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

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  • #121
Could you give an example of assigning one of the scalar to gravity?
 
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  • #122
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
 
  • #123
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
 
  • #124
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?
 
  • #125
jal said:
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
 
  • #126
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
 
  • #127
jal said:
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!
 
  • #128
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”
 
  • #129
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.
jal said:
... 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.
jal said:
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?
jal said:
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?
jal said:
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.
jal said:
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.
jal said:
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).
jal said:
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.
jal said:
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.
jal said:
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.
 
  • #130
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
 
  • #131
jal said:
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).
jal said:
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. ;-)
 
  • #132
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
 
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  • #133
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
 
  • #134
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
 
  • #135
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
 
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  • #137
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
 

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