New discussions on E8
Recently, John Baez posted over at his blog a talk by Bertram Kostant on the exceptional group E8. It is interesting to follow it and the discussions over there if you are studying Lisi’s recent work. Or not. E8 is interesting per se.
Previous posts on this (on inverse chronological order): here, here and here.
March 4, 2008 at 1:14 am
Garrett Lisi has recently made presentations during the past week at the TED and BIL conferences.
According to the programs, each talk was about 15 minutes and both seem to have been very well received.
A blog by Bruno Giussani about the TED talk said:
“… E8 is a mathematical shape with 248 symmetries — a large, complex but elegant bundle (above an illustration from Lisi’s paper). Lisi believes that the relationships between the symmetries represent known particles and forces, including gravity, and hopes that the Large Hadron Collider, the new particle accelerator at CERN in Geneva that will go online later this year (Brian Cox will talk about it tomorrow) may offer indications on whether this pattern contains the response. I am not sure that I fully understand it. If you’re like me, refer to the Wikipedia page, or to the full paper (31 pages, PDF). …”.
Another blog by Ethan Zuckerman about the TED talk said:
“… Garrett Lisi has been getting a lot of attention lately, for putting forth a novel approach towards unifying particle physics based on geometric symmetry. He begins by referencing his surfer roots, putting a phenomenally complex equation on the screen. “Whoa dude, nice equations!”
To try to explain his work, Lisi asks us to think about coral. Each branch of coral is made of thousands of polyps, all genetically related to one another. He asks us to imagine that this coral is hyperintelligent and we can talk to it. We ask how a particular polyp ended up in a particular location. The coral would “admonish us for turning up the temperature, then tell us that we’re being stupid.” He shares his consciousness with each other polyp, and shares his experience with them. That would make him unusually able to understand quantum physics, in comparison to humans, who understand only one reality.
He offers a slightly different version of the Schrodinger’s cat paradox, one where the cat holds Schrodinger in a box and has a 50% chance of killing him through atomic decay. In the box, Schrodinger exists a branching function, alive and unalive at each point. Lisi tells us “everything that can happen does.”
Referencing the Large Hadron Collider, he tells us about the “whole zoo” of subatomic paricles, the 226 particles we know about, including simple particles like electrons and quarks, and their “second and third generation” relatives, which exist at much higher masses. He talks about the forces that effect each particle – the weak, strong, gravity and mass. A major hope for the Large Hadron Collider is that it will allow us to detect the Higgs Boson, which should give mass to other particles.
Lisi shows us force maps of particles, organized in terms of hypercharge and weak charges. They organize into symmetrical patterns – these symmetries are the result of projecting from 4D into 2D. “These pictures are not just pretty – they tell us what’s allowed to happen.” A great deal of progress has been made in physics by drawing these maps ad looking to see what’s missing – broken symmetries often reveal particles that are supposed to exist.
An even more complex pattern involves gravitation and is the projection of six dimensional charge space into two dimensions. Lisi believes that broken symmetries here are solved when we look for more perfect patterns in seven charge dimensions – we should see another force that works like the weak force, only much weaker.
The symmetry he’s looking for is in eight dimensional charge space, and would echo the shape of one of the most beautiful shapes in mathematics, a “smooth, curved shape with 218 [a typo - it should be 248 ] dimensons.” The E8 lie group has helped explain the curvature of spacetime, and Lisi believes it can also help explain the whole particle zoo we’re currently encountering. In other words, he believes this shape could explain… everything.
This idea isn’t quite as wacky as it seems – our understanding of physics is deeply mathematical, and symmetries have helped predict the existence of forces and particles through time. This new model has holes in it – 20 particles that would need to exist. Two have been found so far – Lisi is hoping that particles created in the LHC will match this model. If so, “that will be very, very cool.” If not, it might still be very cool, but for him, it will the equivalent of a surfer wiping out.
We get the sense that this won’t be so bad for Lisi. He’s been living in a van on Maui, moving to various surf spots, and living “a balanced life between physics, love and surfing, my own three charge directions.” It doesn’t sound like a bad life, whether or not the math turns out to work out. …”.
Wired magazine coverage of TED, by Kim Zetter, interviewed Garrett Lisi, and wrote:
“… Wired: If your theory is proven correct, what will the implications be? What will we know about the universe and how it works other than that its structure is incredibly beautiful and ordered?
Lisi: For me, it would be enough to know that the fundamental structure of the universe is incredibly beautiful. I don’t think there would be any practical implications within our lifetime. (Physicist Richard) Feynman put it the best when he said: “Physics is like sex. Sure, it may give some practical results, but that’s not why we do it.”
…
Wired: Your model predicts the existence of 20 mysterious and as-yet-undiscovered particles. Have you been able to calculate masses for those mysterious particles that would help researchers find them?
Lisi: These suggested particles are not so mysterious — they would be a lot like the Higgs particle, but with color charges that keep them in bound states. I haven’t yet solved the problems required to predict their masses, but they would still be recognizable if detected. Of course, if a bunch of particles are detected that are clearly not any of these 20, then this theory is in trouble. And if the Large Hadron Collider (scheduled to go online later this year in Switzerland) finds superparticles or other evidence for strings, I’m going to have to pay out some bets.
Wired: Tell us about your decision to pursue your research independently. Why, after getting your Ph.D., did you decide to mostly avoid academic teaching and research positions?
Lisi: It is extraordinarily difficult, even in academia, to find a job that will let you do whatever you want with your time. If you are determined to spend your time following your own interests, you pretty much have to do it on your own. After my Ph.D., there just weren’t any positions open to support the research I wanted to do. And, of course, the surfing and windsurfing in Maui is amazingly good. I did the best I could to make my daydreams happen — and that didn’t put me in an office.
Wired: You’re used to working in isolation. But this is a theory that’s being developed in the wiki tradition with input from others. Have there been any exciting and noteworthy contributions from others to further the theory?
Lisi: Sure, I’ve made all my physics open source, and documented it as well as possible. I’ve got a personal wiki, Deferential Geometry, where I work on ideas out in the open. Many people have taken ideas from my work and run with them, to advance their own, which is good to see. The biggest help with the theory that I’ve received from others has been from mathematicians, who have provided answers to some of the trickier aspects of E8 group theory. And there has been practical help as well: friends who have offered me places to stay, or donated support, and there’s even a surfboard shaper making me a new board — from 42 Surfboards.
Wired: A media storm ensued last year after New Scientist published a piece about your theory. Since then you’ve been hailed a genius and likened to Einstein. But you’ve also received some pretty sharp ridicule. Does it worry you that so much could be riding on this for you personally? Do you regret putting your ideas out there for public consumption before they were fully formed?
Lisi: The comparisons to Einstein really aren’t well justified — he accomplished much more in physics than I ever possibly will. This story has been sensationalized in the media, which has been quite stressful. Although, the media spectacle has also been pretty amusing at times.
Some of the harsher personal criticism is an unfortunate but understandable backlash. I try to pull what I can from useful criticism, but most of it has been from people encountering unfamiliar mathematics and being confused by it. I’m not worried about being portrayed as amateurish, because I’m not an amateur, and my work reflects that.
As it develops, this theory may or may not turn out to be true about nature, but it’s a solid beginning founded on well-established mathematics. I thought the theory was well enough along to present it to the greater community, get some feedback, and develop it from there.
…
Wired: You said recently: “Since E8 is perhaps the most beautiful structure in mathematics, it is very satisfying that nature appears to have chosen this geometry.” Did nature have a choice? Could the E8 framework be the result of an evolutionary process of trial and error that adapted until the universe got it right or do you think that beautiful structure was “ready made”? I guess the equivalent philosophical question for this would be, which came first — the mathematics or the forces?
Lisi: This is a very unusual aspect of this theory. The largest simple exceptional Lie group, E8, is a unique structure in mathematics. If this structure turns out to be fundamental to how the universe works, then it seems to indicate our universe is not one that exists in a landscape of other possibilities. It would mean our universe is exceptional, and perhaps singular. Of course, it is philosophically questionable to consider other universes to begin with, since we’re only aware of one. But, whether this theory works perfectly or not, it is undoubtedly true that the fundamental nature of our universe can be described by mathematics.
Wired: What’s the connection, if any, between the board sports you pursue and your interest in physics?
Lisi: Surfing and snowboarding are what I do for fun — to get out and play in nature. We live in a beautiful universe, and I wish to enjoy it and understand it as best I can. And I try to live a balanced life. Surfing is simply the most fun I know how to have on this planet. And physics, and science in general, is the best way of understanding how everything works. So this is what I spend my time doing. I do what I love, and follow my interests. Shouldn’t everyone? …”.
Tony Smith
PS – My own take on E8 physics, motivated by Garrett’s work, is on the web at
http://www.tony5m17h.net/GLE8Cl8TSxtnd.pdf