jal said:
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.
starkind said:
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!
starkind said:
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:
Backreaction said:
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):
Garret said:
Coin said:
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, 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 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
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!
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). 
