Last week Steven Weinberg gave a Lee Historical Lecture at Harvard, entitled Glimpses of a World Within. There’s a report on the talk at the Harvard Gazette.

In essence, Weinberg argues in the talk for an idea that first started to dominate thinking among HEP theorists nearly forty years ago, one that is sometimes called the “Desert Hypothesis”. The idea is that by looking at what we know of the SM and gravity, you can find indications that the next level of unification takes place around the Planck scale, with no new physics over the many orders of magnitude between the scales we can observe and that scale, at least no new physics that will affect running of coupling constants for instance. The evidence Weinberg gives for this is three-fold (and very old by now):

- He describes listening to Politzer’s first talk on asymptotic freedom in 1973, and quickly realizing that if the strong coupling decreases at short distances, at some scale it would become similar to the coupling for the other fundamental forces. In a 1974 paper with Georgi and Quinn this was made explicit, and he argues this is evidence for a GUT scale a bit below or around the Planck scale.
- He explains about the Planck scale, where gravity should be of similar strength to the other interactions. This idea is even older, well-known in the fifties I would guess.
- He refers to arguments (which he attributes to himself, Wilczek and Zee in 1977) for a Majorana neutrino mass that invoke a non-renormalizable term in the Lagrangian that would come from the GUT scale.

Weinberg sees these three hints as “strongly suggesting” that there is a fundamental GUT/Planck scale, and that’s what will explain unification. Personally though, I don’t see how three weak arguments add up to anything other than a weak argument. GUTs are now a forty-year old idea that never explained very much to start with, with their best feature that they were testable since they generally predicted observable proton decay (which we haven’t seen). We know nothing at all about the source of particle masses and mixing angles, or the reason for their very different scales, and there seems to be zero evidence for the mechanism Weinberg likes for getting small neutrino masses (including zero evidence that the masses are even Majorana). As for quantum gravity and the Planck scale, again, we really have no evidence at all. I just don’t think he has any significant evidence for a desert up to a Planck unification scale, and this is now a very old idea, one that has been unfruitful in the extreme.

Weinberg ended his talk with another very old idea, that cosmology will somehow give us evidence about unification and GUT-scale physics. That also hasn’t worked out, but Weinberg quotes the BICEP2 value of r as providing yet more evidence for the GUT scale (he gives it a 50/50 chance of being correct). Again though, one more weak piece of evidence, even if it holds up (which I’d give less than 50/50 odds for at this point…), is still weak evidence.

For a much more encouraging vision talk, I recommend listening to Nati Seiberg at the recent Breakthrough Prize symposium. Seiberg’s talk was entitled What is QFT?, and to the claim that QFT is something understood, he responds “I really, really disagree”. His point of view is that we are missing some fundamental insights into the subject, that QFT likely needs to be reformulated, that there exists some better and more insightful way of thinking about it than our current conventional wisdom. In particular, there seems to be more to QFT than just picking a Lagrangian and applying standard techniques (for one thing, there are QFTs with no known Lagrangian). Seiberg takes the fact that mathematicians (who he describes a “much smarter than most quantum field theorists”…) have not been able to come up with a satisfactory rigorous version of QFT to indicate not that this is a boring technical problem, but that we don’t have the right definition to work with.

To make things more specific, he describes joint recent work (for another version of this see here) on “Generalized Global Symmetries” that works with global symmetries associated to higher co-dimension spaces than the usual codimension one case of Noether symmetries and Lagrangian field theory. Evidently there’s a forthcoming paper with more details. I’m in complete agreement with him that there must be better ways of thinking about QFT, and I think these will involve some deeper insights into the role of symmetries in the subject.

**Update**: The paper Seiberg mentions is now available here.