I don't have much of a math/physics background, undergraduate physics and calculus is where I stopped... yet I find theoretical physics extremely interesting. The recent online hype about the "E8 theory" only really discusses the fact that Lisi likes to surf and doesn't wear a pocket protector. On these forums, your discussions of the theory are way over my head. So, can someone please provide a layman's explanation of E8 theory? Also... Are the E8 theory and the string-type theories mutually exclusive? Thanks
Hi! I don't know how close to the beginning that you need to start. A good place to start would be to read the definitions in "wiki" of symmetry. http://en.wikipedia.org/wiki/Symmetry jal
i too would like to hear some easier explanation... from what i understand, E8 is this shape in 8D and they project it to 3D, but I'm not sure why... I think they derive something from that projection... And that every vertex basically is an elementary particle, and the interactions between particles are governed by curvatures joining the particles...? Whatever that means... so really i got nothing :) Plus the above could all be wrong. It's kinda frustrating considering that I am now taking my second course in Quantum Mechanics, and I am third year in Physics, but yet I can't gather much more than I would even if i went to Sociology or something. oh and from what i gather it does not go hand in hand with String theory, it is more like competition to it. Plus it doesn't require 11 dimensions etc.
Yah! You got it! I have been trying to get CarlB's E8 to work for me but I cannot get the changes in color. CarlB could help explain the E8 pattern better than me. .... There are two things that need to be understood ... the E8 pattern and the Standard model. Garrett put the two patterns together. I'm at the stage of still trying to understand the finer points of symmetry. Most of the discussions were on trying to understand how/why the patterns fit together or if the "rules" were being violated. jal
Hmm, it is an interesting question. String theory has E8xE8, so you could look for an inclusion E8 ---> E8xE8 at the level of representations. It could exist.
I am trying to study Lisi's paper using Wiki as a guide. Right now I am getting an idea of what Lie (pronounced 'Lee) groups is about. My current understanding of E8 is that it is a mathematical object in 234 (IIRC) dimensions. The idea of projecting the object onto a lower dimensional surface is kind of like taking a wire model of a cube, holding it above a sheet of paper in the sun, and tracing the shadows. There are several ways you can turn the wire frame cube to get different patterns on the paper. These are symmetries, all of which are required to get an idea of what the higher dimensional object (in this shadow case, the wire frame cube) actually "looks" like. Physics isn't about visualization any more. I doubt if humans will ever be able to visualize in much higher than three or four dimensions. Instead, we have to learn the maths. This is hard to do if you are not in a university where such things are taught, but if you are persistant, you can learn a bit on your own. At first, wandering around Wiki is like a maze, but after a while you start to recognise a few things. My question is about E8 as an object already explored in string theory. Isn't E8 one of the 5 mountains in the landscape? One of the ones supposed to be unified by M theory? I think I recall reading long ago about E8 X E8 as a string object, but I knew less about Lie Groups then than I do now, and Wiki has come a long way in adding onto the maze. I suppose it is not right to discuss these low level topics here. Just thought some of the other amatures would be interested. Maybe we should find a room of our own to discuss these interesting things further? S
There are different levels of Layman. SublimeGD, you could get more background info by looking up 2d packing, 3d packing, kissing numbers etc. All of these things relate to symmetry. You will eventually end up seeing E8 and Gerrett on wiki. ( Yah, somebody addded Garrett's name to the E8 entry. The E8 java by CarlB has incorporated a few rules that are not obvious to the layman. Look at the 3d of the E8 model and you will see that there is a rule being applied to the length and the connections. It is assumed that you know them or that it is obvious. Those who want to understand symmetry have the web to help. My understanding is that Garrett has taken the "ideal" E8 root pattern and the "ideal" Standard Model pattern and found a match. The E8 has the "curvature" due to using same "length rule" for the connections. When the four forces of the SM will be put in then the shape will be affected. Jump in ... and give your "simple explanations" and guiding hints so that a layman can try to learn about what is being done by Garrett.
I'm going to change it so that you pick a color, and then pick a place to put it, where "place" means one of the G4xF2 root subgroups, or the background. That should be more intuitive. And it will show the color scheme while you're doing it. Java is a nice programming language, very tightly cast so that it doesn't let me do [as many] stupid errors. It should take 2~3 hours to make the color selection more intuitive. Give me about 2 hours, first I want to surf the net and see what is going on. I should have new code running this evening. [edit] It's now 4.5 hours later, and I've got the new user interface acceptable. The next step is to do the easy and fun part (the math). But first, a couple hour break.[/edit]
Heterotic string theory makes use of the compact form of E8 to avoid negative norm states, as Lubos mentions in his blog. The non-compact real forms of E8 appear in N=2 and N=8 supergravities in which the scalars take values in a symmetric space. Such E8's then act as groups of spectrum generating symmetries for four-dimensional BPS black holes (arXiv:hep-th/0512296v2).
from http://chronicle.com/jobs/v45/i47/4547ctlyst.htm Richard Feynman, the late Nobel Laureate in physics, was once asked by a Caltech faculty member to explain why spin one-half particles obey Fermi Dirac statistics. Rising to the challenge, he said, "I'll prepare a freshman lecture on it." But a few days later he told the faculty member, "You know, I couldn't do it. I couldn't reduce it to the freshman level. That means we really don't understand it." What I'm seeking is a freshman level understanding of what is going on. I think I understand the concept of symmetry as applied to physics. I will look a little into the mathematics of it, thanks for the link. But again my goal is to just get the gist of it.
The basic question has to do with the nature of matter, which is of course made up of atoms and molecules, as every freshman probably knows. Your first course in chemistry will probably teach you about how atoms are held together into molecules by electromagnetic forces, chiefly between the outermost electrons of the atom. You will also learn that the center of the atom is the nucleus, which in turn is made up of protons, neutrons, and some other smaller particles which appear only when the nucleus is broken into smaller bits by a fission reaction. These smaller particles come in hundreds of varieties, but the standard model of particles has shown that all of them can be explained by adding together the properties of only a few. The key particles are the neutrino, the electron, the muon, the tau, and six quarks, which are called top, bottom, up, down, strange and charm. Almost all ordinary matter is made up of the electron and the up and down quarks. Each of these particles occurs as a triplet. For example, the electron, muon, and tau share many properties, differing mainly in mass. The neutrino comes in three kinds also, called the electron neutrino, the muon neutrino, and the tau neutrino. The quark triplets involve three colors. Each kind of quark can come in red, blue, or green. These are not colors of light, of course, but just a pretty way of doing some accounting. In addition to the above, each member of every triplet has an antimatter dual. These particles together make up the fermions, particles which ordinarily tend to get as far away from each other as possible. The bosons are a kind of particle which obey another kind of behavior, in which they tend to cluster together. There are also “particles” which are thought of as carrying forces. The gluon, the photon, and the Higgs are three of these. However, in my opinion, none of these particles is really a particle in the sense we usually think of matter. They do not have mass in and of themselves, but carry the four forces; electromagnetics for the photons, the weak force for the gluons, the strong force and gravity for the Higgs. All of the particles can be thought of as waveforms in some kind of background. The particles of the standard model have been observed in colliders, and we know of photons directly from light, but the graviton and the Higgs have not been observed, presumably because they require higher energy collisions to become observable. Recall that higher energy collisions happen in smaller spaces. You can think of the Higgs and the graviton as being very small, therefore very high energy particles. Some scientists are hoping that the Higgs and/or the graviton, or maybe even a black hole, will appear in the new generations of colliders, which should be coming on line in the next few years, and which are able to reach energies in the range of one TeV, a tevatron. I think that means a billion electron volts. All of this is background for the next stage in physics, which is now called, euphemistically, new physics. This forum, Beyond the Standard Model, interests people who want to know why the standard model particles have the mass, charge, and spin, or quantum numbers, that they do, according to measurable physics. String theory can explain the quantum numbers, but it has five different explanations, and it is thought by many that there must be some more basic theory, with only one explanation. M theory has supposedly connected the five stringy theories into one explanation, but no one seems to know what that explanation is. In any case, it leaves unanswered the fundamental question, what is the zero state, the absolute vacuum, the space-time continuum. If there are waves, what is the stuff that is waving? What is it, when it isn’t waving? Loop quantum gravity, Dynamic Triangulation, and other ideas have been put forward as a means to explore the fundamental question. It largely comes down to a question of geometry. What is the right geometry, the right mathematics, to describe the most fundamental level that underlies all of matter? The fact that the standard model pieces can be hung on the E8 framework is another proposal for a means of investigation of this question. Essentially, it postulates that the particles of the standard model, along with the graviton and the Higgs, must be an emergent effect of the shape of the universe, which exists in higher dimensions than we poor limited humans can perceive. However, even if we find the answer to the geometry of space-time, there remains the question of what is more fundamental than that? What lies beneath space-time? If the particles can be thought of as being different views of a higher dimensional object, as in the Lisi theory, what is the stuff that causes that higher dimensional object to take the shape it does, and not some other shape? The stakes are very high. Human culture has entered a cul-de-sac, and we must have some better source of energy than oil if we are to survive as a technological civilization. Atomic energy has given us a clue, but it has some problems, mainly involving the deadly poisonous leftovers of fission. A workable theory of everything may be the key to finding ways to harness energies like the strong force that holds quarks together inside particles, or even the pure energies of mass, and hence gravity, the actual curvature of space-time. Dr. Lisi’s model may be the best approximation yet to the structure of space-time. Or not. It has the advantage that it can be verified by tests that may be within reach of current technology. Or it can be falsified by those same tests. String, Loop, and Triangulation have suggested no such tests, or at best only a few tests that are not very clear. The Lisi model predicts a few new particles which may soon be within the reach of our technical tools. If these new particles are found, and have the predicted quantum numbers, then the theory will be useful in finding the unification of general relativity with the standard model of particle physics. Lots to look forward to. Hope this helps. Comments welcome. I am only an independent student, and my understanding is not complete. If anyone here finds I have made a misstatement, I would be very kindly disposed to hear of it. S
Thanks! I was hoping that Feynman quote would motivate someone to give the time of day to a lowly undergraduate like me. I didn't mean to give the impression that I am entirely unversed in physics... although that is probably true from the mathematical sense (undergraduate introductory physics aside). I am aware of the standard model, M-theory, and all that jazz, from reading books by Michio Kaku and Brian Greene (biased string theorists?...) But nonetheless I am at least a little bit aware of what is going on in the physics community. Can someone please expand, if possible, on the above explanations of "E8 theory." I gather that the standard model "particles" are arranged on the E8 framework, which lies in higher dimensions. By rotating the E8, different arrangements of the particles become "visible" in our 3 dimensional space. Depending on the rotation, the different fundamental forces can be seen. Is this a grossly misled interpretation of the Lisi paper? I've read that the "E8 theory" does not predict higher dimensions... yet doesn't the E8 shape require higher dimensions? Or is the arrangement of the standard model particles not on the higher dimensional E8 shape itself, but on a 3D projection of the E8 shape?? Could rotation through higher dimensions account for quantum uncertainty and weirdness? (particles seemingly popping in and out of existence?) Thanks for all and any replies Edit: Okay, I see now that the elementary particles aren't really "placed" around the E8 shape, but are as one of the earlier posters put it.. "every vertex basically is an elementary particle, and the interactions between particles are governed by curvatures joining the particles"
The standard model uses the observable 3 dimensions of space and one of time. The Lisi model does not require extra dimensions of space and time. The dimensions of the E8 system are mathematical, not physical dimensions. The idea that particles pop in and out of physical space from other dimensions is not really it. One version of QG says we live on a higher dimensional brane (a topological surface) and that some particles, specifically gravitons, move through our brane world, becoming briefly part of it, and then they return to a region called the bulk. The bulk is not space as we know it. This idea is invoked to explain why gravity is so much weaker than the other three forces. Some of the force of the graviton leaks into our world, but most of it goes into the bulk. String theory uses extremely small Calabi-Yau dimensions, curled up approximately at the Planck scale, to explain this same weakness of gravitation, suggesting that the extra gravitational force goes into the small curled up dimensions. Some other theorists have suggested that there are large extra dimensions, hoping to show an effect on gravitation at small distances, for example less than a millimeter. No such effect has been demonstrated as far as I know. I don't claim to understand the details of Lisi's idea. But I think I have gotten a pretty good grasp of the dimensions thing. There is commonly a confusion about "higher dimensions" being some kind of 'space' that we just don't see. Physicists don't help clarify this by talking about things like phase space, representational space, momentum space, and so on. These are clearly (I think) not spaces in the sense of a room which you can occupy or not occupy as you so choose. Really a mathematical dimension is any measurement. You can have any number of measurements, or dimensions, but usually physicists like to have as few as is necessary to describe an event. You can describe the shape of any static physical object with three dimensions, the shape of any dynamic object with four dimensions, or maybe five. The one or two additional dimensions are those of time. But what if you need to describe a system that has charge, mass, spin, and so on, which are not really shapes at all? You need more mathematical dimensions to do that. Lisi's model does describe the quantum numbers, so it needs more dimensions, mathematic dimensions, to do that. This coffee house and internet hot spot is closing, but I will look for corrections tomorrow. S
starkind: Yes, you did misspeak on a few points. For example, gluons are the carriers of the strong interaction, not the weak, which is carried by the W+,W-, and Z particles, which are massive. The Higgs is not a gauge boson, and as such is not a carrier of a gauge interaction. It does couple to other particles and gives rise to their masses by virtue of this interaction, but that's not the same as gravity (and has nothing to do with the strong interaction). Gravitons are indeed the carriers of gravity in quantum field theories of gravity, but they're not part of the Standard Model. There are a few other places where I'd question your description of the SM and related matters, but I'll leave it at that. SublimeGD: I think a key point to understand here is why people talk about symmetry groups, and Lie groups in particular, at all in particle theory. E8 is obviously getting a lot of attention, but I think it would be far easier for you to start with the SU(2) X U(1) representation of the Electroweak interaction. If you can get to the point where you're comfortable with how that group represents the gauge symmetries of that interaction, then move on to SU(3) and the strong interaction. It's more complicated, but is even more satisfying (to my eye), once you get how the charge carrying particles (quarks) and the gauge particles (gluons) are described by the gauge symmetry group. There are many descriptions of all this out there (Google is your friend), so just dive in. Once you're comfortable with those ideas, then the extension to E8 as the ultimate symmetry group might be a bit easier.
In mathematics, a dimension is merely the freedom to occupy different states. Spacetime is a construct of human perception. Only 4 quantities are necessary to fix the position of an entity in spacetime [with respect to any given observer]. This does not, as starkind noted, limit the number of additional states an entity may occupy: such as color, charge, mass, spin, etc. These cannot be reduced to units of position, hence are just as fundamental [dimensional] as spacetime coordinates in mathematical terms. In other words, what starkind said.
starkind even though you possibly made a few small errors i greatly appreciate your long post; and thanks to belliott for clarifying. I think however that the point of "E8 Layman's explanation" is that you don't need to dwell into details of symmetry groups to understand it. But from what i gather from the above posts there may not even be such an explanation
Exactly. Its like if I asked in an optometry forum for a layman's explanation of how the eye worked, then got redirected to wiki articles on cell biology and biochemistry. Maybe your right, and there just is no possible layman's explanation for this type of topic. In regards to my question about "quantum weirdness," I retract the question entirely. It was unwise of me to extrapolate about the reasoning behind something I don't understand, from something that I don't understand. To make something clear, I'm using "E8 theory" to mean what is proposed in the Lisi paper, not the E8 mathematical structure itself. I think in one of the other threads I saw Lisi express that he didn't want it called the "Lisi theory" or anything like that. Also in regards to the dimensions question... I understand that dimensions in mathematics are not the same thing as spatial dimensions. But starkind, you say... So you state that elementary particles are an emergent effect of the shape of the universe, which exists in higher dimensions. Then you state that the "E8 theory" does not require more dimensions? I'm confused as to what is going on here...This quote is directly from Lisi in the thread about his paper... "E8 lives in 8D. Sure, it can be projected down to 3D. It then needs to be projected to 2D to be shown on a screen or paper. If we used holograms instead of screens, I'd be making tons of 3D plots. But, as it is, I just project from 8D to 2D, because if I go from 8D to 3D to 2D, the perspective would make a mess of things." So is the shape of the universe "8D"? Or does the shape of the universe have nothing to do with the Lisi paper? I also have a question about the various animations, the one on youtube, and the java applet from CarlB... How is the E8 shape being rotated in these animations? Does the rotation require "higher dimensions"? It doesn't seem like its just a bunch of points of a 3D structure being rotated about a center axis... or is that precisely what the animation is showing? Chronos, what do you mean space-time is a human construct? I thought general relativity pretty much showed that space-time is actually a "something" that can be bent and whatnot? Thanks again for everyones contributions.
Sorry, but I don't think this is really right. What I believe you're looking for is a layman's explanation of how E8 - and specifically its dimensionality - works to describe fundamental particles. I think any such explanation would be a special case of an answer to the more general question, "How does any Lie Group work to describe fundamental particles?" There are many, many such layman's explanations of the latter, so I was suggesting that you start with those. Most of them are much clearer than anything I could come up with. I think the confusing thing here is the difference between the dimensionality of the group itself and that of spacetime. E8 (as well as other Lie groups) describes the symmetries of a geometrical space, so we can try to picture those symmetries by thinking about the higher-dimensional spaces in which those symmetries exist, which requires the projections Lisi describes in your quotation. No one is suggesting that any of those dimensions correspond to spacetime dimensions, as you've noted yourself. Well, actually, I think starkind is suggesting that the dimensions of the space in which E8 operates are the physical dimensions of the universe, and I think I'd object to that. Perhaps I've misunderstood that point, however - I didn't really follow his explanation, I'm afraid.
How does any Lie Group work to describe fundamental particles? YES!! That is my question. I am having trouble making the connection between my undergrad physics and group theory. I am a global learner to the extreme, so I am trying to get an overall sense of the big picture, but it seems to be presented in a sequential format in the places I have looked, with a lot of unfamiliar vocabulary and symbolism. Maybe that is how it has to be, though. I bought a modern algebra textbook, and I have checked quite a few internet sites, but I can't make the connection. If it is just a classification system for particles, I think I can understand that. Maybe a simple analogy would be the multiplication tables a grade school kid would use? The rules are based on algebra, but geometry can be useful for gaining insight. (like illustrating the symmetry) If group theory is really a periodic table for subatomic particles, how is this a theory of everything? how does F=MA or Maxwell's equations come out of that? Am I even on the right track?
I’m going to be the devil’s advocate. A layman can be a dud waiting for the next wave, the 15 year old down the street, the single mom, the doctor who took out your gall bladder or grandma doing her knitting. There are only a handful of “math kids” who understand what Garrett has proposed. If our simple explanation is really “wrong” I’m sure that Garrett, Tom Smith, or even John Baez would be more that willing to step in with a clarification. I think that what has been said so far is a big help to the layman who wants to seek further understanding. I’m going to ask two simple question based on the following info., to try and focus on E8 and see if the answers end up being simple enough to give greater clarity. ( SM can come later) --------- from https://www.physicsforums.com/showthread.php?t=196498&page=7 http://www.measurementalgebra.com/E8.html post #105 11-16-2007, 03:28 PM I’ll use CarlB’s java animation for a base of reference for my questions. 1. How many points did you use? Why? 2. What is the distance between the points? Why? --------------- Don’t answer by saying CarlB has already explained it. Challenger your communication skills and see if you can use the right words so that the concept will get through.