New Scientist this week has a cover story I can strongly endorse, entitled Why physicists are rethinking the route to a theory of everything. It’s by journalist Michael Brooks, partly based on a long conversation we had a month or so ago. Unfortunately it’s behind a paywall, but I’ll provide a summary and some extracts here.
For a more technical description of the ideas I’m pursuing that are discussed in the article, see this preprint, which was intended to be a very short and concise explanation of what I think is the most important new idea here. This semester I’m mainly working on teaching and writing up notes for an advanced course for math graduate students about the Standard Model. I’ll be adding to these as the semester goes on, but have just added preliminary versions of two chapters (9 and 10) about the geometry of vectors, spinors and twistors in four dimensions. These chapters give a careful explanation of the standard story, according to which spacetime vectors are a tensor product of left-handed and right-handed spinors. They don’t include a discussion of the alternative I’m pursuing: spacetime vectors are a tensor product of right-handed spinors and complex conjugated right-handed spinors. I’ll write more about that later, after the course is over end of April (and I’ve recovered with a vacation early May…).
It’s well-known to theorists that the Standard Model theory is largely determined by its choice of symmetries (spacetime and internal). A goal of these notes is to emphasize that aspect of the theory, rather than the usual point of view that this is all about writing down fields and the terms of a Lagrangian. This symmetry-based point of view should make it easier to see what happens when you make the sort of change in how the symmetries work that I’m proposing. What I’m not doing is looking for a new Lagrangian. All evidence is that we have the right Lagrangian (the Standard Model Lagrangian), but there is more to understand about its structure and how its symmetries work. In particular, the different choice of relation between vectors and spinors that I am proposing is not different if you just look at Minkowski spacetime, but is quite different if you look at Euclidean spacetime.
The New Scientist article has an overall theme of new ideas about unification grounded in geometry:
… a spate of new would-be final theories aren’t grounded in physics at all, but in a wild landscape of abstract geometry…
That might strike you as outlandish, but it makes sense to Peter Woit, a mathematician at Columbia University in New York. “Our best theories are already very deeply geometrical,” he says.
There’s some discussion of string theory and its problems, with David Berman’s characterization “It can be a theory of everything, but probably it’s a theory of too much.” The article goes on to describe the amplituhedron program, with quotes from Jaroslav Trnka. After noting that it only describes some specific theories, there’s
Trnka thinks the amplituhedron approach might enable us to go even further. “One can speculate that whatever the correct theory of everything is, it would be naturally described in the amplituhedron language,” he says.
Turning to a discussion of twistors, there’s then a section describing my ideas fairly well:
Woit is using spinors and twistors to create what he hopes are the foundations of a theory of everything. He describes space and time using vectors, which are mathematical instructions for how to move between two points in space and time – that are the product of two spinors. “The conventional thing to do has been to say that space-time vectors are products of a right-handed and a left-handed spinor,” says Woit. But he claims he has now worked out how to create space-time from two copies of the right-handed spinors.
The beauty of it, says Woit, is that this “right-handed space-time” leaves the left-handed spinors free to create particle physics. In quantum field theory, spinors are used to describe fermions, the particles of ordinary matter. So Woit’s insights into spinor geometry might lead to laws describing the holy trinity of space, time and matter.
The idea has got Woit excited. He has spent most of his career looking at other ideas, thinking they will go somewhere, and being disappointed. “But the more I looked at twistor theory, the more it didn’t fall apart,” he says. “Not only that, I keep discovering new ways in which it actually works.”
It isn’t that Woit believes he necessarily has the answers. But, he says, it is good to know that, despite the long search for a theory of everything, there are still new possibilities opening up. And a better, if not perfect, theory has to be out there, he reckons, one that at least deals with sticking points like dark matter. “If you look at what we have, and its problems, you know you can do better,” he says.
Other work that is described is Renate Loll and causal dynamical triangulations, as well as what Jesper Grimstrup and Johannes Aastrup call “quantum holonomy diffeomorphisms.” For more details of the Aastrup/Grimstrup ideas, see this preprint as well as Grimstrup’s website. I can also recommend his memoir, Shell Beach.
The article ends with:
That said, when Woit – who has long been known as an arch cynic – is excited about the search for a theory of everything again, maybe all bets are off. Playing with twistors has changed him, he says. “I’ve spent most of my life saying that I don’t have a convincing idea and I don’t know anyone who does. But now I’m sending people emails saying: ‘Oh, I have this great idea’.”
Woit says it with a grin, acknowledging the hubris of thinking that maybe, after so many millennia, we might finally have cracked the universe open. “Of course, it may be that there’s something wrong with me,” he says. “Maybe I’ve just gotten old and just lost my way.”
