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.
https://www.youtube.com/@Quantumgravity.nordita
Dear Peter,
thanks for this extremely interesting post.
I did not participate, but I watched last September most of the discussion sessions and several of the uploaded talks of the NORDITA program Quantum Gravity: From Gravitational Effective Field Theories to Ultraviolet Complete Approaches .
The approaches to QG that have been represented were very similar to those at the QG 2023 conference in Nijmegen, with a lot of focus on “effective QFT”.
I totally agree on Your main point: “geometry” in practice disappeared from the panorama of modern approaches to QG. All the recent important mathematical developments in (generalizations of) geometry are apparently ignored and irrelevant in the current discussions in physics. In QG, this is usually because of the dominant view that “geometry” is supposed to acquire a meaning only as an “emergent macroscopic property” of fundamental quantum a-geometrical degrees of freedom, in certain states and regimes.
This might not necessarily be the only way forward: quantum theory has imposed the “non-commutativity of phase-spaces”, but the effect of quantum theory on the classical space-time and configurations manifolds has remained unexplored (QFT still treats space-time as a classical Lorentzian manifold) … similarly, as You say, the role of “complexifications” (and the related spinor/twistor geometry) has been somehow ignored.
Although the panorama is very depressing, allow me to give some positive assessment of a few of the many proposals that have been showcased at the NORDITA program (and I would, of course, be interested to know Your opinion on them):
a. Boyle-Turok “CPT symmetric mirror cosmology” is directly related to important aspects of high-energy physics and is (in my opinion) a very appealing and promising alternative to the standard cosmological model;
b. Giddings “quantum-first” proposal (suggesting to investigate the “quantum geometry” arising from “certain sub-structures of Hilbert space induced by the representations of type-III von Neumann algebras of QFT) is somehow in continuity with a long tradition of research in algebraic QFT and (in my “biased” opinion) was the most interesting line of QG research, mentioned at the NORDITA program, directly connected with QFT and quantum geometry.
As regards (table-top) experimental tests of QG: not everything might be due to Planck-scale QG-dynamics; if “modifications to geometry” are already of quantum-field-theoretic origin … the prospects might be a bit different (although equally demanding from the experimental side). I stress that ordinary (free) QFT predicts “modular automorphisms of local observable algebras” and their dependence on the localisation regions (similar to Unruh radiation) can in principle be detected, for example (forget for now the original string-theory / holography related motivations) as in the proposed GQuest experiment (https://gquest.fnal.gov/collaboration/), that I find of extreme interest as a confirmations of the physical meaning of local modular automorphisms in QFT!
Best Regards.
Paolo Bertozzini,
To put the problem even more strongly, “geometry” is much the same thing as “symmetry” (a manifold is something that locally looks like Euclidean space, but Euclidean space is the thing that has the Euclidean group of symmetries). So, by deciding that geometry is not relevant to fundamental physics, you’re pretty much deciding that symmetry is not relevant to fundamental physics, throwing out the main lesson of the subject during the 20th century. Then, when you do this, you, unsurprisingly get nowhere.
I just don’t understand this attitude at all.