Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Gravitation, and Quantum Theory, as Emergent Phenomena

Version 1 : Received: 14 February 2023 / Approved: 15 February 2023 / Online: 15 February 2023 (03:50:33 CET)

How to cite: Singh, T.P. Gravitation, and Quantum Theory, as Emergent Phenomena. Preprints 2023, 2023020253. Singh, T.P. Gravitation, and Quantum Theory, as Emergent Phenomena. Preprints 2023, 2023020253.


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.


quantum gravity; unification; trace dynamics; octonions; non-commutative geometry; standard model; fundamental constants; MOND


PHYSICAL SCIENCES, General & Theoretical Physics

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Comment 1
Received: 17 February 2023
Commenter: Dr.ORiparambil Sivaraman Nirmal Ghosh
The commenter has declared there is no conflict of interests.
Comment: Thanks for your efforts to make it available to us..
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