Jonathan Oppenheim: A postquantum theory of classical gravity?

Witnessing Quantum Aspects of Gravity in a Lab
ICTP-SAIFR
September 23 – 27, 2024

Speaker:
Jonathan Oppenheim (University College London, UK): A postquantum theory of classical gravity?

More Information:

[Achrononmaster]

@11:20 that's not true. GR is a gauge theory, it has three gauges, (1) position, (2) rotation + boosts, (3) scale. It is in fact easier to formulate GR as a gauge theory, and the result is equivalent to Einstein-Cartan gravity. Diffeomorphisms are a "trivial" relabeling of spacetime coordinates and have no physical meaning. Einstein knew this, and was frustrated by it. It is however still a theory where spacetime curvature describes the effect of matter on geodesics. You have not lost diffeomorphism invariances, but split it properly into the relevant physical subgroups.
The difference with GR and the other gauge "forces" is that the others stem from compact Lie groups. That's because they relate to spacetime local topology change, not global spacetime frame symmetries of the background Minkowski manifold. The whole thing is that gravity really is already a quantum theory, because _classical_ spacetime is only _background_ Minkowski, and for a background independent theory you have to abandon strictly local Minkowski topology and admit non-trivial topology. If you do then quantum mechanics is the result. This was shown long ago by Mark Hadley at Warwick University. Hadley did not know what the topology was though, but whatever it is it has to have the Standard Model gauge groups at some appropriate level of energy (inverse length) resolution. Which is just some empiricism. Still no one knows. But it is likely the octonion algebra has something to do with it, maybe with bipartite structure (i.e., minimal hence non-evaporating wormhole topology) since the _e8_ algebra is constructed from octonions in the Freudenthal-Tits "magic square" construct.