Layman's explanation wanted

[SublimeGD]

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

[jal]

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

[Mephisto]

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.

[jal]

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

[arivero]

Also... Are the E8 theory and the string-type theories mutually exclusive?


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.

[starkind]

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

[jal]

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.

[CarlB]

I have been trying to get CarlB's E8 to work for me but I cannot get the changes in color.

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.

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.

[kneemo]

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.

Heterotic string theory makes use of the compact form of E8 to avoid negative norm states, as Lubos mentions (http://motls.blogspot.com/2007/11/exceptionally-simple-theory-of.html) 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 (http://arxiv.org/abs/hep-th/0512296)).

[SublimeGD]

There are different levels of Layman.

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.

[starkind]

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

[SublimeGD]

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...

...If the particles can be thought of as being different views of a higher dimensional object, as in the Lisi theory...

...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...

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?...:blushing:) 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"

[starkind]

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

[belliott4488]

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.

[Chronos]

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.

[Mephisto]

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

[SublimeGD]

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...

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.


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.

[belliott4488]

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. 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.
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 ... 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?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.

[TheRealColbert]

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?

[jal]

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)

---------

starkind
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.

from http://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.

[starkind]

Thanks, belliott4488, for the corrections. I am trying to understand this as a layperson myself, having started with only college physics and calculus. I have been studying these ideas (QG, string, loop, triangulations, cat theory, Lie algebra, etc.) for five years now, on my own and on the internet (mostly Wiki and PF) using books from Dover press, among others, available in national bookstore chains. I have never taken a course that mentioned any of this stuff. So it is no surprise to me to hear that I have made some misstatements. Part of my reason for writing here is to learn to use the language of physics clearly and correctly, so I appreciate any hints you or others may give me to identify areas where I have misunderstood or confused the concepts. At university, you are required to write papers and tests to give you a clue where you may be lacking, but here we have to rely on others for corrections.

I would appreciate if you could say more about your assertion that the Higgs “does couple to other particles and gives rise to their masses by virtue of this interaction, but that’s not the same as gravity.” How is mass different from gravity, aside from the English usage of mass as something a particle can possess, and gravity as a force (or a curved space-time) that affects mass. I am afraid that mass and gravity seem inextricable in my mind. In fact, I think we could do without either idea, (that of curved space-time and that of particles throwing gravitons back and forth at each other) and simply ask what is inertia? Why does it cause some objects to resist acceleration, including gravitational acceleration?

SublimeGD, I agree with belliott4488 that we should first start with trying to get used to how SU(2) and U(1) are used to describe the electroweak interaction. I am trying to study this myself now, and find that Lisi’s paper makes a good motivator. Lisi says the electroweak gauge W is an element of su(2) and the electroweak gauge B is an element of u(1). I think I have learned that SU(2) and U(1) are Lie groups, and that su(2) and u(1) are the algebras associated with those groups.

In the table on page 2, I wonder what the electroweak gauge B is. I guess the electroweak gauge W has to do with the W bosons of the weak force. I don’t know what happened to the third weak force boson, the Z. And I can make a guess that the electroweak gauge B must then be the electro- part of the electroweak, since I have seen B used as a symbol for the magnetic part of the electromagnetic field.

I wonder if ‘spin’ as used in a Lie group algebra so(3,1) has anything at all to do with spin as a quantum number?

The e in the table is a frame, but what is a frame? I know relativistic frame, is it the same?

[starkind]

jal

I'm not sure what you mean by question one. I have a microsoft browser and so can't view the applet. (Ba-a-a-ahhh).

E8 has 248 dimensions, so I guess 248 points. Lisi projects this down to three dimensions as a cubeoctahedron, one of my favorite objects, as on page 5, table one. The cubeoctahedron has only eight vertices, but the projection is onto the midpoints of the lines of the cube, which makes twelve points. The other points are not lost, they are just obscured. Many points of the E8 must project down onto one point in 3 dimensions.

The distance between the points, so far as I know, is undefined. Some lines on a projected image look shorter than others, but in the higher dimensional object, they may be the same length, or even longer. If E8 obeys topological rules, as I suspect it must, the distances can be any length or any relationship.

Is this what you meant?

[jal]

Hi starkind!
I'm trying to get those that say that they want to understand to do a little bit of thinking and to do some observations.
Those that have an understanding, I want them to give a layman's explanation.
Here is some more help.
--------
Pick an outside “dot”… you will see that it rotated from zero to 90 degrees and then back.
“Stop” the rotation and you will see that there is a mirror image in each quadrant (4). What is happening in the first quadrant is also happening in the other quadrants.

Now, … disregard the other 3 quadrants. Find the other symmetries in the first quadrant.

[SublimeGD]

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.

I suggested that "analogy" to illustrate my frustration with trying to get a dumbed down explanation of the contents and implications of the Lisi paper. I am aware that theoretical physics is a different beast all together, and requires a different approach to gain even a grain of understanding. Thanks for the suggestion of looking into how Lie groups describe fundamental particles. But I still feel that a clear explanation of the contents of the Lisi paper could be made from a conceptional point of view, rather than strictly mathematical. Then again, I'm in no position to make that claim, since I don't understand the Lisi paper :redface:

Is anyone "suggesting that the dimensions of the space in which E8 operates are the physical dimensions of the universe"?? This is really one of the key points that must be driven home in a "layman's explanation." Is the E8 symmetry or whatever it is simply a mathematical tool that happens to describe our universe? Or does the "fact"(just assume for sake of argument) that the E8 symmetry describes our universe imply something about our universe, perhaps the "shape" of our universe? This is really what I set out to find out by asking for a layman's explanation. I do want to learn more so I can really understand physics, but I want a simple dumbed down explanation right now! :cry:

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...


Stephen? Colbert? Really? Did you secretly cause the writer's guild strike so you could have some time to learn about particle physics?


I think that what has been said so far is a big help to the layman who wants to seek further understanding.


Very true, thank you guys very much.



SublimeGD, I agree with belliott4488 that we should first start with trying to get used to how SU(2) and U(1) are used to describe the electroweak interaction. I am trying to study this myself now, and find that Lisi’s paper makes a good motivator. Lisi says the electroweak gauge W is an element of su(2) and the electroweak gauge B is an element of u(1). I think I have learned that SU(2) and U(1) are Lie groups, and that su(2) and u(1) are the algebras associated with those groups.


Yea, I have been looking into this too. Somewhere on this forum I saw a thread that showed what type of background one needed to understand the Lisi paper. Graduate level particle physics, group theory... I don't expect to read a couple of wiki articles and suddenly understand the Lisi paper (but I am reading them). That is why I'm trying to hard to get a dumbed down explanation now.

[belliott4488]

Thanks, belliott4488, for the corrections. I am trying to understand this as a layperson myself, having started with only college physics and calculus. I have been studying these ideas (QG, string, loop, triangulations, cat theory, Lie algebra, etc.) for five years now, on my own and on the internet (mostly Wiki and PF) using books from Dover press, among others, available in national bookstore chains. I have never taken a course that mentioned any of this stuff. So it is no surprise to me to hear that I have made some misstatements. Part of my reason for writing here is to learn to use the language of physics clearly and correctly, so I appreciate any hints you or others may give me to identify areas where I have misunderstood or confused the concepts. At university, you are required to write papers and tests to give you a clue where you may be lacking, but here we have to rely on others for corrections.Hey, I'm glad to help in any way I can - I'm just a layperson myself. As jal points out, though, there are different levels of laypeople. I actually managed to complete my graduate studies in Theoretical Physics (long ago), but that's where my career as a professional Physicist ended, hence my status as a layman.
I studied the Standard Model in grad school (note that I say "studied", and not "learned":rolleyes:), and I'd still like to pursue a deeper understanding of it. Maybe if I can help to lead you through some of the underbrush we can each get closer to what we're looking for.

I would appreciate if you could say more about your assertion that the Higgs “does couple to other particles and gives rise to their masses by virtue of this interaction, but that’s not the same as gravity.” How is mass different from gravity, aside from the English usage of mass as something a particle can possess, and gravity as a force (or a curved space-time) that affects mass. I am afraid that mass and gravity seem inextricable in my mind. In fact, I think we could do without either idea, (that of curved space-time and that of particles throwing gravitons back and forth at each other) and simply ask what is inertia? Why does it cause some objects to resist acceleration, including gravitational acceleration?Okay - good questions, with rather far-reaching implications.
The Higgs mechanism is the means by which particles acquire mass in the Standard Model. The Higgs field is a scalar field (i.e. spin zero), and when it interacts with the other particles in the theory, which would otherwise be massless, the effect can be observed as their having mass. A Google search on "Higgs Mechanism" will produce numerous explanations.
As far as the relationship of mass and gravity, of course you're right that they're pretty inextricably related, but that doesn't make them equivalent. Electrons have mass, and are thus affected by gravity, but they are hardly "carriers" of gravity or otherwise responsible for its existence (other than that they do have their own tiny gravitational fields, as does anything with mass or energy). Gravity is the field; mass - or energy, which is equivalent in relativistic theories - is what the field couples to, i.e. it is the quantity that determines the strength of the resulting force (speaking classically).
You are also right to bring up the equivalence of inertial and gravitational mass, although I suspect you might already be aware that this equivalence is the basis for Einstein's General Theory of Relativity.

SublimeGD, I agree with belliott4488 that we should first start with trying to get used to how SU(2) and U(1) are used to describe the electroweak interaction. I am trying to study this myself now, and find that Lisi’s paper makes a good motivator. Lisi says the electroweak gauge W is an element of su(2) and the electroweak gauge B is an element of u(1). I think I have learned that SU(2) and U(1) are Lie groups, and that su(2) and u(1) are the algebras associated with those groups.

In the table on page 2, I wonder what the electroweak gauge B is. I guess the electroweak gauge W has to do with the W bosons of the weak force. I don’t know what happened to the third weak force boson, the Z. And I can make a guess that the electroweak gauge B must then be the electro- part of the electroweak, since I have seen B used as a symbol for the magnetic part of the electromagnetic field.
Okay, this is more that I can explain in detail right here, but let me just try this for now: There are three quantum fields associated with the SU(2) part of the Electroweak symmetry group, SU(2) X U(1) (specifically with the generators of the group), and one for the U(1) group. These don't quite correspond to the physical gauges bosons (read: force carriers) that we see, but instead get "mixed", in the Quantum Mechanical sense.
[This is an example of something that happens a lot in quantum theory, where a field can exist in one "eigenstate", that is, a state where it has a definite value with respect to something, or it can be in a mixture of such states, where it then has a definite value with respect to something else, but it can't be in both.]
In this case, one of the three bosons that correspond to the SU(2) part of the group SU(2) X U(1) (called W0) and the one that corresponds to the U(1) part (called B) mix, and by virtue of the Higgs mechanism, we get two different combinations of these two particles, which are electrically neutral. One becomes the photon and is massless (it doesn't interact with the Higgs field), corresponding to a "mixed" U(1) part that "breaks off" to become the symmetry of the E-M field. The other does interact with the Higgs, and become the massive Z particle. It, along with the two W+/- particles, conveys the Weak interaction. It is their relatively large masses that limit the range of the Weak force.

I recommend the Wikipedia pages on this subject to get a better description than what I've given here.

[belliott4488]

By the way - this is directed to the moderator - should this thread be place elsewhere, since it's not strictly "Beyond The SM" any more? The OP was asking specifically about the use of E8 as a symmetry group, but we've kind of backed up to the gauge symmetries of the SM, for now at least.

[jal]

belliott4488
You have not said one word that grandma could understand.
jal

[SublimeGD]

By the way - this is directed to the moderator - should this thread be place elsewhere, since it's not strictly "Beyond The SM" any more? The OP was asking specifically about the use of E8 as a symmetry group, but we've kind of backed up to the gauge symmetries of the SM, for now at least.

No, the question is still there. Can someone please provide a quick dumbed down conceptual summary of the contents of the Lisi paper?

[SublimeGD]

I actually managed to complete my graduate studies in Theoretical Physics (long ago), but that's where my career as a professional Physicist ended, hence my status as a layman.

:rolleyes: Just a layman with a graduate degree in theoretical physics... :uhh:

I just want a "conceptual" explanation. If that is not possible, can someone please just say its not possible?

For example, if I asked for a layman's explanation of general relativity I would expect something like "gravitational acceleration can be described by the curvature of space and time." I wouldn't be content with a link to a wikipedia article on Riemannian geometry, and a suggestion to "start here".

[staf9]

I am perhaps one of the world's absolute worst teachers, so I'm not even going to try to give a simple explanation of E8 Theory because I know I'll over-complicate it.

However, I can give a little bit of help: Whenever I'm reading a paper on arXiv that I don't understand, I open wikipedia and search every word, then every group of words that I don't understand.

If I find an explanation that I don't understand on wikipedia, I use google or keep digging deeper into wikipedia.

Now, I'm not saying that this is the best way to learn particle physics (some of the stuff on wikipedia is wrong), but searching some key words and reading up can help a little.

Here's what I think would be worthy to look up just to understand what the paper is about: differential manifold, differential structure, E8 (mathematics), principle bundle, and connection (might be listed under principle bundle).


Of course, I may have already overcomplicated it.

[belliott4488]

belliott4488
You have not said one word that grandma could understand.
jal
Hey!! You never met my grandma! :grumpy:

Well, dang ... I did try. I think I was shooting for what I thought was starkind's level of interest and understanding, which was possibly inconsiderate of SublimeGD, who was the original poster, after all.

Okay. I have no idea how to explain at a 'grandma' level what E8 means in this context. I might be able to start with the general idea of symmetries in Quantum Theory, but even that would be difficult for poor granny. I think it would require a lot of careful thought, but at the end I'd have no more to offer than is already available on the web, so perhaps I should take this as my cue to bow out as gracefully as I can ...

[william donnelly]

Part 1 of a basic introduction to E8 is now posted at http://sigfpe.blogspot.com/

So far it's just an introduction to the concepts of Lie group and Lie algebra, but it is written in a very accessible way.

[CarlB]

No one seems to have stepped up to the plate here, so let's have an amateur take a swing at the ball.

I'm going to talk about E8 as compared with the more familiar symmetry group SO(3) or SO(3,R). Wikipedia entries:
http://en.wikipedia.org/wiki/Rotation_group
http://en.wikipedia.org/wiki/E8_%28mathematics%29

The Symmetry Manifold and its Size

SO(3) is the group of rotations around the origin in 3 dimensions. When you rotate something, you get to choose an axis of rotation and how much to rotate around that axis. The axis of rotations choice is like picking a direction away from the origin. Let's count them.

You can move two perpendicular directions which gives you 2 dimensions. Or you can rotate around a spot and that gives you 1 more. Thus the SO(3) rotations are a 3 dimensional "manifold". Another way of saying the "3" is that if you begin with no rotations, there are basically three small movements you can make.

Get a globe and find Albuquerque, my home town. Think about what you can do to the globe, symmetry wise, relative to Albuquerque. You can move Albuquerque to the north/south, or to the east/west, or you can spin the globe on an axis around Albuquerque in a clockwise/counterclockwise direction. That is 3 dimensions and so SO(3) is a 3-manifold.

Our purpose is to talk about quantum numbers, but first let's talk about the dimensionality of the quantum numbers. That means "how many" quantum numbers each particle gets.

The Dimensionality of the Quantum Numbers

You get to have one quantum number for every motion you can do with your symmetry that is "independent" sort of. Two small motions are independent if it doesn't matter what order you do them in (i.e. they "commute" as in obey the commutation law of multiplication AB = BA so order doesn't matter). Independent motions are great. They're easier to analyze because you can fiddle with one without screwing up the other.

For the example of SO(3), the three small rotations do not commute. It might be obvious that rotation around Albuquerque doesn't commute with moving Albuquerque North/South. To see that moving Albuquerque North/South doesn't commute with moving Albuquerque East/West we can discuss the puzzle:

Suppose two people have good GPS systems and start hiking from the same point. Person X goes 1 mile East, and then 1 mile North. Person Y goes 1 mile North and then 1 mile East. Do they end up at the exact same point?

The answer is that, in general, they do not. To see why, get a globe, and see what happens if you increase the 1 mile to 1000 miles. Assuming that the starting point is Albuquerque (which is in the Northern hemisphere), you will find that the person who starts going North first, will end up farther to the east. The reason is that when you travel East at a higher latitude (i.e. more northerly) you cross more lines of longitude.

The same effect occurs for very small rotations. And the result of careful calculations is that none of the small rotations in SO(3) commute and so you can't break things up. By contrast, with E8 you can pick out 8 small rotations that commute. Therefore the quantum numbers of an E8 state requires 8 quantum numbers to specify.

Operators In Quantum Mechanics

The subject we are applying this theory to is quantum mechanics and so should discuss it a little. In quantum mechanics, the quantum states are "eigenvectors of operators". What that means is that if you write the operator as a matrix A, the quantum states are vectors \psi that satisfy the equation:
A \psi = \lambda_A\psi where \lambda_A is the quantum number. This will be familiar to people who've studied even the most elementary quantum mechanics book.

Author is a proponent of the density operator formalism. In that formalism, the above is much sexier, but to discuss it here would unduly confuse most readers. Accordingly, with effort, he will suppress the urge to preach to you sinners.

To fully characterize a quantum state, you first choose as many operators A, B, C, ... which commute, and then define the quantum states as being eigenvectors of ALL these commuting operators. The reason for doing this is that it is always possible (due to some math theorems), and it gives you a nice clean way to describe the quantum states, namely their eigenvectors for A, B, C, which we can write as a vector (\lambda_A,\lambda_B,\lambda_C,...).

With SO(3), only one operator can be chosen, so there is only one quantum number. SO(3) isn't used as much in QM as the very similar symmetry group SU(2). In SU(2), that quantum number is called "spin". With E8, you can pick out 8 commuting operators, so to define a quantum state, you have to define 8 quantum numbers. With SU(2), you only have one commuting operator (which is usually chosen to be "spin in the z direction") so an SU(2) state gets only one quantum number.

Now if you've been paying attention in your elementary particles classes, you know that to distinguish an electron from a neutrino requires more than just 1 quantum number. To get all the particles into one group requires a more complicated symmetry group than SU(2). What Garrett did was to fit the known elementary particles into E8 by carefully assigning their quantum numbers. And he did it in a way that somehow respects gravity in a way that I do not understand yet but certainly got the Perimeter Institute to applaud.

Those who have studied beginning quantum mechanics learned that spin comes in various "representations". In spin 1/2, the quantum number (spin) is either -1/2 or +1/2. The difference between these two quantum numbers is 1.

In spin 1, the spin is either -1, 0, or +1. The difference between consecutive spins is 1. In spin 3/2, the spin is either -3/2, -1/2, +1/2, or +3/2. The difference between each is again 1. This difference between quantum numbers is consistent, and this is true in general. Note that with spin 3/2, you could talk about a difference of 2 or 3 between spin values instead of 1, but that would be a waste of time because 2 and 3 are multiples of 1.

For E8, there are 8 quantum numbers, so in any representation of E8, the difference between two different quantum numbers has to be given by an 8-vector. Similar to the differences between the quantum numbers of 3/2, you can choose a set of differences between quantum numbers of E8 (which are therefore 8-vectors), that are sufficient to get you anywhere you want to go, and are minimal in that you couldn't get rid of one. These weights are the origin of those diagrams with the little circles connected by lines.

Getting back to the pretty applet, the 8-vectors each correspond to the quantum numbers of a particle (in a specific representation of E8).

Did that help? By the way, note that the "Complete Idiot" in the title of this post is me.

[jal]

Hi CarlB!
I like the changes that you made to you E8 java. I've been playing around with it.
I understand (most) of the wiki E8
http://en.wikipedia.org/wiki/E8_%28mathematics%29
and what you did to make your E8 java.
http://www.measurementalgebra.com/E8.html
There is a difference between a layman and an amateur. You are the prime example of amateur and grandma is the layman.
The interest in Garrett's work has been demonstrated in layman's blogs.
I do think that it is possible to explain things (without using BIG WORDS) so that the layman can understand.
That's why I wanted to use your java as a supporting visual and walk through it by observing the different symmetries and reducing them. ( You did read my previous post and my two simple questions?)
Everyone can read from wiki E8.
"A root system of rank r is a particular finite configuration of vectors, called roots, which span an r-dimensional Euclidean space and satisfy certain geometrical properties. In particular, the root system must be invariant under reflection through the hyperplane perpendicular to any root.

The E8 root system is a rank 8 root system containing 240 root vectors spanning R8. It is irreducible in the sense that it cannot be built from root systems of smaller rank. Each of the root vectors in E8 have equal length. It is convenient for many purposes to normalize them to have length √2."

An amateur could understand that but not a layman.
I've done enough babbling ... time for the pros to speak.

[Prologue]

Thanks william donnelly for posting that link, it is very helpful.

Actually thanks to everyone discussing this, I am very grateful. I love getting into the conceptual nature of all of these things but lack the math background (I am getting there though). I know we can all relate to knowing something very well and then it becomes hard to remember where the sticking points are that beginners might have, thanks for doing it though!

[jal]

william donnelly
Part 1 of a basic introduction to E8 is now posted at http://sigfpe.blogspot.com/
So far it's just an introduction to the concepts of Lie group and Lie algebra, but it is written in a very accessible way.

jal
I've done enough babbling ... time for the pros to speak.
When he gets to it he might use CarlB's java.
jal

[starkind]

Jal, I am also trying for a layman’s explanation. In fact, I first started this internet journey at superstringtheory.com, where I met self-Adjoint, both of us under other screen names. I followed him here to physicsforums.com, a little sneakily I’m afraid, as he was hesitant to pose one of my questions here, but he finally gave in and posted a link to PF from SST.

(As I recall, the question had to do with gravity as an acceleration, and if it would be consistent with known physics to consider gravity as an actual outward acceleration of matter from its center of mass. There were no objections to using this interpretation, and I have held it ever since. It has some implications for the idea that the universe is expanding, and the caveat that locally, particles, planets, and galaxies are not expanding. I would have to rephrase this caveat, suggesting that local matter is expanding, but at a slightly different rate, based on relativistic time distortions.)

SelfAdjoint was very kind to me, and to many other people who were trying to learn outside of the university atmosphere. He is fondly and respectfully remembered here at PF. Of course I can’t speak for him, and I don’t pretend to know what he was trying to do, but it seemed to me that he would have been very sympathetic to our trying to find a layman’s explanation of QG. In fact, he seemed a little regretful when I decided I had to learn the math, and not just continue to rely on non-mathematical language. Of course that is my perception, not a fact about sA.

So I, for one, would vote, if I had the status, for continued attempts to find a common-English description of what is happening in theoretical physics. But we have to be very patient, and careful. English language is a slippery thing. Definitions of words change, new words appear, old usages either persist, or disappear. I am not really sure of how to begin such a project. It seems to me it could be that Wiki would be a better format for this kind of discussion, because it allows many people to work together on a single page. It is possible to edit and add to each other’s work. There are side pages for discussion and history.

I will post this now, and go offline to compose some other things on the E8 ToE.

S

[starkind]

Hey!! You never met my grandma! :grumpy:

Well, dang ... I did try. I think I was shooting for what I thought was starkind's level of interest and understanding, which was possibly inconsiderate of SublimeGD, who was the original poster, after all.

Okay. I have no idea how to explain at a 'grandma' level what E8 means in this context. I might be able to start with the general idea of symmetries in Quantum Theory, but even that would be difficult for poor granny. I think it would require a lot of careful thought, but at the end I'd have no more to offer than is already available on the web, so perhaps I should take this as my cue to bow out as gracefully as I can ...


Please don't go away until we find an appropriate place to continue this discussion. I have noticed in the past that the moderaters here (hi ZZ) are not shy, or even polite, about shutting down what they see as useless threads.

[ccdantas]

What about Baez's This Week Finds 253?

http://math.ucr.edu/home/baez/week253.html

[starkind]

What about Baez's This Week Finds 253?

http://math.ucr.edu/home/baez/week253.html

Would John Baez like to host a long discussion of these things in simple English on his blog?

I am thinking we should maybe move to a Wiki site.

[starkind]

CarlB wrote: “You can move two perpendicular directions which gives you 2 dimensions. Or you can rotate around a spot and that gives you 1 more. Thus the SO(3) rotations are a 3 dimensional "manifold". Another way of saying the "3" is that if you begin with no rotations, there are basically three small movements you can make.

"Get a globe and find Albuquerque, my home town. Think about what you can do to the globe, symmetry wise, relative to Albuquerque. You can move Albuquerque to the north/south, or to the east/west, or you can spin the globe on an axis around Albuquerque in a clockwise/counterclockwise direction. That is 3 dimensions and so SO(3) is a 3-manifold.

I rewrote the above like this:

We want to be able to talk in a general way about the rotational symmetries of any shape or kind of object, so it would be better to think of how to turn a sphere, like a globe of the earth. If we can talk easily about the symmetries of turning a globe, then we can easily talk about the symmetries of any shape of object, by imagining that it is totally encased in a ball of clay that turns it into a sphere. We can talk about turning the sphere easily, and then when we want to relate this to the object, we only have to take away the clay to see what it looks like.

So lets talk about turning a sphere in ordinary three space. Or, as physicists might say, consider the SO(3) group of symmetries.

If you are holding a simple sphere in your hand, like you would hold a small plastic ball, and you hold it by two fingertips on opposite sides of the ball, there are three basic ways you can turn it. (Really there are lots more ways to turn it, but any of the other ways can be described by turning it a little in one of the three basic ways, and then a little in another of the three basic ways, and repeating this over and over until you get the exact same movement.)

There are three basic ways to turn the ball in your fingers. Lets count them. First, you can turn your whole hand so that one of the two fingers that hold the ball is closest to you, and the other is on the farther side. The most you can turn in this fashion is when it looks like the top finger is right in the center of the part of the ball that is visible, and the other finger is on the other side. Take the ball away and hold your fingers like that, and you would see the top finger and the bottom finger are exactly in a line away from your eye, with the top finger closer.

A second way you can turn the ball is to turn your hand so that the two fingertips holding the ball are on opposite edges, from your point of view. Now they are both the same distance from your eye and you can see both of them on the edge of the ball at once. You could possibly do this so that one finger is closer to the top of the ball than the other, but that would make the two fingertips unequal…one closer to the top and one closer to the bottom. Instead, to keep our discussion as simple as possible, it would be better to turn it so that the two fingers are both equally far from the top and from the bottom. That is where the orthogonal part of the SO(3) comes from. In an orthogonal description, you will see that poles (where the fingers are touching the ball) turn from the top-bottom line, or axis, to a position in a line at right angles, ninety degrees from each other. We can say that these two lines of axis, top and bottom, and left and right, are perpendicular to each other. In fact, these are two of the basis lines we use to describe the rotations of objects in our ordinary three dimensions of space.

There is one more possible movement you can make, and that is no movement at all. So lets count: one, fingertips are at the top and bottom, two, fingertips are front and back, three, fingertips are on opposite edges. In mathematics, we call these three different axis lines x, y and z. X is generally up/down, y is generally side to side, and z is generally front to back. Mathematicians call this kind of description a manifold.

Another example could be a globe of the earth. Pick any spot on the earth, say your home town. By turning the globe, you can move your home town east or west, or by changing the N-S axis of the earth, you can move your home town north or south. Finally, you can turn the globe on an axis which runs right through your home town, right through the center of the globe, and out the other side. Using this axis instead of the North and South poles, you can turn your town around and around, with the rest of the globe spinning in circles around it. So there are three ways you can move your town: up or down, left or right, or you can spin it round and round, clockwise or counterclockwise. These are the three rotations of the SO(3) group.

[starkind]

CC:

I see John Baez is going to go on vacation! And then to Loops'07 in Mexico. I wish I could go to Loops'07, but I spent my fun money at Waterloo week before last.

CarlB:

I finally got to see the E8 rotation video on Youtube. It is certainly beautiful. I wish I could see your applet but I am one of the microsoft sheep you mentioned in the source document.

As I watched the Youtube vid, I wondered what the thing would look like if you traced all the orbits of all the particles? Or if you looked only at the orbits of the subgroups, like only the gluons, or only the quarks, or only the fermions, or only one generation of the fermions, and so on like that.

[william donnelly]

CC:

I see John Baez is going to go on vacation! And then to Loops'07 in Mexico. I wish I could go to Loops'07, but I spent my fun money at Waterloo week before last.



Actually Loops 07 was back in June (TWF 253 is from June). But you can get some of the audio and slides online.

Also John didn't go to Loops, if you read carefully you will see he is talking about Garrett going to Loops.

[starkind]

CarlB wrote:
“Our purpose is to talk about quantum numbers, but first let's talk about the dimensionality of the quantum numbers. That means "how many" quantum numbers each particle gets.”

In the above, we have talked about the meaning of the SO(3) group in ordinary English. Our goal here is to describe the E8 group in ordinary English. It turns out that the SO(3) group is one part of the E8 group. The E in E8 stands for Extraordinary, and it certainly is.

Before we look at the rest of the parts of E8, lets talk about quantum numbers. Quantum numbers are simply the ways physicists describe the behaviors of sub-atomic particles, like electrons, protons, neutrons, neutrinos, quarks, and many others. Each kind of particle has its own quantum numbers, and there are rules to tell us how different particles stick together or fall apart.

We have seen that the SO(3) group of symmetries describes objects in ordinary space. We will go on to talk about other symmetry groups, which describe how objects behave in other sets of dimensions. But first, lets talk about the dimensionality of the quantum numbers.

When we talk about the dimensionality of ordinary space, as we have seen, we can describe any object using only three numbers. Each number is a measurement of the object’s shape in three dimensions. This means that every point on the surface and interior of the object can be given a name made up of its position related to x, its position related to y, and its position related to z. Every position on the object has its own set of numbers, and no other position has the same numbers. For example, the center of the sphere can be called the origin, and given the numbers (x,y,z)=(0,0,0) The “north pole” of the sphere can be given the numbers (0,1,0). You see that the north pole is one distance unit from the center along the y axis. The south pole would be called (0,-1,0). I hope you can figure out for yourself what the other points we have discussed would be called. If not, we can go further into it to see how it works.

When physicists talk about quantum numbers, they are talking about measurements of the charge, mass, spin, and color of an object. The objects are too small to be seen, but they have these properties which can be measured. Each kind of particle has its own set of quantum numbers. You will notice that I have not mentioned position in ordinary 3 dimensional space here. Nor have I mentioned time.

It turns out that we can think of the quantum numbers as if they were set up as points on an object in ordinary 3 dimensional space, except there can be more than three numbers involved. How do you imagine a space like our 3 dimensional space, if there are more than three numbers?

It is kind of hard to think about, but we do have some familiarity in the ordinary visible world with a fourth number that describes ordinary objects, and that number is time. Using this fourth number, we can talk not only about the object as a static shape, but also about how it moves and changes. We are all familiar with objects that move and change. In classical physics, we talk about this in dynamics, which is exactly the study of how objects move and change in three dimensions of space and one dimension of time.

In dynamics, numbers like x,y,and z are used, but it quickly becomes clumsy to describe motion and change using just those numbers. So we add the fourth number, t for time, and then we talk about momentum, energy, force, and other things about the object which we can measure in four dimensions. In fact, physicists talk about “momentum space,” which is not really the space we think of when we are playing with a ball or entering or leaving a room. Momentum space has to do with the mass of an object, and its velocity, which is to say how far it moves in how much time. Momentum is just mass multiplied by velocity, and momentum space has numbers which describe a body in terms of mass, change in time, and change in position. Often it is possible to talk about change in position on just one of the three dimensions of ordinary space. We don’t even have to talk about which direction the object moved. We can simply say that it had x grams of mass, it moved y units of distance, and it moved that far in z units of time.

Now you see that we have changed our basis units. Instead of up down, we have distance, forward or back. Instead of right left, we have units of time. Instead of z, we have units of mass. Of course if we are talking about simple motion of a single object, the mass isn’t likely to change much, so we put mass on the z axis where we can’t see changes very well anyway.

Then we can make a picture of how the object moved in space and time, as we do when we want to consider the acceleration of an object, say, as it falls off a table. All of this is to help you see that dimensions do not have to be spatial, or even temporal. We can talk about mass as a dimension, and even draw it as an axis on a graph, just as if it were an ordinary distance measurment. When physicists talk about momentum space, or phase space, or quantum space, they are inventing an imaginary space, in some ways like our three dimensional space, and in some ways different. The important thing is, “objects” in “phase space” are shaped, and move and change, with the same mathematical rules that we use to describe objects in our ordinary three dimensional space.

Clearly phase space is not a room you can walk into or out of. I think it might have been better if people had chosen some other word, because it would have avoided a lot of confusion. There is no ‘creature from dimension x,’ because dimension x, if x is greater than three, is not likely to be a place you can pop in and out of. But it was done that way and I guess we are stuck with it. So we have to teach people who are starting out that the tenth dimension is not “another world” where monsters might live. Actually, the things that live in the tenth dimension are not monsters, but are quite well behaved, and they obey the rules and generally do things that would not be likely to upset grandma’s weekly church tea.

When physicists talk about the dimensionality of quantum numbers, they are just talking about how many quantum numbers are needed to talk about what a quantum object does as it goes about its daily business. To do this, they need to know the rules of behavior in the different dimensional sets, and that is one of the uses of the Lie symmetry groups, like S0(3). The rules of behavior in SO(3) are called the so(3) algebra.

[starkind]

Actually Loops 07 was back in June (TWF 253 is from June). But you can get some of the audio and slides online.

Also John didn't go to Loops, if you read carefully you will see he is talking about Garrett going to Loops.

Thanks, william donnally! I guess I knew that but was interested in getting ahead of myself and didn't pay attention to what I was doing. Who in academia would be going on vacation in November? I would like to go to Mexico, where Daniel Sudarski teaches at ICN-UNAM, if my notes from Waterloo are right. He gave an interesting talk called "The Quantum Origin of the Cosmic Structure: an arena for quantum gravity phenomenology." In it he talks about his paper gr-qc/0508100.cqg, 2317 (2006), written in collaberation with A. Perez (of Utrect) and H. Sahlmann (of Penn. State and Utrecht.) His talk was about the shortcomings of standard lore (in physics), the need for an extra element (tied to QG) and then the tests and predicitions which we may expect to see in the comming years. I didn't take many notes because I was trying to listen very closely to what he said. Anyway I imagine the talk is available at Perimeter, online.

[jal]

starkind !
Now you are on a roll.
Next thing we will hear is the the wave dudes explaining their SO(3) in the pipe. hehehe
Don't ask me .... ask Garrett ... he's the surfer. heheh
jal

[belliott4488]

... The E in E8 stands for Extraordinary, and it certainly is.
Heh ... Actually, the "E" stands for "Exceptional", but you're right - it certainly is extraordinary!:approve:

(That's half of Lisi's pun in the title of his paper, BTW.)

[garrett]

Hey all, sorry I haven't checked in -- been kind of busy. I appreciate the effort to produce a good description for the interested public. You're welcome to pull whatever you like from my descriptions at FQXi:
http://fqxi.org/community/index.php
Here are my descriptions of the theory:
http://fqxi.org/community/forum.php?action=topic&id=107
And here's some personal background for the curious:
http://fqxi.org/community/forum.php?action=topic&id=108
Please feel free to extend, change, or incorporate these into your descriptions however you like.
Best,
Garrett

[CarlB]

Hi y'all. Plane rides are the best time to think. I just got off one and realized that the next thing to add to that applet is the ability to choose views from a pulldown menu, and the ability to upload and download stuff you've typed into it.

You mess around with it, eventually it does something you like. You click a button and a "text area" appears. The text area contains all the parameters you used, color, and view. You click ^a ^c ^v and you copy the information to your own data file to save it. (I can't save data files on an internet Java applet without a lot of significant pain. Probably because I'm just an amateur java programmer.)

If you later want to see that again, you click the same button. The text area appears, and you write over the information there with the new data. It then displays this instead.

From there, you can email me the information here on Physics Forums and I can add that view to the pull down menu so that others can use it without having to mess with the textArea. Or you can send the data file to your collaborators directly and they can upload it to the applet the same way.

Also as a result of the plane ride, I've thought more carefully about how E8 arises naturally in a composite model:
http://carlbrannen.wordpress.com/2007/11/20/broken-e8-as-a-result-of-composite-particles-i/

[TheRealColbert]

Thanks guys!! That stuff is gold! A couple more questions to help me bridge the gap, if that is ok.... and please correct any misconceptions in the following.

I see that you need to create a multi-dimensional space to describe all the degrees of freedom a system can have, and Garrett used E8 as the substrate for his "world". Now I try to relate this with something I am familiar with, say mechanics in 3d space. There is the substrate, an XYZ coordinate grid, and some scalar values such as mass. With this you can make a differential equation that you solve to describe the state of the system relative to another variable, such as time. In quantum mechanics, you solve the differential equation (Schrodinger's), to get a wave solution, which you turn into a probability function to tell you stuff about the system.

So does Garrett's theory, in an analogous fashion, provide a differential equation in a wacky multi-space which contains all possible variables (quantum numbers) which you can solve (using whatever relevant boundary conditions) to describe any possible configurations of any possible "stuff" in the universe? Thus a theory of everything?

Or is there another layer of mathematics I am oblivious to? Is the group theory stuff used as a "shortcut" to find solutions? I didn't read Garrett's links yet, the answer might be there...

[jal]

Imagine that you are looking through a microscope into a crystal ball. (R4)
You are observing the Standard Model particles (strong su(3), electroweak su(2) x u(1), gravitational so(3,1) doing their dance. You are drawing the patterns on piece of paper. When you look up and look at the paper, it hits you … E8 can represent the pattern that you have drawn. More than that, … You think that the dance could be interpreted as geometric patterns. Lot’s of work left to do.
From Garret’s paper
http://arxiv.org/pdf/0711.0770
p. 6
The G2 root system may also be described in three dimensions as the 12 midpoints of
the edges of a cube - the vertices of a cuboctahedron. These roots are labeled g and qIII in Table 2, with their (x; y; z) coordinates shown. These points may be rotated and scaled, ….
----------
Reference for refreshing http://en.wikipedia.org/wiki/Cuboctahedron
“Both triangular bicupolae are important in sphere packing. The distance from the solid's centre to its vertices is equal to its edge length. Each central sphere can have up to twelve neighbors, and in a face-centered cubic lattice these take the positions of a cuboctahedron's vertices. In a hexagonal close-packed lattice they correspond to the corners of the triangular orthobicupola. In both cases the central sphere takes the position of the solid's centre.”
http://mathworld.wolfram.com/Tetrahedron.html
The vertices of a tetrahedron of side length can also be given by a particularly simple form when the vertices are taken as corners of a cube (Gardner 1984, pp. 192-194). One such tetrahedron for a cube of side length 1 gives the tetrahedron of side length having vertices (0, 0, 0), (0, 1, 1), (1, 0, 1), (1, 1, 0)
------------
Now, …. I also have a crystal ball (R4) that I have been examining with a microscope. It does not have any Standard Model particles in it. Go read my blog and you will see what I saw.
jal

[TheRealColbert]

You are drawing the patterns on piece of paper

Abstract patterns like Feynman diagrams or observable characteristics like trails through a bubble chamber?

I am not yet up-to-speed on how to think about "strong su(3), electroweak su(2) x u(1), gravitational so(3,1)", but the previous posts are helpful. My apologies if the level is too "low" for the thread. I know people get tired of the same old questions, but sometimes it is nice to "talk" to someone. Thanks for your patience!

[TheRealColbert]

From Garrett's FAQ,

When we have a nice symmetric manifold, like E8, we can mathematically describe how this shape twists and turns over the four dimensional spacetime we live in. This description is called a principal bundle, and the field describing the twists and turns is called a connection, which determines the curvature. What I'm doing is identifying all the standard model and gravitational fields (everything) as parts of an E8 principal bundle connection, and it's working amazingly well -- it appears to have all the correct fields and their interactions. Each symmetry of E8 is a different part of this connection, and each symmetry manifests itself as a different type of elementary particle that we have in our universe. When someone unifies gravity with the other fields like this, it's called a Theory of Everything -- that's what I'm after.

Now I am confused again. Is this an abstract space, describing how quantum numbers (observable properties of stuff) change and interact with each other, or is it a literal description of the "real" world, where things like curvature relate to actual "stuff" out there that could be demonstrated with an appropriate experiment? Or is it a silly question, because regardless of how you model "reality", if you model it completely and correctly your model will give the same result whether in your "math" world or the "real" world, thus they would be indistinguishable? In other words, there would be no experiment you could do in one world that you couldn't do in the other, (hypothetically, assuming magical experimentation abilities)

[jal]

TheRealColbert
I would suggest that you use wiki and refresh and re learn all about geometry and symmetry so that you can reorganize the information that you have in your head. You will certainly learn new info which will help you understand how Garrett has put all of his information together.
The only person who can put an image in your head is yourself.
Until you review what you think you know, there is no way for you to know if ????
.... garbage in ... garbage out ...
jal

[starkind]

Great! This is the most fun I've ever had. If group members think it usefull, I'll try to do more of the kind of translation stuff I did yesterday.

I think a study of the cubeoctahedron, especially as it relates to the packing pattern of similar spheres, is one key to understanding this E8 structure. Packing spheres is a real SO(3) problem, and I started studying how it works years ago using marbles and clay. Styrofoam balls and toothpicks work well, too.

One thing I found out about packing spheres is that a perfect stack has a density of about .74, where a solid would have a density of one. %74 has recently come up in cosmology as one of the key measures of density of the universe, also. Could they be related? I'll have to get the exact number for the density of stacked spheres, and bookmark the %74 in cosmology next time I see it.

Dr. Jack Ng, U of North Carolina, has been working on a model for space-time exploration involving densely packed spherical Planck sized clocks, but I don't think he has seen or thought about the cubeoctahedral geometry of such a thing. Might be worth looking at, see if it sparks any interest. I'll return with a link.

Garrett, for whatever it's worth, I think you did it.

Thanks,

S.

[starkind]

Heh ... Actually, the "E" stands for "Exceptional", but you're right - it certainly is extraordinary!:approve:

(That's half of Lisi's pun in the title of his paper, BTW.)

Thanks for keeping me straight. I'm proud to be accepted in this company.

[starkind]

From Garrett's FAQ,



Now I am confused again. Is this an abstract space, describing how quantum numbers (observable properties of stuff) change and interact with each other, or is it a literal description of the "real" world, where things like curvature relate to actual "stuff" out there that could be demonstrated with an appropriate experiment? Or is it a silly question, because regardless of how you model "reality", if you model it completely and correctly your model will give the same result whether in your "math" world or the "real" world, thus they would be indistinguishable? In other words, there would be no experiment you could do in one world that you couldn't do in the other, (hypothetically, assuming magical experimentation abilities)

Some math oriented people seem to take the stand that our "ordinary" 3space1time dimension view of "reality" is no more or less real than the mathematical higher dimensional worlds which are invisible to most of us. Invisible? Unimaginable, maybe.

Still, I think there is something about our percieved three dimensional space changing in one dimension of time that is somehow more real, at least on our scale. Some work was done on triangulations last year that seemed to show that spacetime may be lower dimensional at very small lengths, very high energies. Anyway I think we are all more comfortable with good old SO(3), and a U(1) time, if for no other reason than that is the space where our favorite arts are played (you can include your favorite sport under my catagory art, if you wish.)

Anyway I think you are right that the dimensional relationships we are less comfortable with do obey rigourous mathematical rules, and so we can use the different groups just as we would use more familiar things like momentum and energy.

[TheRealColbert]

I would suggest that you use wiki ...

Your post implies that I am highly confused :smile: I thought I was approaching a verbal understanding, but in reality I am either highly confused or have done a poor job communicating my "gaps". I don't want to wreck a good thread, so I will happily shut-up if I am taking the thread down the wrong path. (and I will take your advice on wiki).

Previous posts, in particular #33 by Carl and #41 and #44 by Starkind do a SUPERB job of describing things in regular language. For me, the descriptions become somewhat cloudy at the junction of quantum mechanics and group theory. If I am confused, maybe others are too, so I will keep pushing, (with this post at least) Maybe you guys could elaborate just bit more? Maybe I am seeing a barrier that doesn't exist, or I am so off-track that I am not even wrong. All I know is something bad happened in the last part of Carl's post on QM, and it happened about the time letters, followed by parenthesis with numbers inside, began to appear. I follow starkind's description of rotations and how this is in the realm of symmetry and group theory, and how an abstract state space is needed to describe the various quantities that appear in the world, but I can't quite get from here back to Carl's description of the mathematics.

Grrrr, I don't think I am explaining myself well. If only there were some kind of formal language that we could all speak, maybe with symbols so that it would be concise, so that there wouldn't be any confusion. :smile:

[starkind]

ok I'll have another go at the next section of CarlB's post. I'll do it offline and post here as or if sections get done.

The letters followed by parenthesis with numbers inside are Lie groups, which wiki does a good job of explaining. Anyway wandering in circles in Wiki got me what I think I know about it.

More in a half hour, perhaps.

S

[TheRealColbert]

Sorry, my comment about "letters, followed by parenthesis with numbers inside" was a weak attempt at humor. I do actually know they are groups. I was trying to magnify my ignorance of the issue in a self-deprecating way. Isn't that funny!!

Also, my comment about the "formal language" was supposed to be funny. It was a statement about how there is a fabulous language of mathematics available to those who take the time to learn it, but I am trying to have someone translate it into my language, because I am dumb and lazy. (some exaggeration here for the sake of emphasis. more self deprecating humor)

Please don't put any effort into it beyond what amuses you. I greatly appreciate your efforts already!!

[belliott4488]

RealColbert:

No need for apologies - the whole point of this thread, I believe, is to attempt an explanation that can be understood by non-experts (or amateurs, or laymen, or jal's grandma, depending on who's doing the explaining). I think confusion over jal's posts in particular is completely excusable, since it's his grandma who seems to define the lower limit of required knowledge for this thread. ;-) If his posts are confusing, then he should be asked to explain them, you shouldn't feel deficient.

As for your humor - hey, I picked up the ironic tone! But remember, annoying as they may be, that's what smilies were invented for. :-P

Now ... back to our regularly scheduled discussion (which I'm thoroughly enjoying too, by the way - I just haven't recently had any keen insights into how to explain any of this better than what's been posted.)

[starkind]

The Dimensionality of the Quantum Numbers

CarlB said: “You get to have one quantum number for every motion you can do with your symmetry that is "independent" sort of.”

Maybe we should go back a little and talk about what a quantum number is. If you have had chemistry you will recall that when two electrons are in an orbital around a nucleus of an atom, one has to have “spin up” and the other has to have “spin down.” There are no spin states for electrons in an orbital that are in between values, like spin half way between up and down. It is always and has to be one or the other, up or down.

The quantum numbers for particles are always exclusive like that. No two particles can have the exact same quantum numbers. This is kind of like the way two objects cannot occupy the same space. However the space now has more dimensions than our familiar SO(3). Lisi has found that the space of E8, which we are trying to imagine, can contain eight quantum numbers, and these eight quantum numbers describe all the known particles, and a few more, with each particle having a unique address in the E8 structure. The eight dimensions Lisi uses can be seen along the top row of table nine on page16 of his paper.

You see all the particles listed there under the E8. They are listed showing both their standard model symbol, and the icon Lisi uses in his diagrams for each particle. So you see the various circles, triangles, squares, and combinations of triangles or squares in the left hand side of the table under E8, and these are the icons. On the right side under E8 are the formula notations that physicists use for the names of the corresponding particles.

The quantum numbers along the top row on the right of E8 start with two quantum numbers labeled with some numbers and letters. You will recognize the ½, one-half, and the three index above the S or T respectively. The squiggle in the center of all that is an omega, and the one on the left has a subscript “i” next to the two. That means, I think, that the denominator in that quantum number is imaginary, which is a mathematical topic we don’t need to go into right here. I suspect that the T and S have to do with spinners and tensors, another math topic which we may as well ignore for now. Just to note that they are ways the particle can react in certain fields. The omega and the S and T make me think the fields are gravitational.

Then there is a “U” number and a “V” number, each with a superscript 3. These are followed by a w, then an x, y, and z, and then an F4 and a G2. Finally in the top row is a #, which is a count of how many different particles are defined in that row.

I hope someone who knows more about the different quantum numbers will come in now and tell us what these quantum numbers mean, physically. I am not up to that yet.

What I do think I know is that each of these quantum numbers represents a dimension, or degree of freedom, or direction in which the particles can move. Some move in one direction, some in another direction, and how they move under that quantum number tells us some of the information we need to know to tell what particle we are seeing.

CarlB goes on to tell us about some of the features of the geometry which makes all this happen:

Two small motions are independent if it doesn't matter what order you do them in (i.e. they "commute" as in obey the commutation law of multiplication AB = BA so order doesn't matter). Independent motions are great. They're easier to analyze because you can fiddle with one without screwing up the other.

For the example of SO(3), the three small rotations do not commute. It might be obvious that rotation around Albuquerque doesn't commute with moving Albuquerque North/South. To see that moving Albuquerque North/South doesn't commute with moving Albuquerque East/West we can discuss the puzzle:

Suppose two people have good GPS systems and start hiking from the same point. Person X goes 1 mile East, and then 1 mile North. Person Y goes 1 mile North and then 1 mile East. Do they end up at the exact same point?

The answer is that, in general, they do not. To see why, get a globe, and see what happens if you increase the 1 mile to 1000 miles. Assuming that the starting point is Albuquerque (which is in the Northern hemisphere), you will find that the person who starts going North first, will end up farther to the east. The reason is that when you travel East at a higher latitude (i.e. more northerly) you cross more lines of longitude.

The same effect occurs for very small rotations. And the result of careful calculations is that none of the small rotations in SO(3) commute and so you can't break things up. By contrast, with E8 you can pick out 8 small rotations that commute. Therefore the quantum numbers of an E8 state requires 8 quantum numbers to specify.
This idea of commutation works as in the GPS example in our good old SO(3), but it also works between some others of the dimensions, and how we do calculations depends on if the two dimensions we are multiplying are going to commute or not.

[starkind]

Hi RealColbert and belliott4488

Sorry I missed the humor. Anyway, I would probably have gone on in the same vein even if I had got the joke the first time. I am taking the tack, as belliott4488 said, of trying to explain this so my grandma would understand it. An additional advantage of doing it this way is that if I am in error about something, which is not unlikely as we all know, it will be an error for which we all may be able to understand the correction. And I do ask for any corrections, even if I get to be the butt of the joke. Sometimes I even make myself laugh, which is not a good trait in a standup comedian. So I'll just continue on as far as I am able, and hope that when you are done laughing at me, you will let me in on the joke, too.

Anyway it is a pet peeve that specialists in any field do not define their jargon, at least the first time they use it in a paper, or at least give a reference of some kind so we ordinary mortals have a chance to look it up on Wiki. So I try to start from the grass roots and work my way up.

Thanks for keeping me company on this journey.

s

[starkind]

Ok, well, the rest of CarlB's post assumes some familiarity with QM. I've never had any formal training in this stuff and my familiarity with QM is spotty. So, I am going to go follow Garrett Lisi in his generous offer to let us use his work on the fx site. I'll get back when I think I have something grandma would understand.

S

[jal]

Hi!
I think the groundwork has been done ... proceed. If there are questions ... I'm sure someone will ask and someone will rephrase in their own words.
We are approaching the "amateur" level.
TheRealColbert ... An error on my part .... Although I used your name it was meant as a general comment "learning is a self generating process" meant for all the readers who want to be spoon feed rather than putting in the effort required to learn. We can only make things easier when we use everyday language. Precission is thereby lost but would be regained by the "seeker" of a deeper understanding.
Okay???
jal

[starkind]

Ah, well, it is closing time at the coffee hole again. I read Lisi's posts at fqxi, and it all sounded very sensible and promising, and fit for a general public who really don't need to understand anything but they like to look at the pretty pictures. Do we really have to dive into the maths to go any further? Maybe so.

I'm going to go back into working my way through the paper. It could be that elaborations of CarlB's computer images will be the best way to study the E8 without having to do the maths.

Best regards...

S

[jal]

Going from a layperson to an amateur just means doing a little bit more digging to get a better understanding.
The first step is to dig in the citations.
Below are three that could be interesting and informative.
citations
(# 1)
http://arxiv.org/abs/0704.3091
Triacontagonal coordinates for the E(8) root system
Authors: David A. Richter
(Submitted on 24 Apr 2007)

The next step is to find out what some of the words mean.

http://mathworld.wolfram.com/CoxeterGraph.html
The Coxeter graph is a nonhamiltonian cubic symmetric graph on 28 vertices and 42 edges. Three embeddings are illustrated above …
http://mathworld.wolfram.com/CubicSymmetricGraph.html
cubic symmetric graph
-----------
(# 2)
http://arxiv.org/abs/0705.3978
Mapping the geometry of the F4 group
Authors: Fabio Bernardoni, Sergio L. Cacciatori, Bianca L. Cerchiai, Antonio Scotti
(Submitted on 28 May 2007 (v1), last revised 1 Oct 2007 (this version, v2))

The third step is to “click” on the authors and see the other work that they have published that might give you more information.
http://arxiv.org/find/math-ph,math/1/au:+Cacciatori_S/0/1/0/all/0/1
Showing results 1 through 5 (of 5 total) for au:Cacciatori_S
The fourth step do a search for some of the terms that are used in the papers
http://www.gregegan.net/SCHILD/Spin/SpinNotes.html
Greg Egan's Spin Networks
Mathematical Details

Or
http://www.gregegan.net/APPLETS/30/30.html
In the E8 lattice in 8 dimensions, each hypersphere makes contact with 240 nearest neighbours; 112 of these lie at the centres of the 112 6-cubes of an 8-cube centred on the representative hypersphere, while the other 128 lie on half the 256 vertices of another 8-cube which is half the size of the first. The 240 neighbours lie on 120 rays which split up into 15 octads of orthogonal rays, which again determine the colouring scheme.
http://jdc.math.uwo.ca/spin-foams/
Spin networks, spin foams and loop quantum gravity
Dan Christensen

------------
(3 #)
http://xxx.lanl.gov/abs/gr-qc/9704009
Is ``the theory of everything'' merely the ultimate ensemble theory?
Authors: Max Tegmark (Institute for Advanced Study, Princeton)
(Submitted on 3 Apr 1997 (v1), last revised 1 Dec 1998 (this version, v2))
----------
Depending on your level of layperson you will now be an amateur. As you progress in your understanding and learning, you will soon realize that “the more you know the more questions you will have”. ( Not to mention, that you will realize the huge amount of training and learning that is necessary to be able to do the work that you read in those papers.)
Cheers for the “math kids”.
Although life dealt you a different kind of hand, with the web, you can get a greater appreciation of science than any other previous generation.
Grandma can knit and I can’t. (I envy her skills too)
jal

[garrett]

Hey guys, just checking in real quick. IMO, the best references to start with would cover the basics of Lie algebras and representations:
http://deferentialgeometry.org/papers/Semi-Simple%20Lie%20Algebras%20and%20Their%20Representa tion.pdf
http://deferentialgeometry.org/papers/Loeh%20-%20Representation%20Theory%20of%20Lie%20Algebras.p df

[jal]

Sorry can't talk. I'm in bed with "Lie" :biggrin:
jal

[starkind]

So for the short easy answer, how about something like "E8 is an extraordinarily beautiful geometric figure in higher dimensions, which projects onto our three dimensions of space and one of time in a way that fits the particles of the standard model and their interactions along with gravity into a single object. This model unites the standard model of particle physics with the theory of general relativity, and predicts new particles and interactions which are expected to be confirmed or denied by experiments at LHC Cern in the near future."

Have a great long weekend.

[jal]

From the thread, "An Exceptionally Simple Theory of Everything!"
“I am seeing this reference in several places that E8 is the lie group of an icosahedron (and for that matter E6 is same for a Tetrahedron and E7 is the same for an octahedron). This seems like a very interesting way to approach E8,”

Garrett
All fields of the standard model and gravity are unified as an E8 principal bundle
connection.
Unless I’m mistaken, All that Garrett has done is shown that, “…the leg bone is connected to the hip bone…”

The G2 root system may also be described in three dimensions as the 12 midpoints of
the edges of a cube | the vertices of a cuboctahedron. These roots are labeled g and qIII in Table 2, with their (x; y; z) coordinates shown. These points may be rotated and scaled,
Since the cuboctahedron is the root system of so(6), we have obtained g2 by projecting along a u(1) in the Cartan subalgebra of so(6),

What we have is a 4 legged baby elephant. The fourth leg (gravity) is the same as all the other legs. It doesn’t need to be longer (to planck scale).
This makes it easier to work with LQG. There are link to LQG which I have gathered at http://www.physicsforums.com/blogs/jal-58039/dynamics-797/
For instance
http://arxiv.org/abs/hep-th/0608210

Loop Quantum Gravity: An Inside View
T. Thiemann
29 Aug 2006

---------
Wiki is getting better at explaining all of these symmetries. Here are some links.
http://en.wikipedia.org/wiki/List_of_spherical_symmetry_groups
List of spherical symmetry groups
http://en.wikipedia.org/wiki/Icosahedron
The icosahedron can also be called a snub tetrahedron
http://en.wikipedia.org/wiki/Tetrahedron
tetrahedron
http://en.wikipedia.org/wiki/Tetrahedral_symmetry
Tetrahedral symmetry
http://en.wikipedia.org/wiki/Polyhedral_compound
polyhedral compound
http://en.wikipedia.org/wiki/Stella_octangula
stella octangula
http://en.wikipedia.org/wiki/Snub_%28geometry%29
A snub is a related operation. It is an alternation applied to an omnitruncated regular polyhedron.
http://en.wikipedia.org/wiki/Uniform_polyhedron#Definition_of_operations
A uniform polyhedron
-----------
jal

[belliott4488]

So for the short easy answer, how about something like "E8 is an extraordinarily beautiful geometric figure in higher dimensions, which projects onto our three dimensions of space and one of time in a way that fits the particles of the standard model and their interactions along with gravity into a single object. This model unites the standard model of particle physics with the theory of general relativity, and predicts new particles and interactions which are expected to be confirmed or denied by experiments at LHC Cern in the near future."

Have a great long weekend.I think this is a really good concise explanation, and I think it's very close to being exactly correct.

I do have one objection, although I could well be wrong about this. When you talk about projecting the higher-dimensional space in which E8 lives into 3 dimensions, I'm not sure it's right to identify those as the three space dimensions of our regular 4-D world (Minkowski Space). When you project a higher dimensional space to a lower dimensional one, you implicitly assume that the lower dimensional space is embedded in the higher one, i.e. it's a subspace. For example, when I want to visualize a 4-cube (something I do for fun), I first project it into a 3-D subspace, and then to draw it on paper or a computer screen, I have to project that 3-D object to a 2-D subspace. The geometry I use to do this, however, always assumes that I can connect points on the higher-dimensional object to points in the lower dimensional space with straight lines in the higher-D space, i.e. the lower-dimensional space is a subspace of the higher-dimensional one.

Now, in the case of Dr. Lisi's E8 representation, we can certainly project the root space down to three dimensions in order to picture it at all, and then we can project the resulting object down to a 2-D space to draw it on a computer screen or a paper page. These subspaces are just 3- and 2-dimensional geometric spaces, however - in fact, we're really imagining them to be Euclidean spaces, not the curved space in which we live.

More to the point, (and this really is my point, at long last), I don't believe it is correct to say that our 4-D spacetime is a subspace of the higher-dimensional root space of E8. That space is a space of quantum states - a Hilbert Space if you like - and "motion" in that space corresponds to changing states, not to movement in spacetime.

Any thoughts on that?

[jal]

belliott4488
More to the point, (and this really is my point, at long last), I don't believe it is correct to say that our 4-D spacetime is a subspace of the higher-dimensional root space of E8. That space is a space of quantum states - a Hilbert Space if you like - and "motion" in that space corresponds to changing states, not to movement in spacetime.
Any thoughts on that?
Sounds good!
When we are "moving" the icosahedron all that we are doing is looking at the different connections. It is still the icosahedron. There is no dynamics, YET, in the connections. The icosahedron is still at t=0. What it will look like when we look at t=1 might be different. Hopefully, the dynamics will be in a "circular" pattern that can last 10^ 35 (a proton).

[starkind]

Hmm. Yes, objects in the space we inhabit seem to obey strict physical laws. Objects in conceptual space do not seem to have to obey any such laws.

I suppose I would have to agree that E8 is more a conceptual space, at this point anyway, than an habitual space. And there do seem to be differences between habitual spaces and conceptual spaces. I guess I am still not certain if the space of particles on E8 is an habitual space or not. Could the fact that habitual objects (particles) seem to fit onto a conceptual structure (E8) imply that there does exist some habitual structure dual to the conceptual structure?

I suppose I can avoid the horns by just saying that I am thinking of the Euclidian dual to habitual space, not habitual space itself. However I have to reserve my doubts. In agreement with the holographic model, our habitual space, which we think of as specially separate from conceptual mathematical space, may not be any more than an artificial construct either.

The difference here seems to be that "real" space time, which we seem to inhabit, is apparently resistant to change. We have to work hard to lift a real stone to the top of a tower, but we can imagine it there instantly without any work at all.

I noticed that Garrett says in the first line of his introduction to his paper "We exist in a universe described by mathematics." I was tempted to quibble with this. After all, we have not yet described it all by math. I thought of suggesting that we exist in a universe describable by math, but that isn't defendable either. Can we be sure everything is describable by some kind of math? Is quantum foam, for example, mathematically describable? We don't know that it does exist, but we do not know that it does not exist either. Part of the universe is chaotic, and it seems to me that chaos is indescribable by definition. We can refer to it and describe it as the opposite of what it is not, but there is no precision possible. And math is nothing if not precise.

I guess I still have to be convinced that there is something special about the three space one time that we seem to inhabit. Plato thought it a shadow of a better reality. We have no idea, really, how consciousness functions. Our habitual world could after all be nothing more than habitual thinking.

But the point is really not arguable in physical terms. Therefore I yield. If you prefer that conceptual space cannot be mapped to ordinary space on the grounds that ordinary space is somehow special, I will not object.

[belliott4488]

starkind: I'm afraid I don't agree with your distinction between "conceptual" and "habitual" space. We make physical observations, and those are usually what we loosely think of as "real", although they need not correspond to either distance or time (e.g. charge, field strength, temperature, spin, etc.). We can also predict the values of such observations by use of mathematical calculations, which are abstract by nature. All mathematical spaces are abstract, whether they represent spacetime measurements, phase space measurements, Hilbert space measurements, or what-have-you. I might bump into a physical table in the dark, but I'll never bump into a vector, even if it is a spacetime vector.

My point was only that the parts of our theory that represent spacetime measurements belong to an abstract space that doesn't happen to be a subspace of the abstract space that represents quantum states - they're just separate mathematical beasts. Neither is more or less physical, inasmuch as each one is a bit of mathematics that corresponds to something physical, i.e. some set of observables.

My impression is that there has been some confusion that the assertion we're discussing (that the higher-dimensional E8 representation space might describe the universe we live in) means that our spacetime dimensions are part of that space. I don't believe that's so. There is a subgroup of Dr. Lisi's E8 representation that reflects the symmetries of our 4-D spacetime, and it lives in its own subspace of the E8 root space, but that space is not the same thing as spacetime.

[By the way, I'm not sure why you say that "Part of the universe is chaotic," but if you're referring to chaos theory, then that certainly is describable. That's exactly what chaos theory does - it provides a mathematical framework for describing phenomena that exhibit what appears to be random behavior, typically involving nonlinear differential equations.]

[jal]

Hi starkind, … belliott4488!
I understand what you are saying.
Let’s keep in mind that E8 is the MINIMUM LENGTH pattern of the positions of all the SM “particles” that Garrett found that should exist at > 10^-15 and CERN will have to find those other 20 BIG GUYS so that the pattern can be completed.
Think of one of those wonderfull pyramids that are made by those extraordinary chinese atheletes. The curtain is not open all the way and we cannot see all of the atheletes. (20) We do know where the athletes must be positioned so that we can see the (quark) athlete.
Eventually, Garrett and others will make the “pyramid drawings” and we will be able to see the pattern that is required to support the (quark) athletes.
Eventually, the right cuboctahedron will be demonstrated.
Reading the different blogs, it is apparent that this approach is making a lot of people go into denial. Garrett has proposed a model that does not include gravity going past 10^-18. It all depends on what CERN will find. Something tells me that there will be a shortage of paper bags due to hyperventilation.

----------
For those who do not like wiki, here is reference from mathworld.
http://mathworld.wolfram.com/Cuboctahedron.html
In cubic close packing, each sphere is surrounded by 12 other spheres. Taking a collection of 13 such spheres gives the cluster illustrated above. Connecting the centers of the external 12 spheres gives a cuboctahedron.
--------
If you have not noticed, I have a bias for the hex. packing.
jal

[starkind]

Hi belliott4488

I think we may be closer that you suppose. Anyway, I am not locked into an opinion about the difference between mathematical dimensions and “real” dimensions, or even that there is a difference. I think it is an interesting thing to think about. Maybe this is not the place to discuss it. It is pretty slippery and not a matter for measurement.

Really I think the interest here is how the E8 representation does ‘connect’ to the real world. Garrett talks about this in section two, with a nice picture and graph of the part of E8 which includes quarks and gluons and their interactions, table 1 on page 5. You can select one of the quarks, act on it with one of the gluons, and by simple vector addition, out pops the resultant quark. That is pretty neat.

I guess you have a strong point in arguing that the cubeoctahedron on which this occurs is not a space-time figure. There is an element of time in it, as you have to follow the lines, or vectors, to make the connections. But the space is not demonstrable as something into which you might poke a finger. We don’t have any idea what shapes the quarks take inside a particle. I would like to point out, if we cannot say our real space is a subset of E8, we cannot absolutely rule it out as a possibility either.

One might, I suppose, think of it as a sort of table of numbers, like the multiplication table, only in more dimensions. It is true that a farmer might use a multiplication table to figure out how many beans he can expect from an acre, but that does not mean that the multiplication table or its calculations are in any way connected to the soil in which the beans are going to grow. Maybe E8 is entirely like that.

On the other hand, it seems to me provocative that densely packed spheres (oranges or cannonballs) do stack up in a real space exactly dual to the G2 root system. It seems to me to be too good a clue to dismiss without at least some consideration. The promising connection, I think, would have something to do with Planck space-time spheres in a ‘frozen’ four dimensions. A Planck sphere would be the space an event would fill in a Planck time. It would be a sphere two Planck lengths in diameter. An event at this scale would necessarily exclude any other event from cohabiting the same time-space. If two such events did occur in one time-space sphere, they would result in an instantaneous implosion and so be un-measurable even in theory.

I am happy with the status quo that you will take the view that the space we inhabit is not a subspace of E8, while I continue to amuse myself by looking for connections.

As for chaos, my understanding of chaos theory is that if you add three or more periodic motions, the result is a motion which has unpredictable behaviors. It is not just difficult to predict. It is mathematically impossible. Perhaps there are exceptions, but in general three randomly selected periodic waves, when combined, will have periods of relative stability, followed inevitably by a period of increasing amplitude variation, with more frequent extreme events, followed by a phase shift in which the old stability pattern ceases, and a new stability pattern is started. The thing that is impossible to predict is where on the amplitude scale the new pattern will show up. Now that I think of it, this process resets the zero scale of the periodic stability, and may have a bearing on zero point energy problems.

It has been a long time since I studied chaos theory, and my study was informal, not part of a rigorous course in mathematics, so as usual I welcome corrections from people who are better informed.

The cuboctahedron in table 1 is presented in one possible view, that using g3 and g8 as orthogonal axis. I am thinking now about what the relationship of the points might tell me if arranged on a 3d cube, one which I can hold in my hand and rotate at will. My first insight doing this has been that the gluons form a plane, and that the quarks are another plane on one side of the gluon plane, and the antiquarks are a third plane on the other side of the gluon plane from the quarks. If each quark and antiquark and gluon was represented by a sphere, and the spheres were densely packed on the structure, there would be one more sphere in the interior of the 3d structure. Nothing is shown in that position in Table 1. Is this position one of the missing particles in the E8 theory?

Also, where do the up and down quarks that make up most of our universe sit on the cube? Can we infer something about reality from the fact that we see those quarks commonly and the others only rarely?

I’ll be glad to see any comments.

Thanks,

S

ps I am not ignoring you jal but I have to take a break. More later.

[jal]

Staying on the subject…. A new field of study … neucleonagraphy.
http://en.wikipedia.org/wiki/Crystallography
jal

[cinacchi]

StarKind: I much appreciated your explanation about symmetry of SO(3). Great job! I am going to use it for a small lesson to my niece (she's in 4.th class of secondary school. Thanks!

[jal]

I'm satisfied that there are enough different explanations for the layperson and the amateur.
I did a search of the web.
Youtube presentation/explanation of E8
http://www.youtube.com/watch?v=-xHw9zcCvRQ
Views: 101,702
------
An Exceptionally Simple Theory of Everything
Hits 11,200
--------
E8
Hits 2,330,000
---------
I think that our explanation was not covered by anyone else.
jal

[Coin]

Hi starkind, … belliott4488!
Let’s keep in mind that E8 is the MINIMUM LENGTH pattern of the positions of all the SM “particles” that Garrett found that should exist at > 10^-15 and CERN will have to find those other 20 BIG GUYS so that the pattern can be completed.

So... I am basically in the "layman" camp here and don't understand a lot of this, but I think it's worth observing that as far as I understand things, although there are 18 particles predicted, these 18 particles are all kind of "the same" in a certain sense. They're different particles, but all 18 are colored scalars-- excitations of scalar fields which carry a color charge. The reason why there are 18 of them is there is one such field for each combination of (3 colors X 3 quark generations X (particle+antiparticle)). A colored scalar would be as I understand it quite a strange thing to find, so for E8's purposes I think it might be sufficient to find just one of the 18 fields. No?

This said, I have seen several people in this thread say things along the lines that we "should be able to tell if E8 theory is true" at the LHC at and I don't think this is at all a sure thing. I've not seen any argument that we should specifically expect Lisi's colored scalars to be within the range that the LHC can detect them-- Lisi's theory has the same problem of supersymmetry in this regard, probably worse because we know how to get predictions out of SUSY without actually observing a superpartner and E8 doesn't seem to there yet.

(Of course, Lisi's E8 theory does have an unusually high degree of falsifiability at the LHC, since it's packed EVERYTHING in current physics into the E8 structure and left room for nothing else but those colored scalars. If the LHC discovers ANYTHING, it falsifies Lisi's current formulation of E8, because there is no room for anything new! The only possible thing the LHC can find without breaking Lisi's E8 model is the single higgs-- finding supersymmetry, or a technicolor higgs (unless the colored scalars turn out to be part of the higgs mechanism? I don't know if that's possible) would simply not fit into the E8 root system as this month's paper formulated it.)

[starkind]

jal

I am very interested in the way the cubeoctahedron comes out naturally in large enough regions of densely packed spheres. Of course they have to be densely packed, that is the distances between spheres have to be MINIMUM LENGTH, for the pattern to show itself. Is this what you mean?

Could you say more about the “model that does not include gravity going past 10^-18?” I am afraid I have to admit I don’t know what that means. Still I am sure you have better understanding of this model than I do. So far I’ve only got to the quarks and gluons in G2, and I’m still working on getting the implications of that part.

An interesting feature of the close packed stack of similar spheres is that the hex pattern comes out naturally, and is easy to see. There are also orthogonal planes, some rectangular, some square. Then there are parallelograms. It all depends how you split the lattice. I was actually surprised when first thinking of this structure that it also includes a cubic pattern. The most basic 3d shape in there is the tetrahedron.

Finally, I started thinking about how the dense pack structure might develop in an infall regime, where spheres are added to the outside of a growing crystal. It turns out that some very complex surfaces can be generated after the third layer goes on. There is a right hand and a left hand pattern, and if they come into competition for spaces in the lattice, flaws develop where there is still a gap, but the gap is too small for another sphere to be fitted into it. These flaws develop in three dimensions in an infinite variety as the sphere grows.

For a while I played with the idea that the flaws are responsible for the broken symmetries which generate laws of conservation, but I never got an understanding of the Noether principles and decided about then that I couldn’t visualize enough to make any more progress without getting the math.

Best regards, and more later
S

[jal]

coin
The points that you make are not at the layman level.
You said,"If the LHC discovers ANYTHING, it falsifies Lisi's current formulation of E8, because there is no room for anything new! The only possible thing the LHC can find without breaking Lisi's E8 model is the single higgs-- finding supersymmetry, or a technicolor higgs (unless the colored scalars turn out to be part of the higgs mechanism? I don't know if that's possible) would simply not fit into the E8 root system as this month's paper formulated it.)"

Barrett said,
"... The weights of these 222 elements|corresponding to the quantum numbers of all gravitational and standard model fields | exactly match 222 roots out of the 240 of the largest simple exceptional Lie group, E8.
... After all algebraic elements of the standard model have been fit to the E8 Lie algebra there are a few e8 elements remaining, representing new, non-standard particles.
... Because the 18 algebraic degrees of freedom inhabited by x appear amenable to the same sort of factorization as e (see Table 9), it is natural to factor it into three x fields and three colored and three anti-colored Higgs fields, . It could be possible that this new x gives difierent masses to the different generations of quarks and leptons, producing the CKM and PMNS matrices.

The G2 root system may also be described in three dimensions as the 12 midpoints of the edges of a cube | the vertices of a cuboctahedron.
-----------
http://mathworld.wolfram.com/Cuboctahedron.html

In cubic close packing, each sphere is surrounded by 12 other spheres. Taking a collection of 13 such spheres gives the cluster illustrated above. Connecting the centers of the external 12 spheres gives a cuboctahedron.
--------
Although I spent a bit of time in bed with “Lie”, I’m not familiar enough to answer using Garrett’s approach.
I will try to answer from the point of view of… neucleonagraphy.
http://en.wikipedia.org/wiki/Crystallography
I have a bias for the hex. packing and I think it would give the same answers.
------------
The E8 ---> cuboctahedron ---> 12 spheres in close packing. If you put in the “particle” positions of the SM then there will be 240/12 = 20 “particles” in each sphere. If all of Standard Model can only supply 222 (as presented by Garrett), then there would be a shortage of 18 or 18/12 = 1.5 “particles” per sphere. The pattern would not be completed.
In order to maintain the the symmetry, it is necessary to have the 240 “particle” positions. With a litle bit of spinning the 20 “particles” that are in a “sphere” are replicated into the other spheres. There is still no dynamics involved in drawing the positions of the “particles.”
Garrett does include the Higgs, so if there is no Higgs then using the neucleonagraphy approach, it would be necessary to use a smaller and different pattern than E8.
I expect to see more proposed patterns and eventually there will be one that will prove to be the right one. (There are more than one SUSY proposals)
All of this E8 is for only ONE “nucleon/proton” within the drip line.
Nobody has yet got to the stage of combining multiple E8, “nucleon/proton” together.
If multiple E8 are put together then I would expect to see the emergence of Crystallography.
---------
starkind
“Could you say more about the “model that does not include gravity going past 10^-18?”
That is my prediction not Garrett’s. If there is a “particle” representing gravity, that fits into the E8 pattern or any other pattern then I cannot see how it could be smaller than 10^-18. There are proposals (Randall) that would put gravity “particles” in this size range.
-------
carlB
How is the E8 java coming?
--------
Maybe, Garrett will have time to give a few comments.

jal

[starkind]

Hi Coin

Actually it sounds like you are getting a lot of stuff that I have not yet had time to evaluate. Could you provide the reasoning for your statements, or a link to where the information comes from? For example, about those 18 colored scalars being hard to find…I am not sure what you mean.

On page 15 Lisi says “The weights of these 222 elements---corresponding to the quantum numbers of all gravitational and standard model fields---exactly match 222 roots out of the 240 of the largest simple exceptional Lie group, E8.” Hence the number, 18, of E8 roots which are not matched to the standard model.

I hope to post next on a study of how the roots of E8 are used to show the quark-gluon relationships in G2. Eventually I would like to understand the fundamental physical-geometric reasons for this amazing correspondence to E8.

I don’t know if we should find confirmation (or denial) for E8 at LHC, but it seems the best current hope that we may find it.

Could you say more about your assertion that “The only possible thing the LHC can find without breaking Lisi's E8 model is the single higgs-- finding supersymmetry, or a technicolor higgs (unless the colored scalars turn out to be part of the higgs mechanism? I don't know if that's possible) would simply not fit into the E8 root system as this month's paper formulated it.)” I thought Lisi was saying there were a handful of particles that could fit in E8 which are not yet discovered. His section 2.4.1 beginning on page 21 is titled “New Particles.”

In his discussion and conclusion section, on page 29, Lisi says “Future work will either strengthen the correlation to known physics and produce successful predictions for the LHC , or the theory will encounter a fatal contradiction with nature.”

In my child-like imagination, it seems to me that Lisi is hanging the known particles and interactions on E8 like bulbs on the branches of a Winter Solstice Conifer. What we know about the standard model of particles fits perfectly, but leaves 18 of the 240 branches bare. If the corespondence to the E8 model is really more than a coincidence, reality will contain some new physics to fill in the remaining 18 branches. Not?

[starkind]

Hi jal

The cubocahedron comes naturally out of a stacking of densely packed spheres of equal size (I am going into simpler descriptions here because I want to keep Grandma involved.) For example, the stack of oranges on a grocer’s display table, or the stack of cannon balls in the public square. If anyone is hesitant about this shape, just get some marbles and a not-too-small box, and start by laying in a single thickness of marbles on the bottom of the box. Lay the first row along one wall, and then add the next row in the dimples, so each of row 2 is supported by 2 from row 1. Continue stacking on third and fourth rows, and you will see a triangle shape develop, and if you look closely after there are three rows, you will notice that the triangles fit together in the plane of the bottom of the box into hexagons.

Then, when you have enough in the first layer, add a second layer, placing the new layer marbles in the dimples of the first layer. Notice that now each marble of the second layer is supported by three marbles in the layer under it. Continue to add layers, and eventually you will see a pyramid develop.

Now the cubeoctahedron is inside this pyramid. It is kind of hard to visualize, but anyone should be able to do it with some work. It consists of one marble in the center, with twelve marbles surrounding it. Or, it may be easier to visualize by thinking of the single layer first, where each marble (except the ones on the edges) is surrounded by six others. If this is still too hard to visualize, start with pennies on a table, and then you can easily verify that one penny laid on the surface can be surrounded by exactly six pennies laid touching each other all around it.

Now imagine the seven marble hexagonal unit suspended in mid-air, and you may be able to see that you can add exactly three marbles on each side of the hexagonal plane. When you have done this, you will see that you have one marble in the center of twelve marbles. Styrofoam balls and toothpicks work well to build this part of the structure, also. You can find a nice picture of this structure in the link jal provided to Stephan Wolfram’s Mathworld page on the cubeoctahedron earlier in this thread.

There are actually two ways to add the three marbles to the top of the hexagonal plane. If you experiment a little, you will see that placing the first marble determines where you can place the next two marbles. There are actually six dimples available, but as soon as you place one marble, it becomes impossible to fit a marble in to the other three dimples. You have to use the two remaining dimples where there is enough room.

Because of this fact, it is possible to make two different dense packings of the thirteen marbles. In one form, the cubeoctahedron, the marbles on each side of the hex layer are opposite each other, and in the other, they are opposite to the alternate dimples, the ones that are blocked by the placement of the first marble. This is hard to see in words. If you really want to see this, get some Styrofoam balls and toothpicks. Or, marbles and modeling clay works, too.

Jal, I wonder if your scheme of dividing by 12 is affected by this explication of the geometry. Should you divide by thirteen instead of twelve? If not, why not? Perhaps justification could be made on the basis of the desired effects being confined to a surface?

Thanks,

More later

S

[jal]

If we assume minimum length, then the smallest sphere (living in 3D) that can be made is with 6 “particles” on it’s surface. The sphere would have a surface area of 24 units.
If it was a cube then there would be one particle on each face.
If we assume 20 “particles” on the surface of a sphere then the size of the sphere would be 80 units. (X12=960 units) Obviously, by assuming minimum length it should be possible to distribute the 20 “particles” inside the sphere without violating minimum length.
I have not done the calculations to arrive at the smallest sphere that could contain the 20 particles or what kinds of symmetrical arrangement would be possible.
I expect that carlB will need to do it in order to make his E8 java model.
These 20 “particles” will be in a symmetrical arrangements. Repeating the pattern 12 times around a central point and you got a 3d E8.
As you can now imagine it is possible to build different spheres containing more than 6 “particles” up to the 20 “particles” for E8.
Those patterns in those 12 spheres must fit into the size of a proton (10^-15).
One of those options will end up matching with the “particles’ of the Standard Model with the complement of the data from CERN.
Apparently, SU(5) as a unifying theory does not work.
We are at the beginning of neucleonagraphy.
----------
jal

[Coin]

The points that you make are not at the layman level.
You said,"If the LHC discovers ANYTHING, it falsifies Lisi's current formulation of E8, because there is no room for anything new! The only possible thing the LHC can find without breaking Lisi's E8 model is the single higgs-- finding supersymmetry, or a technicolor higgs (unless the colored scalars turn out to be part of the higgs mechanism? I don't know if that's possible) would simply not fit into the E8 root system as this month's paper formulated it.)"

Barrett said,
"... The weights of these 222 elements|corresponding to the quantum numbers of all gravitational and standard model fields | exactly match 222 roots out of the 240 of the largest simple exceptional Lie group, E8.
... After all algebraic elements of the standard model have been fit to the E8 Lie algebra there are a few e8 elements remaining, representing new, non-standard particles.

Right, but what I was trying to say is that although there are 18 "new" mystery particles in Lisi's E8, corresponding to the "leftover" roots 223 through 240, I do not think it is the case that these particles could be just anything-- it is not known what EXACTLY those particles are, but Lisi's formulation does predict certain properties for those particles.

As I understand the way Lisi's paper was constructed, he does predict the quantum numbers of these particles-- Lisi's current construction assigns specific spin values and specific charges (?) of various types to the 18 new particles, and says "look for particles that look like this". This means that although there's lots of different functions those 18 extra roots could perform (like assigning masses, as you quote) there's only a limited number of things they could be. They couldn't be, say, fermionic superpartners of the bosons, as far as I know, not without changing the E8 construction majorly, because that wouldn't fit the predicted quantum numbers. So if we found a fermionic superpartner at the LHC, Lisi's E8 wouldn't be able to explain that even though there are still those 18 unassigned roots.

This is to be viewed as a positive feature of Lisi's E8 formulation-- it is good to be specific and it's good to be falsifiable.

Actually it sounds like you are getting a lot of stuff that I have not yet had time to evaluate. Could you provide the reasoning for your statements, or a link to where the information comes from? For example, about those 18 colored scalars being hard to find…I am not sure what you mean.

I'm sorry, I don't mean that they will be hard to find-- I just mean that we don't know whether they will be hard to find or not. Maybe they are easy to find and they will show up at the LHC. Maybe they will be hard to find and they will not become visible until some far-future accelerator. I am just saying, I don't think we know enough about this theory yet to say whether one should expect to see those particles at the LHC. One can hope, of course!

Could you say more about your assertion that “The only possible thing the LHC can find without breaking Lisi's E8 model is the single higgs-- finding supersymmetry, or a technicolor higgs (unless the colored scalars turn out to be part of the higgs mechanism? I don't know if that's possible) would simply not fit into the E8 root system as this month's paper formulated it.)” I thought Lisi was saying there were a handful of particles that could fit in E8 which are not yet discovered. His section 2.4.1 beginning on page 21 is titled “New Particles.”

So to clarify, my statements about the 18 extra particles and "colored scalars" are based on the section 2.4.1 you cite:

After all algebraic elements of the standard model have been fit to the E8 Lie algebra there are a few e8 elements remaining, representing new, non-standard particles. There are two new quantum numbers, X and w... This field factors into three generations, x1=2=3, corresponding to different w quantum numbers, and a new Higgs scalar, PHI, for each color and anti-color. The new field, xPHI, is a joining of x and PHI in the same way ePHI is a joining of the gravitational frame, e, and the Higgs, PHI.

I'm a little confused about some of what that means. But you'll note here that besides just positing these extra fields exist, Garret has specified a number of fairly specific things about what they should "look like". Anyway you'll notice here that beyond just positing the new X and W, Garrett says specifically what to do with them-- you use them to create new Higgs-like scalar fields, exactly 18 of them, in fact, each identified in a specific way. The rest of the section consists of speculations by Garrett as to what these Higgs-like scalar fields might be doing.

I think that this is the correct way to read all this, for one thing because Sabine at Backreaction seems to have read it that way:

He finds a few additional particles that are new, which are colored scalar fields

And also because if you look on page 16 of Garrett's paper, in the big table where he identifies the mappings of roots to particles-- where it is explained what the "symbols" in the diagram pictures mean, that is, and what the quantum numbers for each one are-- the last three rows consist of the xPHI symbols, and exactly 18 of them are listed.

Finally, I actually asked Garret about it, or I tried to anyway. This is from the comments section of Not Even Wrong (emphasis mine):

Also a little confused: so counting up all the fields we expect to see in nature we find they fit with 222 of the roots in your E_8 root system, leaving 18 “extra” roots whose properties as fields are described on page 22 of the paper. The paper seems to be saying that these 18 new fields each act kinda like the Higgs, and each one is identified with a specific one of three generations and a specific color or anti-color. If this reading is correct, what do these generation/color identifications refer to? Does this have to do with the color or anti-color of quark that the field is able to interact with, or is the idea that the field carries color charge, or…?
Yes, exactly so. These new scalar fields have color quantum numbers, and so interact with the quarks and gluons.
In my dreams at night, these new Higgs fields give the CKM matrix, but I don’t know how that works when the sun comes up.
They’re also a potential dark matter candidate, but I don’t say that in my paper because I think that’s a cliche.

(The CKM matrix is this gadget (http://en.wikipedia.org/wiki/Cabibbo-Kobayashi-Maskawa_matrix), which according to wikipedia "The CKM matrix describes the probability of a transition from one quark q to another quark q'". Garrett also suggests this possibility that the "new higgses" could have something to do with the CKM matrix in the paper, and in the paper he also suggests there could be relevance to "the PMNS matrix"; according to wikipedia PMNS is to neutrinos as CKM is to quarks, and PMNS appears to explain why neutrino oscillation (http://www.ps.uci.edu/~superk/nuosc.html) happens. Incidentally I don't think the dark matter comment should be taken too seriously, a later commenter made some points giving reasons why a colored scalar would not do a good job as a dark matter candidate, which I don't think Lisi responded to.)

--- --- --- ---

...okay, have I lost you all yet?? I might have gone too far away from "layman" terminology here. Let me try to phrase this simpler:

To sum up: Lisi predicts 18 new particles. But he doesn't just predict any old particle: He is able to predict some specific things about the new particles, enough so that if we detect a new particle in a particle accelerator we should be able to say whether that is a particle which Lisi's E8 predicted or not. The particles Lisi predicts are extremely special and distinctive. They are "colored scalars". What does this mean? Well, the "scalar" part means the particles are spin 0. Particle "spin" has to do with how many degrees of freedom that a particle field has. Spin 0 is the least freedom that a field can have-- a spin 0, "scalar" field is the simplest kind of field you can have. When you have a field of this type, you basically just have a number assigned to every single point in space, and those numbers are the "field". Sometimes there is a ripple that passes through the numbers in the field, and we call this ripple a "particle".

Even though they are as simple as a field can get, scalars do a lot of stuff. The most famous (actually I think it might be the only) scalar field that we know about right now in nature is the Higgs field, and the Higgs is just all kinds of useful. For example it is the reason why particles have mass. One of the main things the LHC is trying to do is prove the existence of the Higgs. The LHC is hoping that it will observe a particle called a "Higgs Boson", which is a ripple in the Higgs field. If we see this ripple in the Higgs field, then we will know this field exists. However, maybe we will see something different! There are nonstandard theories that say there is more than one Higgs, and that the different Higgses do different things. (This theory is called for example "technicolor" theory-- although technically supersymmetry predicts more than one Higgs as well.)

So Garrett predicts we'll just see one normal Higgs, like the standard model predicts. However in addition to this he predicts 18 fields that are like the higgs, but special. These higgs-like fields interact with the "color force", also called the "strong nuclear force" which is the thing that holds things like protons and neutrons together. Every quark has a "color" (not actually a color, they just call it that), and the way the colors attract each other binds the quarks together into things like protons very tightly. Garrett's 18 scalars also have colors-- each of the scalar field interacts with one particular kind of quark. So for example one of the scalars interacts with the red generation-I quark and another one interacts with the blue generation-II anti-quark. This is very special! Looking on google I find there are other theories which have tried to incorporate colored scalars before, but this is very very rare. A colored scalar would probably do very interesting things, and it would be very easily identifiable if you built a big enough accelerator to see it (in other words it would be "easy to find", but maybe/maybe not "easy to find at the LHC").

Of course, this is just how I understand things so far, based on the things I quote above. (There are some things I am worried I could be wrong about: First off, maybe it is possible that a future version of E8 theory could take those "x" and "w" quantum numbers that result in the 18 colored scalars, and break them down in some different way that produce some different kind[s] of particle; I just don't know. Second off, in the quote from 2.4.1 of Garret's paper I put above, I ellipsised past something about "a non-standard pair of fields B... interacting with right-chiral fermions". I clipped this part because I don't understand it, and also I can't find any further discussion on it which implies it's not such a big deal. But I don't know what this "B" refers to and maybe it is a bigger deal than I thought. If anyone who understands this more than I do could correct any errors I've made here I'd appreciate it.) So again a reminder, take everything I say with a grain of salt!

[jal]

Some layperson that you are!!!!
I think that your post came in at just the right time in the development of this simple explanation.
I read Bee's thread and could not follow all (heheh most) of the discussion.
Now, I feel, it is where the other amateurs on this forum will feel more comfortable with what Garrett is doing. (that should be just about everyone heheh)
I hope others will repond .... I'm going to listen and learn.
Thanks!
jal

[SublimeGD]

Wow, this thread has far exceeded my expectations. Everyone keep up the good work.

[marcus]

Wow, this thread has far exceeded my expectations. Everyone keep up the good work.

Congratulations on an excellent thread Sublime! the last couple of posts by Coin are really helpful. Quick somebody ask a question, in hopes that Coin will continue:biggrin:

[TheRealColbert]

For my listening enjoyment during holiday travels, I spun "Particle Physics for Non-physicists" from the teaching company. In chapter 14, the section on symmetry breaking, there was a quote that seemed to fit this topic.

"There's not always a starting point when you are learning about some complicated thing. It's just a big ol' mess and you just gotta jump in somewhere and begin to learn more about it and then the big picture begins to appear."

[jal]

Hi coin!
I was hoping for more input from other people too.
I have one more observation (at this time).
--------
The present status of Garrett’s E8 could be compared to a blank template. It needs to be completed. At present it is ideal for applying the tools of project management. http://en.wikipedia.org/wiki/Project_management
Here is where the amateur can help. E8 can be mapped on a program such as PERT. You could then ask it to show an up quark or a down quark etc..
http://en.wikipedia.org/wiki/PERT
Program Evaluation and Review Technique
The Program (or Project) Evaluation and Review Technique, commonly abbreviated PERT, is a model for project management designed to analyze and represent the tasks involved in completing a given project.
-------
jal

[starkind]

I have been looking at the E8 simulations on Youtube

http://www.youtube.com/watch?v=oycE0r_azP8

and have noticed a thing or two that may be of interest here. One thing is that the undesignated branches of the E8 particle model are central to the simplest projections. At about 14 seconds into the vid, you can see the eighteen red-blue-green squares congregate at the center of the figure. Of course it is the projection onto two dimensions that seems to congregate, and their proximity to one point only indicates that they are on a common axis in the E8 structure, not that they are "close" to each other. But they do share a common axis, on which all other dimensions have value zero.

Then again at about 32 seconds, a simple configuration occurs in which the colors separate into six outer circles, each a cluster of similarly colored quarks, around one inner circle. Each of the outer circles is centered on a square, indicating an undesignated branch. There is however no square, or anything else, in the center of the central circle.

The other thing I want to mention is the physical meaning of the geometric relationships, as illustrated by table 1 on page 5 of the paper, where the gluons are shown to be related to the quarks in such a way that simple vector addition predicts the result of any quark-gluon interaction. Vector addition, for grandma’s sake, is simply a matter of placing the tail of one vector at the head of the other. The head of the first vector then shows the position on the figure occupied by the result. In this way the red-green gluon is shown to interact with the green quark to produce a red quark.

Presumably the other geometric relationships (where the connecting lines are vectors) are also related to possible interactions and their results.

I would like to be able to select certain groups of particles and suppress the others to get an idea of how, say, electrons rotate through E8. Or perhaps just the electrons and the up and down quarks that commonly make up almost all visible matter. Do the visible matter particles cluster in certain lines and planes also, at a different point in the rotation? What underlying physical reality could be responsible for the preponderance of only two of the six quarks? Can we see something in the structure that might suggest a relationship between the commonly visible bits of matter and the underlying structure of time-space?

S

[jal]

I would like to be able to select certain groups of particles and suppress the others to get an idea of how, say, electrons rotate through E8. Or perhaps just the electrons and the up and down quarks that commonly make up almost all visible matter. Do the visible matter particles cluster in certain lines and planes also, at a different point in the rotation? What underlying physical reality could be responsible for the preponderance of only two of the six quarks? Can we see something in the structure that might suggest a relationship between the commonly visible bits of matter and the underlying structure of time-space?
I don't think that Garrett put up a chart of E8 and the flicked paint at the template and called it the standard model representation.
I guess we will just have to wait for the next papers.
---------
inserted: Bee's 2d (6 sphere packing)
http://backreaction.blogspot.com/2006/08/quark-gluon-plasma.html
By Bee on Wednesday, August 23, 2006
Quark Gluon Plasma
The pictures come from this presentation.
http://th.physik.uni-frankfurt.de/~scherer/qmd/cscus2004_stefan_scherer.pdf
jal

[jal]

Garrett
The G2 root system may also be described in three dimensions as the 12 midpoints of the edges of a cube | the vertices of a cuboctahedron.

Since this thread is for a layman’s explanation of trying to understand Garrett’s E8 Standard Model let’s look at how the particles could be distributed in a simple symmetric pattern? Let’s look at some possibilities by assuming that the proton is a sphere containing those “particles”.
1. You could divide the sphere into 12 inner spheres and divide the 240 “particles” into those 12 spheres. That makes 240/12 = 20 particles per sphere.
2. If you wanted to combine the 12 spheres and the vertex of LQG then you only need one double tetra in the center and assign a group of “particles” to the 8 vertex and to the 4 mid-point of the vertex, for a total of 12 groups of “particles” around the center. Each of those 12 vertex would then contain 20 “particles”. Adding tetras between the spheres could be done but there is the problem of “double counting” of “particles”.
3. There are other combinations that could be made. Garrett will eventually work out the ones that he feel works the best with E8 and tetras.
Here is my image with a hex. packing configuration.
http://www.geocities.com/j_jall/3dspace.gif
If you don’tget the image it is because the site has crashed from too much traffic. You could try doing a search for "12 sphere packing" to get an idea of possible arrangements.
Or start at your search at http://www.grunch.net/synergetics/readings.html
jal

[jal]

Did you continue your searching/learning? Did you find the following explanations? Can you make the link with what the “math kids” are doing?
-----------
http://www.scienceu.com/library/articles/isometries/index.html
Introduction to Isometries
------------
http://www.math.uchicago.edu/~farb/papers/isoms.pdf
Isometries, rigidity and universal covers
Benson Farb and Shmuel Weinberger
December 31, 2006
-----------
http://www4.ncsu.edu/~loek/research/res.html
work on symmetric spaces
------------
http://www.verbchu.com/crystals/patterns.htm
Mapping the Hidden Patterns in Sphere Packing
--------------
http://www.mdstud.chalmers.se/~md7sharo/coding/main/node38.html
Applying Coding Theory to Sphere Packing
-------------
http://math.berkeley.edu/~reb/papers/bcqs/bcqs.pdf
A Monster Lie Algebra?

We define a remarkable Lie algebra of infinite dimension, and conjecture that it may be related to the Fischer-Griess Monster group.
The Lie algebra of this paper is indeed closely related to the monster simple group. In order to get a well behaved Lie algebra it turns out to be necessary to add some imaginary simple roots to the “Leech roots”. This gives the fake
monster Lie algebra, which contains the Lie algebra of this paper as a large subalgebra.
See “The monster Lie algebra”, Adv. Math. Vol. 83, No. 1, Sept. 1990, for details.
----------

Chapter 30 of “Sphere packing, lattices and groups” by Conway and Sloane, and Adv. in Math. 53 (1984), no. 1, 75–79. R. E. Borcherds, J. H. Conway, L. Queen and N. J. A. Sloane
----------
http://www.research.att.com/~njas/doc/splag3.pdf
Sphere packing, lattices and groups
Material for third edition, Sept 16 1998
-------------
http://www.research.att.com/~njas/index.html
Neil J. A. Sloane: Home Page
=========
Finally! …. I have reached the end of this simple presentation. ( I think)
If you want to learn …. You got to continue searching.
I found that by doing a search for sphere packing and Isometries that I got the essentials and a simple way to begin to understand the math (Lie) which is used to do physics. It will not make you “a math kid’, but it will make one more person who can have some appreciation of what they are doing.
I hope that all the people who know more than me have not found mistakes in this presentation which would lead the layperson astray.
Good hunting in your quest for understanding!
Jal

[starkind]

Thanks for these links, Jal. We had the first real snow of the season and I have been busy all weekend, but today is a study day. I'll take a look at the links and return here later.

S

[starkind]

I've been speculating again. I do hope this is not against the forum rules. The speculations began when I looked at

http://th.physik.uni-frankfurt.de/~s...an_scherer.pdf

Beautiful! Shows hex relationships in a quark-gluon liquid model.

Relativistic Pb-Pb collisions produce extremely high energies in extremely small spaces, resulting in a primordial fireball in which quarks and gluons are freed from confinement. Exotic hadrons are found (I didn't quite get this part....who found them? Is this actual data or only part of a model?) involving five quarks in a single particle.

The implication seems to me to be that we can now expect to work with the idea that quarks can be extracted from existing hadrons and recombined into exotic matter. The fireball is so dense with data that models are needed to interpret the results. So it seems to me now that it may be appropriate to speculate on what kinds of models could be tested against the data in hopes of finding a mathematical fit.

Here is my current speculation: the quark-gluon liquid may contain all of the quarks and gluons, not just the few we see in common hadrons. As hadrons freeze out of the q-g liquid phase, they form into lattices in which the up and down quarks are on the visible “surface” of the lattice, while the rest of the quarks are “hidden” “inside”.

Of course, “hidden” only means that our measuring apparatus does not detect them, and “inside” is higher dimensional, so that the inside of the object can very well be bigger than the outside. Think Calabi-Yau.

Don’t panic, the hidden inside dimensions are still measurable, because the hidden structure determines the behaviors we see on the surface. We detect the surface behaviors, and use them to infer the interior structures. We will know when we have the right model if the hidden inner relationships can be shown to determine peculiar behaviors seen on the surface.

Grandma, dear, this is like in the old days before electron microscopes when scientists looked at nearly pure mineral samples and found that they often occur in nearly perfect crystals. Some form cubes, some form octahedrons, some form complicated rhomboid structures. Back then, no one had actually seen an atom, but by using a model in which extremely small spheres of one or two sizes were densely packed, the various crystal lattices could be explained in compelling detail. It was a couple hundred years before x-ray crystallography and electron microscopy actually showed that the tiny spheres really exist, just as the model predicts.

In the old days, scientists used this model to take apart solids and reassemble the parts into other kinds of solids. We call this chemistry, but they thought of it as alchemy. The alchemists were hoping that they could discover how to make gold out of lead, but of course we now know that this cannot be done by rearranging atoms. It can be done, and is done today, at huge expense, by means of various fusion and fission reactions. In these reactions, we rearrange the neutrons and protons that are found in the nucleus of the atom. Unfortunately, the leftovers from the fusion and fission reactions are often deadly poisons. It isn’t profitable or practical to make gold this way.

Now just as we went from banging rocks together (mechanics) to banging atoms together (chemistry) to banging protons and neutrons together (nuclear physics), we now have progressed to the stage of evolution where we can bang together the quarks and gluons that exist within and make up the protons and neutrons. I am not aware that anyone has thought of a suitable name for this new kind of hammering on matter, but the possibilities are interesting.

For example, it may be possible to take apart the quarks in neutrons and protons in a lump of lead and recombine them into the protons and neutrons that make up an equal mass of gold. There would be no leftover poisonous stuff to worry about.

That will be a trivial result. The really exciting goal would be to take apart the protons and neutrons and not recombine them into matter at all. Instead, we may be able to transform them into pure energy in the form of electrons or photons. Again, there would be no leftover poisons. This could even be a way to make energy densities deep enough to warp space and time, deep enough to create gravity fields at will. Warp drive, anyone? Tractor beams? Anti-gravity?

One of the subsets of E8 describes how quarks and gluons inside hadrons (like protons and neutrons) dance around each other. The model shows six quarks and their anti-quarks, each of which has three colors. The colors have to add together to make the hadrons white. The charges on the quarks have to add together to make the hadrons positive, neutral, or negative. These peculiar facts are some of the results we should try to explain using the model.

Experimentally, we need to look for starting conditions which may have an effect on the types of hadrons which freeze out of the fireball. Are there initial conditions which produce more protons than neutrons? Are there initial conditions which produce more anti-matter than matter? Are there initial conditions which produce only energy and no matter at all? Which initial conditions can we control and modify for experiments? Electromagnetic fields? Angle of collision? Presence of strong acelleration fields, such as those which may occur near a black hole?

We have a lot of studying to do.

[jal]

Hi!
Simple description!
Could you fix your link.

[jal]

The following link has some very interesting images.
It should make you wonder if the mechanisms and the pattern for these structures are also at a smaller scale (inside the proton).
http://wwwphy.princeton.edu/~steinh/quasiphoton/
Experimental Measurement of the Photonic Properties
of Icosahedral Quasicrystals
Weining Man, Mischa Megens, Paul M. Chaikin and Paul J. Steinhardt

[staf9]

Is it just me being crazy, does the first-ever imaging of the 3d quasicrystal Brillouin zone look familiar?

I'm gonna go read their paper.

[starkind]

jal
Here is the correct link. I found it on your link to Bee's 2d (6 sphere packing) as "stefan's talks". For some reason I don't understand, the link gets mutilated every time I try to copy it here. It shows up complete on my edit screen, but only partial on the board. So I am going to try to work around.... the below has replaced each back-slash with an asterisk. I guess if you want to follow the link from here, copy it to your address bar with backslashes insterted in place of asterisks.



http:**th.physik.uni-frankfurt.de*~scherer*qmd*cscus2004_stefan_scherer .pdf

Otherwise, go to the link for Bee's backreaction in jal's post, number 94. I see that the link to stefan's paper is also mutilated in post 94. But if you click the backreaction link in 94, you can find the paper by clicking Bee's link in her blog to "stefan's paper".

[starkind]

Is it just me being crazy, does the first-ever imaging of the 3d quasicrystal Brillouin zone look familiar?

I'm gonna go read their paper.

The crystal lattice model used to be just that...a model, without direct physical evidence, until the kind of crystallography as shown in the images linked above. Now we can say with a very high degree of certainty that macroscopic physical matter is made of what amounts to tiny spheres in dense packed structures.

This was enough to provoke the speculation that within the atom there are parts which also form a dense packed spherical structure, namely the nucleus, made primarily of protons and neutrons. As far as I know, there are still no images made directly from the protons and neutrons in a nucleus, but it is usual in college level courses to depict the protons and neutrons as small, hard, mutually exclusive spheres.

We are now pushing this crystal lattice model another level down the spectrum, thinking that the quarks and gluons in a proton or neutron are also composed of some smaller scale densely packed spheres. As far as I know there is no physical evidence of any kind to suggest that the crystal lattice model still holds at the quark scale. However, the work Lisi has done is highly provocative.

It is still problematic that the SO(3) geometry calls for a lattice structure connecting all the kinds of quarks and gluons, and in extension to E8, all the kinds of particles. The behaviors of protons and neutrons can be entirely accounted using only two kinds of quarks, the up and down. If we suggest that E8 and SO(3) are physical spaces inside the proton and neutron, then we are saying that all the other quarks and gluons are somehow present physically inside the proton or neutron.

We are a long way from having direct evidence to support this idea, and furthermore, it calls for a much more complicated picture than the current idea that protons and neutrons are composed only of three quarks of two kinds, along with their related gluons. By Occam’s razor, such apparently needless complications should be cut away. Worse, the idea that all those other quarks and gluons are present inside the hadrons requires us to wave into existence some kind shielding to explain how they can be present and yet not affect the known behaviors.

Still, all is not lost. Geometry is one of the oldest applications of mathematics, and geometric rules have been shown to apply in a physical way to chemistry. It also works very well in conceptualizing structures in nuclei. It certainly has applications in explaining the composition of nucleons. And, some respectable academic researchers sitting on piles of credentials have seen fit to explore even more remote regions of physical knowledge using geometry to explain the behaviors of space and time at the Planck scale.

So we are not entirely out of order in thinking about how nucleons may be composed of spherical quarks in a dense packed lattice structure. But any idea we may put forward will have to be compelling if it is going to stand. We will have to have a simple easy model that explains known behaviors on the basis of a lattice geometry in which most of the components of the lattice are invisible. The model will have to explain the known behaviors, and also have a mechanism to explain the invisibility.

I am going to suggest a phase structure in which the three generations of the standard model come from our measurement “in the present instant” being bracketed by instants immediately past and instants immediately next to come. Physical objects in the immediate future may be in a state analogous to a gas, physical objects in the present instant of measurement may be in a state analogous to a liquid, and physical objects in the immediate past may be in a state analogous to a solid. All of our measuring apparatus is in the present or liquid phase. Only at the extreme limits of measurement do we get a means to infer the physical nature of the generation just past and the generation just to come.

This phase shift becomes more obvious as we measure smaller and smaller spatial separations. As the spatial component of the measuring process becomes small, the time component gets closer and closer to unity with the spatial component. At the Planck scale, time and space is one thing, while at the Fermi scale, space predominates to the extent that time units become infinitely small. The present instant becomes a two dimensional space-time surface with no measurable time-like thickness.

Then we may think of the up and down quark, along with related gluons, as embedded in the present instant, while the next and past instants contain the other two generations of the standard model. In this way, the unification of space-time joins smoothly with the macroscopic realm at the Fermi limit. Below the Fermi limit, the “objects” are seen as embedded in a space-time geometric lattice, while above the Fermi limit, the “objects” are seen as having three extended spatial dimensions and a single instantaneous two dimensional layer in a foliated time-like sequence.

The three dimensional space-time lattice is then fundamental at least down to the Planck scale. At macroscopic scales we are measuring such large spaces that the time dimension seems to become continuous.

This model may be tested by examining data on standard model particles from current and near-future collision experiments. What signature might we see to support the idea that the uncommon generations of particles are in advanced and retarded time frames?

The universe is expanding. Future generations would seem much larger than present generations. Past generations would seem much smaller. Energy is a function of size. Mass is a function of energy. I am going to go look for the mass relations among standard model generations.

Best regards,

Richard

[belliott4488]

The crystal lattice model used to be just that...a model, without direct physical evidence, until the kind of crystallography as shown in the images linked above. Now we can say with a very high degree of certainty that macroscopic physical matter is made of what amounts to tiny spheres in dense packed structures.
Well, you want to be careful with that metaphor; even at the molecular level, there are no "hard spheres."
This was enough to provoke the speculation that within the atom there are parts which also form a dense packed spherical structure, namely the nucleus, made primarily of protons and neutrons. As far as I know, there are still no images made directly from the protons and neutrons in a nucleus, but it is usual in college level courses to depict the protons and neutrons as small, hard, mutually exclusive spheres.
Well, that's unfortunate, and it should certainly be taken as a cartoon of reality at best.
We are now pushing this crystal lattice model another level down the spectrum, thinking that the quarks and gluons in a proton or neutron are also composed of some smaller scale densely packed spheres. As far as I know there is no physical evidence of any kind to suggest that the crystal lattice model still holds at the quark scale. However, the work Lisi has done is highly provocative.
Not that his work actually suggests anything about a physical crystalline structure, right? I wouldn't want people to get the wrong impression about what he has proposed.
... If we suggest that E8 and SO(3) are physical spaces inside the proton and neutron, ...
But WHY would we ever say such a thing? Are you thinking that the geometric properties of the Lie Groups that describe fundamental symmetries have a physical realization? (see my final comments, below.)
then we are saying that all the other quarks and gluons are somehow present physically inside the proton or neutron.
Well, it's part of the standard theory of quantum fields that you have "soup" of virtual particles all popping in and out of existence for minute periods of time, but I don't think that should be confused with the existence of real observable particles.
*****************
Once again, I have to stress that it is not correct to think that the space of quantum states (Hilbert Space) is not the same thing as space-time. More to the point, there is nothing about the use of Lie Groups in Quantum Field Theory in general, or in Lisi's model in particular, that suggests that the representation space of the group in question (i.e. the space where the multi-dimensional geometric structure lives) contains or is equivalent to the space-time in which we live.

You've seen the description of the group O(3) as the group of rotations in 3 spatial dimensions. Maybe you also recall where it was stated that it is mere coincidence that in this case the representation space and the space in which the rotations take place are both 3 dimensional. That's because they're entirely different spaces. (As a counter-example you could consider the group of rotations in 2-D space, which is a 1-dimensional group, requiring only one parameter to define a rotation, or group element.)

I really think it's important to keep these spaces straight and not to confuse them. And of course, I hope I haven't just confused things all the more ... :rolleyes:

[starkind]

Thanks belliott4488

I am glad you are here. You are right of course about there being no “hard spheres” in the absolute sense, at least macroscopically. I add the “at least” because we don’t know anything about what really goes on below the particle scale. And even a spherical chunk of the hardest stuff we can obtain is not really absolutely hard, in the sense of inelastic. Every surface we can touch is made up of tiny bits of matter held in place by electrostatic forces. The tiny bits are truly tiny; there is much more space than there is bits in any available object. So I need to be clear that “hard spheres” are only hard in the sense that elasticity is extremely limited, and then only until the energy of a probe exceeds the binding energy of the particles involved.

I hit on the term “hard sphere” when trying to find a commonly descriptive way to separate the bits from the spatial fields in which they exist. Grandma doesn’t get the idea that matter isn’t really solid. She isn’t going to understand that in field theory there are no absolutely hard bits of any kind at all. I know you already get this, but I assume there may be some reader who does not have field theory to work with. Really, I am writing the kind of explanations I might have understood myself at the age of 15 or so when I first encountered and was fascinated by the concept of special relativity. That was a year before I first got to study chemistry.

I wrote: “it is usual in college level courses to depict the protons and neutrons as small, hard, mutually exclusive spheres.”

You replied: “Well, that's unfortunate, and it should certainly be taken as a cartoon of reality at best.”

Indeed. I guess anyway I should have said it was usual in college level courses when I took them, thirty years ago. Even then, the professor was careful to caution us not to take the drawings too seriously.

Nowadays I have come to the understanding that most if not all of what we think we know is little more than caricature. Table surfaces aren’t really hard, atoms aren’t really hard, protons aren’t really hard. But the dense pack spheres model does work for crystallography, doesn’t it? Each atom in a crystal is pretty much trapped in a spherical shell from which other atoms are excluded. The shell mostly stays where it is in relation to its neighbors. No other atom of the same size or larger can squeeze between them without the application of enough force to break the lattice.

The atoms are not hard little balls, and the teacher will be sure to tell you so, but in a shorthand sort of way, when doing chemistry, we can think of them like that. Do introductory organic chemistry classes still use those little colored wooden balls with holes in them in which you place sticks or springs to attach them to each other? Did Watson and Crick use the little wooden balls and springs and sticks when building their model of DNA? It works well enough when dealing with objects all on a similar scale.

As I recall astrophysics, massive ordinary stars sometimes collapse to neutron stars….made all of neutrons. The neutrons are not really hard little balls, but to some degree they act that way. When the density of the star gets to such a point that the hard little balls break down, the matter in the star continues to collapse and become even more dense as it forms a black hole. The fact that the neutron star resists further collapse until a certain energy density is reached suggests that the hard little ball model of neutrons works in there, as well.

So I suggest we may continue to use the hard little ball caricature at least into the nucleus, and since it has done us such service, we may as well allow ourselves to use it provisionally when thinking about quarks and gluons. Maybe it is only coincidence that E8 has an SO(3) cubeoctahedral subset which can be modeled with densely packed hard spheres and which encompasses quarks and gluon behaviors. Probably it is only coincidence. Surely it is only coincidence. Almost certainly. But we cannot rule out the application of the model on a provisional basis until we find contradictory evidence.

Garrett Lisi presumably would accept a career in academic physics if offered by the right school. Of course he has to be very careful not to say anything that may compromise his future. What a disaster for a career in academics to assert something that later proves erroneous. I am lucky that I don’t have to worry about that sort of thing. I can wander down dark alleys looking for an open door others might have missed. If there is no open door and the alley is a cul-de-sac, I am free to back out of it and continue my search elsewhere.

I don’t speak for Garrett Lisi, but only from my own understanding, and to other amateurs who may be looking for non-mathematical conceptual tools to grapple with this interesting topic. I think I can safely say that Garrett Lisi’s work is provocative. It provoked me anyway, and evidently quite a few other people. I will take any responsibility required of the assertion that E8 may represent some physical relationship that enforces its mathematical behavior.

You wrote: “But WHY would we ever say such a thing? Are you thinking that the geometric properties of the Lie Groups that describe fundamental symmetries have a physical realization?”

Well now I have to turn this around and ask if WHY is ever a question that can be answered by physics. But nevermind. I’ll entertain it anyway. Why not?

Not to evade the question. The geometric properties of the Lie Groups that describe fundamental symmetries do have a physical realization. It is realized in the physical behavior of quarks and gluons, which are accepted as part of the standard model. If it is not the geometric properties of the Lie Groups, then WHY do they behave that way?

Consider this. The multiplication table has nothing, physically, to do with the surface area of a bean field. And yet it is useful as a model of the field when calculating harvest yields and fertilizer applications. It could even be physically laid out on the field, just as it is on a piece of paper, to prove a point. It fits exactly. The fact that E8 model is a mathematical description does not rule out the possibility that it might be laid out exactly in a physical space to describe and predict physical behaviors.

I think the problem may be that you believe somehow physical space is qualitatively different from mathematical space. It is a common assertion. But I should be able to ask you what evidence you have to support your view. What is special about physical space that makes it unique and separate from mathematical space?

You wrote: “Well, it's part of the standard theory of quantum fields that you have "soup" of virtual particles all popping in and out of existence for minute periods of time, but I don't think that should be confused with the existence of real observable particles.”

Are you saying if a particle doesn’t last long enough to be observed that it is not real? How is it not real? Is Hawking radiation real? IIRC Hawking radiation is formed when a virtual particle pair is formed in a place where one member of the pair is trapped inside the horizon, while the other one is left outside, in our ‘real’ world. Unruh radiation, again IIRC, is virtual particles made ‘real’ by a horizon-like separation caused by the accelerated field of the observer. Again, if you think there are two conditions, real and virtual, that should not be confused, I should ask you to explain in what critical way they are different.

You wrote “it is not correct to think that the space of quantum states (Hilbert Space) is not the same thing as space-time. More to the point, there is nothing about the use of Lie Groups in Quantum Field Theory in general, or in Lisi's model in particular, that suggests that the representation space of the group in question (i.e. the space where the multi-dimensional geometric structure lives) contains or is equivalent to the space-time in which we live.”

I agree that there is nothing about Lisi’s model suggesting representation space is equivalent to the space-time in which we live. However you seem to be asserting that they are in fact different, in which case again you should be specific about how they are different. (By the way, I am assuming the double negative in the quote above was unintentional. Please correct me if I am mistaken about this point.)

In summary, how is mathematical space uniquely different from physical space in such a way that it is important not to confuse them?

Thanks for an interesting couple of hours. I hope we get more of them.

S.

[belliott4488]

starkind:

If I tried to respond to all that you've written here, it would probably take an entire forum page. More importantly, it would almost certainly take this thread even farther from its original topic than it already is. For that reason, I'd like to respond in detail directly to you and to post only a general high-level response here. If the details of our conversation are interesting to others, then I suggest that we start another thread to continue it there.

I don't seem to have made my point very clearly, so let me try again. First, the distinction between "physical space" and "mathematical space" is yours; I don't believe I made it, but if I did, then I was possibly being a little sloppy. I meant to distinguish between different mathematical spaces, all of which are abstract by definition, and all of which correspond to various physically measurable quantities.

Physics is the business of creating mathematical models of physical observables with a well-defined correspondence between the observables and the entities in the mathematical theory. One possible set of observables is that of spatial measurements, such as relative position. We can model this set with a 1-d mathematical space, perhaps to describe the position of a bead on a wire; a 2-d space, as we regularly do with street maps; a 3-d space, as we do for all sorts of problems in classical mechanics; or a 4-d space if we're doing relativistic mechanics. These spaces are all abstract, but they correspond to physical observables, specifically to relative positions.

There are also other physical observables that can be modeled by other mathematical spaces. Those abstract spaces also have various properties, which might well correspond to relationships between the physical observables being modeled. An example is momentum space, which is often used to model classical mechanics. It's no more or less real than position space, but you shouldn't confuse the two because points, or coordinates, in each of these spaces correspond to different (and incompatible) physical observables.

When we talk about the symmetry groups of fundamental particles, those groups have representations, which may well be described by geometry. The points in this space do not correspond to points in position space, however; they correspond to particle states. Just because, for example, an up quark might appear to the left of a down quark in a particular visualization of the group, that has nothing to do with where it is in position space, and therefore has nothing to do with where we might measure its position (assuming we could even do that).

My point boils down to this: the mathematical model has parts that correspond to positions in space and parts that don't. The root space that we've all seen in Lisi's E(8) theory has geometric properties, but they do not correspond to geometric properties of relative positions of particles.

[jal]

You guys are doing great!
I want to underline your comment...
The points in this space do not correspond to points in position space, however; they correspond to particle states. Just because, for example, an up quark might appear to the left of a down quark in a particular visualization of the group, that has nothing to do with where it is in position space, and therefore has nothing to do with where we might measure its position (assuming we could even do that).


Do you want to try to answer another question?
Electricity and magnetism inside the proton. What is doing it?
jal

[belliott4488]

o you want to try to answer another question?
Electricity and magnetism inside the proton. What is doing it?
jalHm ... "doing it"? I'd have to say it's those -1/3e and +2/3e charged quarks ... any other suggestions?

[jal]

=========
belliott4488 We’ll leave electricity and magnetism as an open question.
Let’s look at the gravity question.
I want to talk at the level of “amateur”.
Garrett
It should be emphasized that the connection (3.1) comprises all fields over the four dimensional base manifold. There are no other fields required to match the fields of the standard model and gravity. The gravitational metric and connection have been supplanted by the frame and spin connection parts of : A. The Riemannian geometry of general relativity has been subsumed by principal bundle geometry | a significant mathematical unification.
Devotees of geometry should not despair at this development, as principal bundle geometry is even more natural than Riemannian geometry. A principal bundle with connection can be described purely in terms of a mapping between tangent vector fields (difieomorphisms) on a manifold, without the ab initio introduction of a metric.

I don’t know how it’s done, (a mapping between tangent vector fields).
I’m doing some reading to get ready for an explanation that I might understand. I’m finding that there are ways to include gravity into QCD. (Ie. SO(10), SUSY and other ways)
http://arxiv.org/abs/gr-qc/0506063
The roots of scalar-tensor theory: an approximate history
Authors: Carl H. Brans
(Submitted on 10 Jun 2005)
---------
http://en.wikipedia.org/wiki/Vector_field
Vector field
--------------
http://www.sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Flow/flow.html
Flows of Vector Fields
----------
http://en.wikipedia.org/wiki/Scalar_field
Scalar field
---------
http://en.wikipedia.org/wiki/Scalar_field_%28quantum_field_theory%29
Scalar field theory
---------------
I’m also finding some "Old" approaches.
http://en.wikipedia.org/wiki/Brans-Dicke_theory
In theoretical physics, the Brans-Dicke theory of gravitation (sometimes called the Jordan-Brans-Dicke theory) is a theoretical framework to explain gravitation. It is a well-known competitor of Einstein's more popular theory of general relativity. It is an example of a scalar-tensor theory, a gravitational theory in which the gravitational interaction is mediated by a scalar field as well as the tensor field of general relativity.
-----------
http://en.wikipedia.org/wiki/Self-creation_cosmology
Self-creation cosmology (SCC) theories are gravitational theories in which the mass of the universe is created out of its self-contained gravitational and scalar fields, as opposed to the theory of continuous creation cosmology or the steady state theory which depend on an extra 'creation' field.
As an alternative gravitational theory SCC is a non-standard cosmology in which the Brans-Dicke theory (BD) has been modified to allow for mass creation. It relaxes the requirement of the conservation of energy-momentum (or four-momentum) so the scalar field may interact directly with matter.
------------
At this time, there are similar questions in “An Exceptionally Simple Theory of Everything!”. Could an “OLD” approach work?

[Dave0101]

I'm sorry guys, but if I can be that dope who wants to bring the layman's version down to a total dummies version... I'm hoping someone can lay this bag of snakes out straight for me.

As I understood it, there are two separate sets of rules for describing the behavior of things... one for very tiny things, and one for very large things. I was also under the impression that the two sets of rules don't relate to each other well, and that the goal of a "theory of everything" was to create one set of rules that works for both. Is that right?

Now as I'm trying (and I think, failing) to wrap my head around this "exceptionally simple" theory, I'm getting the impression that what it actually does is describe, geometrically, all existing particles and their behaviors. I'm seeing it, as someone else said, more like a periodic table of everything physicists have seen and hope to eventually see? I'm getting the impression that it's reliability is derived from it's ability to make everything we know about fit, somehow, on the vertices of this E8 model in a way that properly describes their known behaviors? If so, what about the model illustrates each particle's properties?

Is this at all accurate? Is it actually a unification theory?

Again, my apologies... I've never had a physics class and my math is so bad I can barely balance a checkbook. :rolleyes: I'm just trying to get a dummies picture of what this means to people smarter than me.

[belliott4488]

As I understood it, there are two separate sets of rules for describing the behavior of things... one for very tiny things, and one for very large things. I was also under the impression that the two sets of rules don't relate to each other well, and that the goal of a "theory of everything" was to create one set of rules that works for both. Is that right?Yes, that's about it.
Now as I'm trying (and I think, failing) to wrap my head around this "exceptionally simple" theory, I'm getting the impression that what it actually does is describe, geometrically, all existing particles and their behaviors. I'm seeing it, as someone else said, more like a periodic table of everything physicists have seen and hope to eventually see? I'm getting the impression that it's reliability is derived from it's ability to make everything we know about fit, somehow, on the vertices of this E8 model in a way that properly describes their known behaviors? If so, what about the model illustrates each particle's properties?
Again, I think you've got it about right. The comparison with the Periodic Table of the Elements (PT) that we all saw in high school is apt, because both it and the current understanding - the Standard Model (SM) - show fundamental particles (or "elements" in the case of the PT) that fit nicely into an apparently well-ordered structure but with no explanation at all of why that particular structure exists.

In the case of the PT, the explanation came from Quantum Mechanics, which predicts the observed structure from a basic set of simple assumptions. In the case of Garrett Lisi's paper, what he's doing is trying to start with a basic assumption (the group E(8) as the fundamental symmetry group of elementary particles) and from that to derive not only the nice ordered structure of the SM, but also the required symmetries of gravitational theory.

As for your question about what properties of fundamental particles are described by this model, it has to do with "Quantum numbers" that are used to describe the different states in which particles can exist. In the SM certain different "flavors" of particles are forever different, i.e. there's no way to see an electron and a quark as two different states of the same thing. In Lisi's model, these particles are related by "symmetry transformations" or "gauge transformations", so that they really are just different states of same thing. You can think of rotations of the group's root structure, which move one vertex to another, as a way of identifying physical processes that allow such transformations.

This kind of thing is not new, since the SM allows such transformations, e.g. from an electron to a neutrino by the emission of a W+ particle. Lisi's theory extends this by allowing all fundamental particles to be related by such transformations; presumably there would be a mechanism for an electron to transform into a quark.
Is this at all accurate? Is it actually a unification theory?
To assess its degree of accuracy, physicists will have to use it to come up with experimental predictions and then to perform the experiments to see how well they match the predictions. That's a long way off. Nonetheless, if the theory is mathematically sound (the jury's still out), then to the extent that it at least reproduces the predictions of the SM and gravity theory, then it would be as accurate as they already are. The real test is to look for new and unique predictions from it, however.
Again, my apologies... I've never had a physics class and my math is so bad I can barely balance a checkbook. :rolleyes: I'm just trying to get a dummies picture of what this means to people smarter than me.Well, I'd say you're doing pretty well for a "dummy"!

[jal]

Tony Smith has been at this long enough to produce a lot of input for E8
http://www.valdostamuseum.org/hamsmith/E8GLTSCl8xtnd.html
--------
I must say that when I first got on the web, Tony's page was one of the first that I found. His explanations/presentations have improved .... a lot...
My understanding improved only a little bit. Tony is moving too fast for me to catch up.

[starkind]

Hi Belliot

You said: “The points in this space do not correspond to points in position space, however; they correspond to particle states. Just because, for example, an up quark might appear to the left of a down quark in a particular visualization of the group, that has nothing to do with where it is in position space, and therefore has nothing to do with where we might measure its position (assuming we could even do that).”

This is fine. I surrender the point, although I suspect it will continue to resurface. For future reference, may we agree that: “there is no evidence in position space, which has observable objects moving around each other in three spatial dimensions and one temporal dimension, that it is special or preferred or primal to (in short, more ‘real’ than) any other abstract mathematical space.”?

Hi Dave0101

You asked “what about the model illustrates each particle's properties?”

I would like to expand on this a little.

On page five of Lisi’s paper, you will find in Table 1 a list of particles in the column labeled G2. These particles are quarks and gluons, each with a superscript indicating its color properties. The quarks (q’s in the bottom part of the table, shown in the picture as triangles) are red, green, and blue, and each one has an anti-particle, shown with a bar over the letter. The anti-particle is anti-matter. The red green and blue are just quantum numbers, not really colors as our eyes see them.

The gluons, g, have two superscript colors each, because they act on quarks to change one color into another color. To see how the diagram works geometrically, you should start by labeling each triangle and each circle according to its coordinates on the diagram. If you are looking at the page in color, this will be easy, because each particle is shown in a different color….real color this time, a color you can see with your eyes. You can just match the symbol under column G2 in the table with the symbol on the diagram. I happen to be working with a black and white copy, so I have to look at the values in the table under g-superscript-3 and g-superscript-8. These ‘g’ are just labels of the axis of the two dimensional plane on which the diagram is shown. You can see these labels in the diagram at the top and at the right of the drawing, in faint gray. (Well, mine are gray.) Just think of the top vertex as having value one on the g8 scale and zero on the g3 scale. The quark on the right of the diagram has value one on the g3 and zero on the g8. If you calculate or measure the other positions as on any two dimensional graph, you will see that the circles and triangle positions are shown in the g3 and g8 columns, identifying which particle goes at which position.

Then you can do vector addition to see the possible reactions. Vector addition just means that you place the head of one vector at the tail of the other, keeping the lengths and angles of the vectors unchanged. In this case, the vectors are shown as the faint lines connecting the particle symbols.

For example, the circle on the far right of the diagram represents the red anti-green gluon. If this gluon reacts with the quark at -1/2, 1/2sqrt3, which you can read off the table as a green quark, you simply take the line that goes from the center to the green quark and slide it to the right until the bottom end, or tail, of the line is located at the head of the line from the center to the red anti-green gluon, at the right of the picture. Don’t change the angle or the length of the line, which is to say the vector, and you will find that the head of the transported vector is now on the red quark. This means that a red anti-green gluon reacts with a green quark to produce a red quark.

The column labeled V_beta is a table of root vectors, aka eigenvectors, spanning the E8 space. Each root vector corresponds to a type of particle. The fact that they span the space means that they are present in every view of E8. There is no part of E8 which they do not reach across. This is not true of every vector in the subspaces, which may appear or not appear in different views of the E8 structure.

For the rest, what Belliot said.

Hope this helps. It’s all in the paper. I recap it here to improve my own grasp of the mechanics, and in hopes that others will point up any flaws in my explanation.

S.

[patfla]

Hi – newbie here. Or if I want to be kinder to myself “educated layperson”.

I’ve read the whole topic and know where that puts me: at the bottom of the totem pole. Which is just fine since then there’s no way to go but up.

Have read several Smolin’s books; Peter Woit’s Not Even Wrong and others. So my ears perked up when I first learned of Garrett and his latest paper.

Well there are things that I knew already; things that I’ve learned over the last mth or whatever reading around; and now I have a whole new set of questions. I’ll limit myself to just one of those here. (although as you can see below, it'll hardly be a single sentence).

The components (observables?) of the 8-vectors which are the objects that inhabit the E8 Lie algebra (its operator being the ‘bracket’ or commutator). The components would be the quantum numbers. I’m trying to figure out just what they are.

This topic pointed me to Tbl. 9 on p. 15 of Garrett’s paper. The 8 components seem to be columns 2-9 and they read something as follows (my first stab at TeX):

\frac{1}{2i}\omega ^{3} _{T} \;\;\; \frac{1}{2}\omega ^{3} _{S}
\;\;\; U^{3} \;\; V^{3} \;\; w \;\; x \;\; y \;\; z \;\;

You should see 8 terms above.

Scroll up just slightly from Tbl. 9 in Garrett’s paper where he explains what these are.

The first four are from F4. 2 are associated with so(3,1) gravity and the other 2 are the 2 fields associated with the electroweak. I’m guessing that the omegas on the left are so(3,1) gravity and U^{3} and V^{3} are the electroweak’s 2 fields?

That’s the first half of my question. The other half consists of the remaining 4.

Here, Garrett explains, one has 3 and 1. 3 are the fields associated with the electrostrong and the remaining 1 is something associated with u(1)_{B-L} (whatever that is).

The division of labor here would seem a little clearer: the 3 are x\;\;y\;\;z. And the final one (u(1)_{B-L} ) is w.

Is that right?

All for now – pat

[jal]

Hi!
I'm reviving this old thread to ask a few questions and I don't want to litter the technical discussion.

Is having more than one copy on the standard model a problem?
What would it mean?

What model would you use to try to describe what quarks were doing when they were not confined, which would be in the early universe, before decoupling?
jal

[starkind]

hi jal

I've been cutting teeth on the other thread too.

I guess you mean having more than one copy OF the standard model....just a typo, probably, but let me know if you mean ON because I don't get that usage.

I wonder if the three copies could represent a time progression....one instantaneous moment and its immediate future and past instants?

[jal]

Yes, it's a typo.
You did get my drift ... physical meaning ...how is it to be interpreted.
jal

ps. I had trouble with the audio of J. B. intro to the E 8 presentation.
The audio went out a one of his explanation ... how he got more spheres of the same size in between the other spheres and still keept them one unit away from the center.
If someone could clarify.

[jal]

Let’s leave the questions, in the previous post, aside for now.
Since the boys at An Exceptionally Technical Discussion of AESToE are standing around kicking dust I went and did some searching that might help the amateurs.
If you do a search for, "Pierre Darriulat" ELEMENTARY PARTICLES; you will get a doc file that will give a good explanation of elementary particles and their interaction.
I expect that there are probably new info that might modify some of these explanations.
jal

[starkind]

Yes, it's a typo.
You did get my drift ... physical meaning ...how is it to be interpreted.
jal

ps. I had trouble with the audio of J. B. intro to the E 8 presentation.
The audio went out a one of his explanation ... how he got more spheres of the same size in between the other spheres and still keept them one unit away from the center.
If someone could clarify.

Hi jal

I'm also still having problems with the vid player. Very frustrating. MIT has a whole world of courses I can't access because the player won't play. I suppose this is because of my Microsoft platform. I'm not savy enough to try to change over to one of the open software platforms. Probably buy an apple next time.

About the one unit away from center question, I think he is saying that the added spheres are kissing the original sphere....so that they are one unit away (one radius) by definition. Of course fourth dimensional problems do not scale the same way three dimensions do. I think you can add the fourth dimensional spheres in between the three dimensional ones because their volume can be extended in the fourth dimension, which we don't see in 3d representations. This is analogous to the way same-sized 3d objects in a 2d picture (such as a photograph) can appear to be different sizes (far away objects look smaller). A 3d rep of a 4d object can be larger or smaller depending on the viewpoint of the observer. Rotations and translations that preserve an object's volume in 4d may rotate and translate in or out of the 3d space such that the 3d cross section is larger, smaller, or even non-existant in the 3d space. So, fitting more identical volume 4d objects into a 3d rep is not a problem.

If this is still difficult, think about a 2d painting of a large crowd of people. The people are all about the same size in the 3d world, but any number of them can be fit into the 2d picture because the ones that are farther away in 3d look smaller in the 2d pic. So 4d spheres can easily fit into the space left over in a 3d dense packing.

[jal]

Hi starkind!
Although your description sounds good, it still leaves a funny feeling.

I hope that the amateurs read and SAVE the doc from "Pierre Darriulat". Things have a habit of dissappearing from the web.

I have another bothering some question.

We have measured gravity down to the size of a hair.
We have gravity when we have matter/particles.
We can justify extrapolating gravity down to the size of quarks.
However, when working with scalars, there are no particles.
What is the justification for assigning one of the scalar to gravity?
jal

[starkind]

Could you give an example of assigning one of the scalar to gravity?

[jal]

Hi starkind
Boltzman constant (temp.), is related to activity of particles. There are no particles prior and during inflation.
Planck mass relates to mass of particles. There are no particles prior and during inflation.
Gravity relates to particles. There are no particles prior and during inflation.
There are only massless scalars or very weakly interactive scalars.
The phase transition, from scalar to particles, occurs after “inflation”.

==========
http://en.wikipedia.org/wiki/Boltzmann_constant
The Boltzmann constant (k or kB) is the physical constant relating energy and temperature at the particle level.
----------
http://arxiv.org/abs/astro-ph/0703566
Thermal fluctuations in loop cosmology
Authors: Joao Magueijo, Parampreet Singh
(Submitted on 21 Mar 2007 (v1), last revised 8 Jun 2007 (this version, v2))
----------
http://arxiv.org/abs/0708.0429
Observing the temperature of the Big Bang through large scale structure
Authors: Pedro Ferreira, Joao Magueijo
(Submitted on 2 Aug 2007)
Finally, we remind the reader that we are considering a universe that starts off in thermal equilibrium. The
hallowed example is that of what has become known as new Inflation: as the Universe cools down, the scalar field settles down into a slow roll regime and it is potential energy dominated. This is not, however, a generic feature of the inflationary cosmology. One appealing alternative is a Universe that emerges through quantum tunneling into an inflationary era [16]. Another possibility is that our local patch has entered into an inflationary regime as a result of a Planck scale fluctuation of the Inflaton [17]. The initial state for the onset inflation would not necessarily be thermal. In both of these scenarios we don’t expect a thermal imprint on space time on large scales.
-----------
This is going off track and the references are somewhat technical.
Mixing of scalars and particles is like mixing apple and oranges.

jal

[jal]

Don’t be fooled by the title. This is a comprehensive overview that will benefit most students and most amateurs.

http://arxiv.org/abs/0708.4361
Fundamental Constants
Authors: Frank Wilczek
(Submitted on 31 Aug 2007)
Finally: If the values of fundamental constants vary from place to place, they might also be expected to evolve in time. If different effective universes differ discretely, and are separated by large energy barriers, transitions might be very rare and catastrophic. But if there are light fields that vary continuously, their evolution might manifest itself as an apparent change in the fundamental constants. Thus for example changes in the value of a scalar field η that couples to the photon in the form L ∝ ηFμνFμν would appear as changes in the value of the fine structure constant.
=======
This concept, which would be a permanent change, impossible to go back, and would change "the bounce", to fluctuations within a range of parameters. For example, fluctuation between planck scale and GUT scale,
followed by fluctuations between GUT scale to Baryogenesis,
followed by ....Standard Model ...
Therefore, E8 might be very capable of "capturing" each of those phase changes.

Just a thought ....
jal

[jal]

Maybe, John G can drop in and answer.
I've asked the question elswhere but in relation to E8, I could not see how you treated mass outside of the neucleons.
Where are the Higgs boson particles supposed to be located?
Is there one in the electron, neutrinos, proton, neutron?

[belliott4488]

Hi starkind!
Although your description sounds good, it still leaves a funny feeling.

I hope that the amateurs read and SAVE the doc from "Pierre Darriulat". Things have a habit of dissappearing from the web.

I have another bothering some question.

We have measured gravity down to the size of a hair.
We have gravity when we have matter/particles.
We can justify extrapolating gravity down to the size of quarks.
However, when working with scalars, there are no particles.
What is the justification for assigning one of the scalar to gravity?
jal

Hi, jal; hi, starkind,

I didn't realize you'd resurrected this thread; for some reason it doesn't show up on my list of subscribed threads. Now it should, though.

I hope I haven't missed something crucial, but here's my take on your question re: scalars. First, what do you mean when you say "when working with scalars, there are no particles"? The Higgs is a scalar; would you not call it a particle? It's the only fundamental one, but it's still usually referred to as a particle, I believe. Also, there are composite particles, e.g. mesons like the pions, that are scalars, and they are certainly particles, aren't they? Scalar just means spin-zero, right?

Maybe I misunderstood what you were asking.

In any case, I'm also wondering what you mean when you ask, "What is the justification for assigning one of the scalar to gravity?" The graviton is a spin-2 particle, so it's a tensor particle, not a scalar. Are you referring to something else?

- Bruce

[jal]

Hi belliott4488!
My confusion.
A particle has mass and cannot go at the speed of light.
Therefore, what would you call something that goes at the speed of light.
Just trying to elliminate confusion.
jal

[belliott4488]

Hi belliott4488!
My confusion.
A particle has mass and cannot go at the speed of light.
Therefore, what would you call something that goes at the speed of light.
Just trying to elliminate confusion.
jal
Ha, ha - I'd call it a massless particle! You've probably heard photons referred to that way, and neutrinos certainly used to be called that, before they were interrogated and finally confessed that they had very small masses.

I wondered if by "particle" you meant "matter particle", as fermions are sometimes called, or even baryons, which didn't exist until the time of baryogenesis, of course. I'd object to the latter, since electrons are undoubtedly particles (fundamental ones at that), but they are not baryons, of course.

Bosons (including scalar particles) don't fit with the classical notion of particles, since they obey Bose-Einstein statistics and can do weird things like pass through each other or even coexist in the same state simultaneously. Nonetheless, the gauge bosons -- the photon, W+/-, Z0, and gluons -- are all described as "the particles that mediate the fundamental forces". So .... well, I hope that shed some light on a previously dark spot!

[jal]

I want to keep E8 in mind. Let’s see if I can do a simple paraphrasing of some concepts to see if someone can make a link to E8.

If it is a force or a field then it is massless and moves at the speed of light.

First, gravity.
The gravity force/field that we notice on earth, is affecting spacetime and the result is that the moon is in orbit around the earth. The gravity field/force that is associated with the moon is also affecting spacetime and we notice the tide.

There is a habit of naming the origin/position/location of a force/field as a particle and giving it a special name. In this case it would be a graviton.

Next, Electromagnetic force/field.
In this area we have named all kinds of origin/position/location and tried to classify them into patterns. As a result of using the particle concept for origin/position/location we have had great success in manipulating the EMF and gotten all kinds of technologies.
So far, no one has suggested that EMF is affecting spacetime like gravity.

Next, Strong and Weak Force.
Here, as with EMF, the concept of particles has been used for the origin/position/location of the field/force and again we have tried to classify the the origin/position/location into patterns.
There is the suggestion that spacetime is affected because we have confinements of some forces/fields (The quark and gluons.)
There is a suggestion that in the neucleons, the pions might also have some mass which would then mean that they would not be massless and we would be able to analyse them within a particle approach.

All of these patterns seem to follow some kind of symmetry SU(3) × SU(2) × U(1), ( E8?) and we refer to all of those particles as The Standard Model.

Next is Mass
Not too much is known. There is a lot of speculation.
The approach being used is a force/field which originates from a particle, origin/position/location, which has mass and that this force/field gives mass to the other origin/position/location particles.
That is refered to as the Higgs mechanism. Then the question becomes what gives the Higgs mass and where is origin/position/location of the Higgs?

Finally, massless Preons, and massless scalars
At this stage we are looking at massless scalars or as some would call them massless preons where everthing is moving at the speed of light. Therefore, there are no particles.
This is the study of spacetime, the early universe, and the investigation of possible structures. (E8? LQG?, LQC?)
This is where we find dark energy, Lambda, and vacuum energy.

I have links in my blog, “Recipes: How to make particles”, “A LAMBDA, dark energy, vacuum energy question”

[belliott4488]

Okay! I vow to keep my responses short, so that our posts don't start to experience their own inflationary phase! I'm editing your post to leave just the words that I'm responding to, to keep the overall length down.
... If it is a force or a field then it is massless and moves at the speed of light.
What about the Z0 and W+/-? They mediate the weak force, but they are quite massive.
First, gravity.
... There is a habit of naming the origin/position/location of a force/field as a particle and giving it a special name. In this case it would be a graviton.
No objection, here. I'd just say that it's not the origin or location of the field, which is infinite in many cases, but rather the mediator of the force that is a particle. Close enough?
Next, Electromagnetic force/field.
In this area we have named all kinds of origin/position/location and tried to classify them into patterns. As a result of using the particle concept for origin/position/location we have had great success in manipulating the EMF and gotten all kinds of technologies.
So far, no one has suggested that EMF is affecting spacetime like gravity.
I'm not sure exactly what you're getting at, e.g. when you speak of "manipulating the EMF" - that sounds like what I do when I turn on a light bulb - but again, maybe we're close enough in understanding that we can accept this and move on. One thing, though: I expected you to name the photon as the mediator of the EM interaction, similarly to how you named the graviton. Any disagreement with the comparison?
Next, Strong and Weak Force.
Here, as with EMF, the concept of particles has been used for the origin/position/location of the field/force and again we have tried to classify the the origin/position/location into patterns.
You've used "origin/position/location" to refer to the mediating particles of the fundamental interactions, i.e. photon, W+/-, Z0, gluons, but the patterns that fit the gauge groups you name shortly really include the fermions that interact via these interactions, i.e. the charged leptons and their neutrinos, as well as the {u,d,s,c,t,b} quarks, (for SU(2)XU(1)), and the {r,g,b} quarks (for SU(3)). I would have mentioned them as well.
There is the suggestion that spacetime is affected because we have confinements of some forces/fields (The quark and gluons.)
There is? I'm not aware of this. I thought it was simply a result of the nature of the strong interaction.
There is a suggestion that in the neucleons, the pions might also have some mass which would then mean that they would not be massless and we would be able to analyse them within a particle approach.
Of course the pions are massive - you can look up their masses! They have to be since they are mesons, and as such are bound states of a quark/antiquark pair. Bound particles always have a binding energy, so even if the constituent particles are massless, the resulting composite particle has a mass equal to at least the binding energy (to first order, anyway).
All of these patterns seem to follow some kind of symmetry SU(3) × SU(2) × U(1), ( E8?) and we refer to all of those particles as The Standard Model.
Yup. As long as you include the families of fermions, too, then I agree. Without them, the patterns are kind of empty.
Next is Mass
Not too much is known. There is a lot of speculation.
The approach being used is a force/field which originates from a particle, origin/position/location, which has mass and that this force/field gives mass to the other origin/position/location particles.
That is refered to as the Higgs mechanism. Then the question becomes what gives the Higgs mass and where is origin/position/location of the Higgs?
Well, I'm not sure what you mean by origin/position/location, but perhaps that will become clearer. Also, I'd balk a bit at your use of the word "speculation". While the Higgs boson has yet to be detected, the Higgs mechanism is a crucial part of the Standard Model, and there is no debate that I am aware of about how it fits there. Models beyond the standard model might well offer deeper explanations for the Higgs field, so perhaps that's what you meant.
Finally, massless Preons, and massless scalars
At this stage we are looking at massless scalars or as some would call them massless preons where everthing is moving at the speed of light. Therefore, there are no particles.
This is the study of spacetime, the early universe, and the investigation of possible structures. (E8? LQG?, LQC?)
This is where we find dark energy, Lambda, and vacuum energy.
As I indicated before, I object to the notion that massless particle are not particles, but if you want to think of them that way, then I guess there's no harm. We'll just have "particles" with mass and ... what? "field quanta" with no mass? I'm not sure what else to call photons, gluons or even the W and Z bosons before symmetry breaking, when they are massless.

[jal]

Hi belliott4488 !
That what Happens when doing a simple paraphrasing. Details are left out.
This is better than a detective story or science fiction …. The plot thickens and has taken an unexpected deviation …
What about the Z0 and W+/-? They mediate the weak force, but they are quite massive.
A force that does not travel at the speed of light!
How can that be? What could have happened to cause that?
Next …
Bound particles always have a binding energy, so even if the constituent particles are massless, the resulting composite particle has a mass equal to at least the binding energy (to first order, anyway).
Another mystery … and possibly and explanation …. How to make a massless scalar obtain mass!!!
I'm not sure what else to call photons, gluons or even the W and Z bosons before symmetry breaking, when they are massless.
It’s a good thing that there are “pros” trying to find possible structures (E8? LQG?, LQC?) that go beyond the Standard Model.

I’ll keep reading the various proposed solutions, (approaches), and enjoy every minute.
jal

[belliott4488]

A force that does not travel at the speed of light!
How can that be? What could have happened to cause that?
What could have happened? Why, spontaneous symmetry breaking, of course! To wit, the Higgs mechanism. The most notable effect of the massive nature of the W and Z bosons is that it limits their range, thus the weak interaction is a short-range interaction, as opposed to E-M and gravity, which are both infinite in their reach (as far as we know today).
Another mystery … and possibly and explanation …. How to make a massless scalar obtain mass!!!
Just ask Prof. Higgs - he keeps the answer under his Mexican hat. ;-)

[jal]

Understanding of a lots of recent threads would be made easier by reading the following paper
http://www.math.tu-berlin.de/~fpfender/papers/AMS.pdf
Kissing numbers, sphere packings, and some unexpected proofs
FLORIAN PFENDER_ and G¨U NTER M. ZIEGLER
April 19, 2004
jal

[bockerse]

Hi, so I don't distract from the thread topic more than necessary this will be my only post on this, but you'd mentioned cuboctahedra earlier... my question is, do you or any physicists you know of seriously entertain Buckminster Fuller's Synergetic geometry as explanations for structure in general in physics? Maybe a bad way to phrase the question, and if you don't know who the guy is then just forget it, but he worked very hard to develop an internally consistent description of structure in the universe with the basis of spherical geometry, involving 'close-packing' and various shapes like cuboctahedra. Just thought it was sort of random to read that shape's word on a Physics forum. He's one of the coolest people I've ever heard of even aside from his grand attempts, since he worked to apply the stuff he observed to engineeringly help humanity live better.

Incidentally, to his smartness credit, he was also summoned to a private meeting with Einstein who gave him permission to publish a chapter in one of Bucky's early books detailing practical application of the special theory of relativity. The utterly honest Fuller claimed repeatedly that Einstein told him: "Young man, you amaze me. I cannot conceive of anything I have ever done having the slightest practical application." My first and last post on this in this thread.... sorry for the brief interruption.

-Gerrit

[starkind]

Hi bockerse

yes, cubeoctahedrons have a math which is apparently part of the E8 apparatus. And of course, Synergetics has seemingly evolved into a field alone. I have read some Buckminster Fuller, but nothing strictly mathematical, nothing connecting the mathematics to something physical. I am mostly Ignorant of the current state of the ideas Fuller elaborated. I certainly don't know of the status of his ideas on this forum.

If you return to this dissappointing post, I would be interested in writing some more on the topic another time. It is late as I find this and it has been a full day for me....

So goodnight.

R

[starkind]

Gerit

I didn’t mean to be short last night…apologies and excuses. Certainly Buckminster Fuller deserves his Kudos. I have found in the past that his popularity sometimes subsumes the rational discussion of his ideas…… some well-meaning people seem to prefer his personal deification to any analytical thought about his visionary proposals. I suspect his name will be around as long as we humans persist, as his ideas were far-reaching.

Johannes Kepler also figures tall in the annals of sphere packers.

My recollection is that I first came on the term ‘cubeoctahedra’ when looking for the name of a geometric structure I thought was a good candidate for simplex tiling in three dimensions. I had a lot of fun returning to my childhood, playing with marbles and modeling clay, trying to work out the details. Styrofoam craft balls stuck together with toothpicks made a more workable model.

My thoughts about this pretty much ended when I found out about E8 as one of the foundations of M theory. It appeared to me that the mathematics of E8 was most probably the mathematics to describe the structure I was interested in, but unfortunately for me, I couldn’t make much sense of the mathematical statements. I knew the 3 dimensional sphere packing problem had to be extended to four dimensions, and had some ideas of how to do that, but the mathematical formalism of E8 was chock full of terms and symbols I found completely mysterious.

So I set out to study mathematics, knowing I would never probably learn enough of that language to describe where my visual thoughts were taking me. I haven’t regretted my forays into math, but I am not much closer to being able to use what I know to describe what I see. I am still stuck with English, a language I love, but which is hopelessly unsuited to precise discussions of space-time relationships.

Events are overtaking me again today, but if you, Gerit, or anyone here is interested in some non-technical speculations, which may or may not parallel ongoing mathematical investigations, I still have some that haven’t found words. But now I am called away.

Best thinking….

R

10345

[TheLizardKing]

http://www.ted.com/index.php/talks/garrett_lisi_on_his_theory_of_everything.html

Here we get Lisi describing his theory without mathematics. It is truly sublime.

[bockerse]

I like that Lisi mispronounces Schroedinger's name. It reminds me that he's a guy who probably spent lots of time reading the stuff and not hearing lecturers in courses or seminars actually saying words and names. When I heard the Feynman lectures I likewise realized how mispronounced by me some of the words I'd read were (although Feynman was notorious for misspelling words so maybe mispronouncing them too). My point is that it's encouraging to be reminded that a 'no-name' like Lisi (not that Lisi's necessarily right) or Einstein can make a fantastic contribution with their isolated line of learning and reasoning.

Rock on,
Gerrit