What is E8 Theory and How Does It Relate to String Theory?

[staf9]

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

I'm going to 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 going to 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.



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 ...

 

[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?
jal

Hm ... "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_(quantum_field_theory)
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]

My Apologies

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. 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. 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]

Quantum variables

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}<br /> \;\;\; 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 referred 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 everything 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 referred 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 everything 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]

Starkind

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