--Question 1: What exactly is a gauge group?
A gauge group is a high dimensional surface with many symmetries. Basically, it's a pretty shape. The complete set of these shapes was discovered and organized by mathematicians at the beginning of the twentieth century, and they're the centerpiece of modern mathematics and theoretical physics. Among the groups there are five "exceptional" groups that have special structures distinguishing them from the others -- of these, E8 is the largest, and the most beautiful, with 248 fundamental symmetries. The symmetries of a gauge group can be described by a pattern of points in eight dimensions, one for each symmetry.
Essentially, what I've done is associate each E8 symmetry with an elementary particle field of physics, including the entire zoo of standard model particles and gravity. Other physicists have previously matched the standard model particles to gauge groups, including E8 -- these are called Grand Unified Theories -- but I'm including gravity as well, which is something new, and technically this makes it a Theory of Everything.
--Question 2: What is a "principal bundle"? If the explanation is very technical, perhaps you could explain in which field principal bundles appear? What are they usually used to describe? How do they help you understand the symmetries that you are looking at?
A principal bundle is a playground for group symmetries.
If you have a group, it just sits there, looking pretty -- but when you let a group dance over another space, like the one we live in, you get all sorts of fields with interactions and dynamics. Mathematicians call this a principal bundle. These are the main object of study of differential geometry -- which is where calculus ends up if you stay in college for ten years. The basic idea is to allow a gauge group, such as E8, to twist around the spacetime we live in -- the twists are described by the "connection field." This way, each group symmetry looks to us like an elementary particle field -- parts of the connection. The dynamics of the fields, and their interactions, corresponds to the curvature of the twists.
--Question 3: You talked (in a separate message) about the symmetries of the particles in the standard model. How do you relate particle symmetries with symmetries in general relativity? That is, what features of general relativity have symmetry and then how do you compare those features with the particles of the standard model, in order to unify them? It seems like trying to compare apples and oranges.
You're right, it's strange. I didn't think it was possible to describe gravity purely as gauge symmetries until I saw Lee Smolin, Laurent Friedel, and Artem Starodubtsev do it in a 2004 paper. They referred to a somewhat obscure discovery made by MacDowell and Mansouri in 1977. They revealed that gravity can in fact be described using a particular Lie group. This was the seed idea that led me to combine gravity with the other fields, and led to the unification of... well, everything, using the E8 gauge group.
I'm not sure why someone didn't come up with this idea long before I did -- my guess is the physics community was distracted by string theory. Also, there's a theorem by Coleman and Madula that discourages this sort of unification. But the MacDowell-Mansouri trick gets around the Coleman-Madula theorem by using a different Lie group for spacetime.
--Question 4: What do you mean by a "really weird pattern"? How do you analyse the pattern? If it something purely mathematical, how do you interpret it and what features stand out as weird?
I had described the fields as elements of a big matrix, and this matrix was... lopsided. I had never seen a matrix that looked like that related to a group -- it looked weird.
--Question 5: Once you began to see this connection, how did you test it? What convinced you that it was correct? Did the theory predict features that we see in general relativity and the standard model (e.g. masses of the standard model particles, strength of forces)?
It didn't dawn on me slowly -- the realization struck all at once, and my brain buzzed with the implications. So it wasn't a "hmm, maybe this will work" kind of thing, more of a "holy crap, that's it!"
The interactions between the two hundred or so fundamental particle fields we know of are all known. This exact structure is there in the E8 root system. As far as I've been able to tell it's a perfect match of tens of thousands of interactions, all corresponding to the most beautiful mathematical structure there is. How cool is that!
There are still features of this correspondence that I don't completely understand. I'm learning more about it every day. And, you know, as good as these things start out looking, they can always turn out to just not be true about nature. So, this theory I've cooked up may be wrong. But it's looking very good so far. I haven't gotten to the point with the theory yet where I can confidently predict new relationships between the physical constants such as mass, but that's where it's heading. This theory is only a few months old. What I'm going to do is write up what I've found so far and publish a paper, so others can see the details and play with it.
--Question 6: Is there a way that we can test your theory? Are there predictions that it makes that will help it stand out from rival theories? Does your theory do away with the need for supersymmetric particles, or predict other particles that we could perhaps look for at the LHC?
That's correct, there are no superparticles in this theory. I made a bet with a pair of string theorists that superpartners won't be seen at the LHC -- we'll get to see how that goes. I think I'll be able to use this theory to predict a handful of new particles that might be seen at the LHC, but I'm not yet far enough along to say more. It's very exciting. I have a fun year of work ahead of me.
--Question 7: You mentioned that you weren't interested in working on string theory? What advantages does your approach have over rival theories, such as string theory, both in terms of what it can explain, and also aesthetic appeal?
There are lots of good things about string theory. It appears to be quantizeable, and can accommodate gravity in a fairly natural way. It also has restrictions that come out, due to anomaly cancelation, that say what can and cannot be a "good" quantum string theory. Originally people thought this would be enough, when coupled with the right background manifolds, to get all the standard model particle fields to correspond to oscillations of a string. But it's never worked quite right. In order to get it to work at all, string theorists have to bend over backwards and put in all sorts of things by hand. This is the main warning sign that a theory doesn't correspond to nature. What happens is, a theory looks promising, so people invest time in developing it. If it looks like it's matching nature, that's great. But if it doesn't quite fit nature, people have already invested a lot of time in the theory, so instead of abandoning it, they try to revise it -- they add stuff and try to patch it up. But the more you have to add by hand, without any experimental guidance, the worse the theory looks and the less likely it is to be true about how nature works.
I suspected at the end of the 90's that string theory had left nature behind, and was going off in its own direction without any connection with reality. And it wasn't spreading out in a proper search either, it was barreling along in one direction like a freight train, guided by a handful of theorists with many followers who were devoting their lives to the theory. I've never been much of a follower, so I walked off to search on my own.
For the record, I do think it's good that very talented people, like Brian Greene, are working on string theory. Everyone should be able to work on what they want, and strings may yet turn out to be the true theory of nature. I just have other ideas.
(If you write about my dislike of string theory, please include that I do think it's worthwhile for some people to work on it.)
This theory I'm working on has the main advantage of being testable -- it will very clearly be right or spectacularly wrong about nature. If it's wrong, I'll try to figure out if it's fixable, or I'll abandon it and move on. Another advantage with this theory is its relative simplicity -- there is just one geometric field, the connection over spacetime, and the interactions and dynamics come from its curvature. And, at the heart of this theory is the most beautiful geometric structure in mathematics -- it's very pretty.
--Question 8: What next? If you have unified general relativity and the standard model, does that mean that all the four fundamental forces are now accounted for? What is left for you to do? What do you think you will need to do or demonstrate to gain support for your theory?
Yes, all fields are present and accounted for. Nevertheless, there is a ton of work to do. First, I need to confirm that the particle assignments and interactions are all in agreement with known physics. Any deviations could be fatal. Second, I need to see what new predictions come out: existing particle masses, coupling strengths, new particles, etc. Third, the proper quantum description needs to be worked out. Right now the theory matches up well with methods of loop quantum gravity, which is why I've been hanging out so much with the LQG community. To tell you the truth, it's much too much for one person to work on -- but if it keeps going as well as it has been, it won't be just me working on it.
The talks I've been giving have generated a lot of interest -- one week ago I delivered a one hour talk to a packed seminar room at the Perimeter Institute. That went VERY well. I'm going to have a paper out on the arXiv soon, with full details, so people will be able to consider it and play with it for themselves.
I feel funny calling it "my" theory, since I've learned so much from the work of others. And if it works as well as it looks, other physicists will play with these ideas and develop the theory far more than I could. It's a little early to say, but what I think, at this point, is that this is nature's theory.