Quantum Theory, and Gravitation, as Emergent Phenomena

This way of presenting the octonionic theory is perhaps more attractive and insightful than saying `Quantum Theory without Classical Space-time' although both phrases mean the same thing as far as physics is concerned.

The most important takeaway from this title is that this emergence does not have anything to do with energy scale! It is not necessarily an emergence from a high energy Planck scale, to our present day low energy universe.

The emergence is from an underlying situation in which microscopic sub-systems in superposition give rise to superpositions of space-time geometries. A system is said to be microscopic if its action is of order \hbar. As we know, microscopic superpositions arise at low energies as well, and if they were to dominate, there would be no classical spacetime. We will then need a formulation of quantum mechanics which does not use classical time.

Consider sub-systems S_1, S_2, ...., S_n, in a system S. If most of them are microscopic, then we do not have a classical time, nor classical gravity.

Consider now the limiting case that: a sub-system S_i consists of a critically large number of entangled microscopic entities. Then, S_i behaves classically. If the system S is dominated by classical subsystems, then classical spacetime and classical gravitation emerge. On this susbstrate, sub-systems which are still microscopic are described by quantum mechanics as we know it.

It is in this sense that quantum theory, and gravitation, are emergent phenomena.

The octonionic theory describes the standard model of particle physics keeping in mind that all sub-systems are microscopic. Even at low energies. This yields more information than when we study the standard model (as we currently do) assuming a classical substrate. Doing the latter hides the information coded in the quantum spacetime being produced by the standard model particles. This quantum spacetime dictates and fixes the properties of the standard model - the allowed symmetry groups, charge quantization, mass ratios, number of fermion generations.

The extension of the standard model to the Left-Right symmetric model appends quantum spacetime to the standard model, via the right-handed (would be gravity) sector SU(3)_grav X SU(2)_R X U(1)_grav

I attach a useful figure from a previous post. Interestingly, you see the L-R symmetry in this diagram, though I never realised that while drawing it. In the upper level as well as the lower level, the Left is matter, the Right is gravity. General relativity couples left-handed matter (weak interaction violates parity) to (right-handed ?) gravity. This also implies that right-handed sterile neutrinos do exist.