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

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.

34 pages, 6 figures, pedagogical article, invited contribution for special issue `New advances in quantum geometry', Eds. Shidong Liang, Tiberiu Harko, Matthew J. Lake

References in corpus (7)

• Majorana Neutrinos, Exceptional Jordan Algebra, and Mass Ratios for Charged Fermions
• Why does the Kerr-Newman black hole have the same gyromagnetic ratio as the electron?
• Euclidean Twistor Unification
• Improving self-supervised pretraining models for epileptic seizure detection from EEG data
• Quantum theory without classical time: octonions, and a theoretical derivation of the fine structure constant 1/137
• Trace dynamics, and a ground state in spontaneous quantum gravity
• Relativistic weak quantum gravity and its significance for the standard model of particle physics

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• CKM matrix parameters from the exceptional Jordan algebra
• Causal Fermion Systems and Octonions
• Unification based on the mysterious cubic-structure grouping of quarks and leptons