Elementary particles, black holes, and the octonions

In this approach, quantum theory, and gravitation, both are emergent thermodynamic phenomena, emerging from the same underlying, more general, theory.

If they are both emergent thermodynamic phenomena, in what way do they differ from each other?

Quantum theory (without classical time) holds at thermodynamic equilibrium, and evolution is unitary.

If there is critical entanglement amongst the fermions in the underlying theory, non-unitary evolution becomes significant, spontaneous localisation results in the formation of a black hole, and in emergence of classical spacetime obeying laws of gravitation. This is a far from equilibrium state, at the opposite end from quantum theory. Elementary particle and black hole are two related fermionic states. In particular the charged spinning black hole [Kerr-Newman] has the same gyromagnetic ratio (g) as the electron satisfying the Dirac equation; both being twice the classical value. [With the understanding that interactions will make the electron g value depart from 2].

Gravitation is hence a far from equilibrium thermodynamic phenomenon. A black hole radiates so as to return to thermodynamic equilibrium, described by unitary quantum evolution.

At equilibrium the elementary particles live in 8D octonion space, evolving in Connes time. They obey a Left-Right symmetric dynamics which is an extension of the standard model, with the RH symmetry being the precursor of gravitation. This is true at all energy scales.

This dynamics could be described on the background of the 4D classical spacetime provided by those fermions which have already undergone localisation to form black holes. Such a description justifiably ignores the pre-gravity of the unlocalised fermions, and is given by our conventional QFT for the standard model, which has LH symmetry for the weak interaction. The RH symmetry - the precursor of gravity - is very hard to detect because gravity is so weak, but this RH symmetry is present, even at low energies.

It could well be, keeping in mind that space and time interchange roles inside a black hole, that the inside of the black hole is one half of a split octonion space, the other half being the exterior spacetime. Let us call the inside of the black hole the inner half space. It seems to us that a BH interior is embedded in 4D spacetime; but it is not! It is an extension of the external 4D spacetime to four additional dimensions.

Elementary particles live in the entire 8D octonion space.

Non-black-hole classical objects have a penetration depth (into the inner half space) much less than Planck length. They occupy the ordinary 4D spacetime.

The BH interior maximally occupies the inner half space, distinct from the exterior 4D spacetime - the other half.

By emitting Hawking radiation a black hole returns towards thermodynamic equilibrium and towards unitary quantum evolution in the 8D octonion space.