(Blinkered) Visions in Quantum Gravity

This past summer Nordita ran a program on quantum gravity, featuring lectures and panel discussions on various approaches to the subject. Lecture notes from the six mini-courses are now available here. There’s also a long, 39 author document called Visions in Quantum Gravity, which summarizes the panel discussions and includes further thoughts from the participants.

Reading through these contributions, what strikes me is how much “quantum gravity” has simultaneously become the dominant topic in fundamental physics research, while at the same time narrowing its vision to a short list of approaches that are disconnected from the rest of science and have gone nowhere for many decades. Besides some aspects of the asymptotically safe QG program, the only other approach that connects at all to the rest of fundamental physics (the Standard Model) is the string theory landscape program. That program is based on making “conjectures” about what a string theory/quantum gravity theory would imply if one had one, and then rebranding these “conjectures” as “predictions”, in order to be able to go to battle on Twitter and elsewhere claiming that string theory really is predictive, no matter what the critics say. Whatever this is, it’s not any sort of conventional science.

With quantum gravity cut off from the rest of fundamental physical theory, one can only connect it to experiment by coming up with a proposal for an observable purely quantum gravitational effect. There was some discussion of such proposals at Nordita, but I don’t see anything plausible there (tabletop measurements discussed seem to me to be relevant to quantum measurement theory, not to what the quantum gravitational degrees of freedom are).

Cut off from connection to experiment, there remain the deep connections to mathematics that have characterized fundamental physics, especially modern physics, with GR and the Standard Model theories very much of a geometrical nature. The Nordita program however was completely cut off from mathematics, with no mathematicians among the 39 authors, and minimal representation among them of the field of mathematical physics.

Most seriously, while GR is a very geometrical theory, the approach to geometry used here is very narrow and naive. In particular, modern differential geometry makes clear that one should think not just about the tangent bundle, but also about spinor bundles, which give a more fundamental and powerful structure. That spinors are important is very clear from observational physics: all matter fields are spinor fields. And yet, the word “spinor” doesn’t occur even once in Visions in Quantum Geometry (it occurs in the mini-courses mainly in the technical discussion of the construction of the superstring). As for the fascinating extension of spinor geometry known as twistor geometry, that is mentioned not even once by anyone. The Penrose school of trying to understand quantum gravity using spinors and twistors is completely ignored.

Given the impossibility of getting experiment to tell one how to think about the quantum nature of the gravitational degrees of freedom, putting on blinders and refusing to look at mathematics outside of a naive and narrow conception of geometry seems to me a recipe for continuing a now long tradition of failure.