Gravitation, and quantum theory, as emergent phenomena

Abstract

There must exist a reformulation of quantum field theory, even at low energies, which does not depend on classical time. The octonionic theory proposes such a reformulation, leading to a pre-quantum pre-spacetime theory. The ingredients for constructing such a theory, which is also a unification of the standard model with gravitation, are : (i) the pre-quantum theory of trace dynamics: a matrix-valued Lagrangian dynamics, (ii) the spectral action principle of non-commutative geometry, (iii) the number system known as the octonions, for constructing a non-commutative manifold and for defining elementary particles via Clifford algebras, (iv) a Lagrangian with $E_8\times E_8$ symmetry. The split bioctonions define a sixteen dimensional space (with left-right symmetry) whose geometry (evolving in Connes time) relates to the four known fundamental forces, while predicting two new forces, $SU(3{)}_{grav}$ and $U(1{)}_{grav}$. This latter interaction is possibly the theoretical origin of MOND. Coupling constants of the standard model result from left-right symmetry breaking, and their values are theoretically determined by the characteristic equation of the exceptional Jordan algebra of the octonions. The quantum-to-classical transition, precipitated by the entanglement of a critical number of fermions, is responsible for the emergence of classical spacetime, and also for the familiar formulation of quantum theory on a spacetime background.

19 pages, 8 figures, based on a talk given at DICE2022: Spacetime, Matter, Quantum Mechanics (Castiglioncello, Italy, Sep. 19-23, 2022), published in the conference proceedings

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• Standard model physics from an algebra?
• Why do elementary particles have such strange mass ratios? -- The role of quantum gravity at low energies
• A violation of the Tsirelson bound in the pre-quantum theory of trace dynamics