http://backreaction.blogspot.com/2007/08/garrett-lisis-inspiration.html my candidate for the greatest ever physics blog interview
A disarmingly charming exchange. Einstein played the violin, Garrett rides waves. I like chess, but am not gifted. The geometry is compelling and beautiful.
Einstein would have known that it was useless having blogs. Instead he would have spent time coming up with a unified theory[now that he knows about the other forces also].
Well, I spend a minimum amount of my time in my blog. I'm always intrigued on how "heavy" bloggers find time for writing so many posts, sometimes quite elaborate posts. I can only conclude that at least one of the below must be true: - they do not have a family or a family "life" to care of; - they have very flexible jobs, if at all; - they carry their notebooks *everywhere* and are able to write anywhere they happen to be; - they often have good internet access (specially those who are able to include a link for almost every word they mention in their posts); - they sleep only up to 5 hours per night; :zzz: - etc... (I've certainly forgot several possibilities) :uhh: I would speculate that, if Einstein lived in our time, he would not blog, or if so, he would spend a very little amount of time with it. :tongue2: Christine
Marcus … I did a picture search for E8 and E8 root system. http://aimath.org/E8/ Mathematicians Map E8 and the best image http://homepages.wmich.edu/~drichter/images/splashphoto_small_073106.jpg because it shows the shadow of E8 second place http://en.wikipedia.org/wiki/Image:E8_roots_zome.jpg This is a Zome model of the E(8) root system I also got other interesting pages such as http://www.amsta.leeds.ac.uk/~rjm/parade/R3R1.html E8 singularity Equation: x^3-y^5-z^2 http://www.sukidog.com/jpierre/strings/mtheory.htm SUPERSTRINGS! M-theory I got a different question. What is the total length of the connections?
Hi Jal, Christine, Alejandro, Neutrino et al. Jal I don't know the total length you are talking about. Maybe someone else with a better understanding of E8 can discuss this. Christine, I seem to remember hearing that A.E. was something of a ladies' man. So even when he was not busy playing the violin and thinking physics, he would probably have been too busy chasing women and having affairs. Blogging might have come very low on his list of priorities. So I generally agree with you and Neutrino, but in later life I think Einstein did very much like to write letters! He corresponded with many people, not all of them physics colleagues. Perhaps because he liked to explain ideas, express opinions, and enjoyed writing. Would he have joined the discussion at Peter Woit's blog *Not Even Wrong*? Someone with more knowledge of what the man was like can guess better than I.
jal: I've been talking with David Richter, and I used a paper of his to build this animation of the E8 root system projected into 2D: http://deferentialgeometry.org/talks/FQXi07/video/e8anim.mov (caution, it's 100MB.)
You're fun to talk to. LOL The link did not work for me. Since E8 is such a monster it never the less has a fixed number of conection point and a fixed pattern of conections. I was just wondering if this was true since the different picture imply this conclusion. Be nice to me .... I'm not a mathematician. jal
Hmm, wonder why the link didn't work. Can you play quicktime movies? The E8 root system isn't that monstrous -- it's just 240 points in a finite lattice in 8D. Each root is the same distance from the origin, and each has 56 nearest neighbors. To make the E8 polytope (classified as P421), one draws in these links to the nearest neighbors. The pretty pictures, and the correspondence to the standard model quantum numbers, come from projecting this root system into lower dimensions.
I don't know what that animation is showing us, but it's beautiful, especially when the nodes line up in 2-D and resolves to a much simpler-looking object.
Marcus, the point with E8, and much of the amateur approximations we do here, is that from the point of view of high academia they fall in the category "tried without success, not PhD will be produced from here". Or, Also near of Feynman's analogy about boxes and keys, "did you try this number?". The problem is that one must have a natural method to break E8 into the standard model. (And Garrett wants gravity too!). In the same sense that string theoretists have a lot of vacui to choose from, GUT theoretists have a lot of breaking patterns to choose. The only fundamental (*) advantage of string theoretists over GUT theoretists it that the later do not have a fundamental reason to break the group at all, while the former must do it to go down to four dimensions. BTW, Lumo uses this fact to claim that "Standard Model has been proven to be a consequence of compactified heterotic string theory back in 1985, I mean by Strominger Horowitz Witten Candelas". Fortunately the preprint of this paper is readable online in KEK so you can read and check. As far as I remember, four 27-generations with N=1 supersymmetry and E6 gauge group is not the Standard Model. Yet. (*) they also have to have one technical advantages, better control of V+A interactions, and one half-fundamental one: justification of the high energy cutoff.
Incidentally, the last parragraph of Strominger Horowitz Witten Candelas suggests to try to break E8 into O(10) by using some other kind of undiscovered manyfold. Most probably this possibility has already been settled as negative, has it?
Thanks Alejandro, this is a good description, and the KEK link was helpful. Indeed what I have been doing is GUT + gravity. It came as a surprise to me, three months ago, that the Lie group I had built up to over the years was E8. This has been very exciting, and I'm now playing with many of those symmetry breaking patterns. The difference is, as you say, I'm including gravity in there with the other GUT gauge fields. I can make this more clear, and fun, by starting with a simple question: "What is the rank of the standard model and gravity, as a Lie algebra?"
Hi garrett! How would you explain to someone who has never heard of extra dimensions ( more than 3 dimensions)? Where would you start? (Without using compactification) This must be a challenging communication/teaching situation. Would you, For example.... Assume that there is another direction (a fourth) from the corners of a cube.... 240 points 8d 56 neighbors 240/4=60 (one extra direction on each corner of a cube) 60/6=10cubes That does not seem to work or .........??? jal
jal, we have to be careful here. There are several different spaces we're dealing with at once when we work with a principal bundle. (This is probably why Sabine said YM is not so simple.) We have the spacetime we move around in. We have the 248 dimensional E8 manifold, which serves as the fiber or "internal space." And we have the 8 dimensional vector space that the 240 E8 roots live in, that describe the structure of E8. If you want to think about Yang-Mills theory the same way people think about Kaluza-Klein theory, then you have to imagine the 252 dimensional "entire space." Or, if you don't want to think about extra dimensions at all, you can just think of all this as the familiar four of spacetime and a bunch of algebra.