomorphisms of Minkowski spacetime.

Reference: arXiv:2110.02062