Why do elementary particles have such strange mass ratios? -- The role of quantum gravity at low energies

TL;DR

This paper proposes a non-commutative geometric framework using octonions to unify the standard model with chiral gravity, explaining particle mass ratios through quantum gravity effects at low energies.

Contribution

It introduces a novel octonion-based non-commutative geometry model that unifies particle physics and gravity, deriving mass ratios from first principles.

Findings

Unifies standard model with $SU(2)_R$ chiral gravity.

Derives quantization of electric charge.

Provides a theoretical explanation for particle mass ratios.

Abstract

When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This is true even for quantum gravity in the infrared. Using the octonions as space-time coordinates, we construct a pre-spacetime, pre-quantum Lagrangian dynamics. We show that the symmetries of this non-commutative space unify the standard model of particle physics with $SU(2)_R$ chiral gravity. The algebra of the octonionic space yields spinor states which can be identified with three generations of quarks and leptons. The geometry of the space implies quantisation of electric charge, and leads to a theoretical derivation of the mysterious mass ratios of quarks and the charged leptons. Quantum gravity is quantisation not only of the gravitational field, but also of the point structure of space-time.