A. Pisko and N. Elsfeld:
El Naschie's work looks rather complicated, and I'd just rather not spend a lot of time with it right now. Also, I seem to need to repeat this again:
Please don't post in this thread -- use one of the others for questions or comments. This thread is mostly for posting interview responses. If you post here anyway, I will make fun of you.
It is impressive that your fanaticism overrides respect for my wishes. You aren't perchance also involved with the Ron Paul campaign?
From a recent interview:
--Here at SciAm we never jumped on the bandwagon regarding your E8 theory,
I had kind of wondered about that, since the representation theory involved has a visually appealing aspect that would probably make for a good SciAm article. But I certainly appreciate and commend conservatism, especially since some of the media response went overboard.
--but I _am_ doing a short "second day" story (more like "second month" at this stage) briefly assessing where things stand now that the shouting has died down.
OK, great, I'll help out however I can.
--Mainly I just need to confirm that I have the right impression (from following various threads online, such as the PhysicsForums thread) about what you are doing with regard to the theory. Namely, you continue working on it to try to overcome the various problems that were pointed out (some of which you had already mentioned in your preprint as being areas needing further research).
Yes, that's correct. The largest problem is the description of the second and third generation fermions, and this was discussed extensively in the paper.
One thing I could have done a better job of, but will try to remedy as things develop, is describing the fact that this general technique of describing all fields of the standard model (bosons and fermions) using one connection does work to describe what we currently know. It is only the fit to E8 that is rather tenuous at this point -- but this fit to E8 was such an exciting possibility that I ran with it in this paper.
--Also, do you have any real collaborators at this point?
I prefer to work on my own, although I've certainly been communicating with a great number more people. It's been so long since I've worked with a collaborator, I'm not sure I remember how. But I have been talking with people as they've worked through the paper and used parts of it to pursue their own ideas, which has been good.
--Have you been invited to give talks anywhere recently?
Yes. My earliest upcoming talks will be at the TED conference on Feb 28, then I'll be talking with physicists at UC Davis on March 7.
--About the problems... I know from the beginning you've been saying that the issue of getting all three generations of fermions "needs further research."
Yep, right now there are just many interesting clues.
--About Distler's claims that even one copy of the proper chiral representation does not sit inside E8 as it needs to, I understand your position is: you're not sure if Distler is right in his claims
Yes, I think he may be making a mistake in his choice of complex structure when he uses conjugation to replace right-chiral fields with anti-left-chiral fields in describing the standard model. It's a subtle calculation, and it's possible that either of us could be confused on this point. I prefer to work through these things slowly and carefully before enjoining arguments though.
--even if he is, using the complex form of E8 instead of the real will, without any doubt, fix the problem.
Yes. If you read his argument, he's unhappy with the way the real spinors in E8 are being twisted in this theory to build complex spinors. If you start with complex spinors in complex E8, there's no problem -- at least not for the first generation. But at this point I'd prefer to stick with a real form of E8 if possible.
--I have to say the issue that bothers me the most is the fundamental one of mixing fermions and bosons so closely together without having some kind of superalgebra.
Ah. There is actually a large but unfortunately somewhat byzantine literature on this construction -- it's part of the BRST formulation.
But the mathematics of this construction are rock solid. The place I first learned about it was in this review paper:
http://arxiv.org/abs/hep-th/0201124
where, on page 70, it's defined and described as a "generalized connection":
w = A C
in which A is a 1-form and C is a Grassmann valued field, both valued in parts of a Lie algebra.
Using the algebraic structure of the exceptional groups, the C can be a spinor field algebraically. Unlike in supersymmetry, these A and C never mix -- so they can have different units without difficulty. The main advantage of formally adding them is for the distributive property in the Lie bracket -- giving an expression referred to as "The Russian Formula." (Have a quick look at page 70 of the above reference).
For a more mathematical description of this kind of BRST extended connection, this recent math paper is typical:
http://arxiv.org/abs/0710.5698
Unfortunately, this sort of BRST symmetry is less familiar to people than supersymmetry, even though it plays an essential role in QFT.
You might have noticed that Peter Woit also likes the idea of possibly interpreting these "ghost" fields, C, as fermions.
I can go into more detail if you're still not happy with this formal addition of A and C -- it's bothered other people as well, but I'm quite confident in this aspect of the theory.
--In any case, I look forward to your reply.
Sure, let me know if you have other questions. Good luck with the writing.
While I don't understand the incredibly difficult math and other operations you have used to assemble this theory dude I think you may have gotten it.
I have been trying to get a feeling that string theory was the way to go for many years now. To no avail. Calebi Yau? Vibrating strings? While it was getting close, it IMO missed some things. Things that I could not get. Brian Greens book was the best book out there that I read.
Intuitively, it seems that you have something here.
Keep at it and good luck.
Garrett,
Can BANG CRUNCH BANG be right if it is a balanced equation.
The energy equation for ex-nihilo does not balance it is 2E=2M*2C^2.
But the energy equation for the big crunch balances it is.
1/3 APPLE 1/3 ORANGE 1/3 ORANGE= 1 APPLE/ORANGE.
Iam amazed by the intolerance of this community.
The equation for the universe must balance for evolution since you cannot get energy from outside the universe from another dimension like in ex-nihilo.
The four states of matter become one.
1/3 FERMI DIRAC EQUATION 1/3 BOSE EINSTEIN 1/3 BOSE EINSTEIN= 1 BOSE EINSTEIN/FERMI DIRAC.
And one unstable state of matter explodes to become four.
Of course this can be a better bomb but it can also be a better nuclear reactor.
Particles X an Y cannot be in the SAME STATE at the SAME TIME in the SAME PLACE except before the big bang.
The previous universe may have been a Godel one and a contradiction in terms of time so that it gives rise to a non contradictory explosion and the laws to our universe.
What is so silly about that that you can't print it.
Are people not allowed to talk anymore about religion.
Steve
Jim,
Thanks for the encouragement.
Richard/Steve,
I will put this as politely as I can: As far as I can tell, you are spouting complete nonsense. I don't wish to insult or anger you, but you should consider whether you want to waste your time communicating with someone (me) who doesn't appreciate your effort.
Hello Garrett,
I'm only a physics amateur, I write from Pesaro, Italy; I would ask you this question (or more probably to correct my question if badly formulated):
Which kinds of "charge" are beyond the 8 dimensions of the E8 root space illustrated in the famous beautiful animation ?
Perhaps I did't understand enough your phrase ("And each of these has eight coordinates, corresponding to the eight quantum numbers (charges) for the particle"), but I would expect somewhat like:
Axis 1: electric charge
Axis 2: strong interaction "colour"
...and so on.
Of course, I'm an enthusiastic fan of your E8 theory, I'm 45 and it is what I hoped to see when I was 20 and I read about electroweak unification... Please continue to keep us prophanes informed! Thank you and good work!
Dear Dr. Lisi
I am 85 years old and thought the following may encourage you to continue your excellent work. What the young W. Heisenberg had to do to get his Nobel prize and invent quantum mechanics was to make sense of thousands of numerical results found
experimentally. Without really knowing what he was doing, he told me he went on making patterns out of these numbers and invented rules to make them follow any system at all. Later on his Prof. Max Born discovered that his student Heisenberg had rediscovered an obscure part of mathematics called matrix multiplication which does not commute. You and your colleagues are not doing numerology when you are fitting the standard model into E8. You are doing basic and fundamental physics modeling. Those who say this is numerology do not understand either physics or mathematics, or in fact numerology which was an important part of the work of Backmeister Fuller.
With my best wishes to you, El Naschie, Lee Smolin and all free thinking and adventurous young men like you.
Hi Garrett,
Have you had an opportunity to read my book on "New Approaches Towards A Grand Unified Theory"?
Upon reading your theory again (and I still don't understand everything!), I think I can better translate the bosonic component of your theory into my theory. As a Particle Physicist, I preferred to call my theory a GUT, because TOE is String Theory nomenclature, and I was slow to embrace the importance of multiple (10, 12, 26?) dimensions. In Sections 7.3 and 7.4 of my book, I came to the conclusions that the first ten dimensions are composed of spacetime and two hierarchal (in the sense that one is more physically relevant to our spacetime than the other) 3-branes; that these dimensions unite as a 10-dimensional SU(11) "Bosonic GUT"; and that the forces relate to dimensions as follows: Strong (1st and 2nd D), Electromagnetic (3rd D), Weak (4th D), Hyperflavor (5th and 6th D), Gravity (7th D), and WIMP-Gravity (8th through 10th D). In Section 7.5, it looks as if the three dimensions of WIMP-Gravity might collapse into one dimension that interacts with tardons, and two dimensions that interact with tachyons; which implies that my 10-D SU(11) "Boson GUT" may collapse into an effective 8-D SU(9) "Boson GUT" of order 8 x 10 that could coexist with fermions in your 8-D E8 TOE of order 8 x 31. I agree with the possibility of an effective 8-D GUT/TOE, but String Theorists will not be happy with such a small number of dimensions.
I thoroughly enjoyed your G2 approach to the Strong force. It is very similar to my U(1) x SU(2) x SU(3) approach to Hyperflavor-Electroweak. The difference is that your 2-D approach uses nested 2-simplices of quark and anti-quark colors, whereas my (2+1+1)-D approach uses nested 3-simplices of quark and lepton hyperflavor-weak isospins.
The biggest difference between our approaches is that I introduced a (2+1+1)-D Hyperflavor-Electroweak and a (3+1)-D Gravity/WIMP-Gravity (that might collapse into a (1+1)-D Gravity/WIMP-Gravity model), whereas you used a (2+1)-D Pati-Salam Electroweak model and a (1+1)-D Cl(3,1) Gravity model. It looks like you have projected the four dimensions of Hyperflavor-Electroweak into the three dimensions of a Pati-Salam Electroweak, so you have potentially ignored details associated with my GUT's fifth and/or sixth dimensions.
In Section 2.4.2, you implied that the E8 triality may break down. Figure 2 implies that the 240 roots of E8 may decompose as 240 = 8 x 30, and 30 is divisible by three. Are there any significant 5-fold symmetries (30 is also divisible by 5) within this geometry? My GUT theory implies five generations of fermions.
Occam 's razor is a good philosophical approach (I also like KISS - Keep it simple, Stupid! and PhD - Push here, Dummy!), and we shouldn't introduce more complexity into the theory than is required to explain our observations (String Theory with 10500 parameters is definitely guilty of this, and my GUT might be as well). However, I think that our approaches towards the Weak and Gravitational interactions imply that there is more to both forces, and we shouldn't call this a TOE if these 8 dimensions imply extra dimensions that aren't described. For that matter, can a True Theory of Everything exist in less than 26 dimensions?
Good Luck!
Ray Munroe
If I understand Lisi's work correctly, he does not develop an ad hoc model for the spacetime of particle physics nor put a model of particle physics into a spacetime of this or any other dimensionality. In other words, he does not proceed as in string theory or in loop quantum gravity. He also does not extend quantum field theory to become a quantum gravity field theory.
What Lisi does is take an already existing symmetry group and its corresponding Gosset, i.e. a four-dimensional polytope upon which the E8 manifold is based. Then he works carefully a one-to-one correspondence between the different points marked by eight-dimensional vectors called octonions and particles with the aim of recovering the standard model and making some prediction for extending it to conform at ultra high energy to the idea of unification, by showing that all the fields of all the different fundamental interactions could be obtained from the same E8 manifold. Professor Lee Smolin an open-minded guiding light in quantum gravity concluded that it is a neat way to seek the unification of all fundamental interactions in this basically non-conventional way.
Lisi's work is therefore combinatoric in the spirit and quite near to that of Sir Roger Penrose's program. Also not surprisingly it does not collide with the loop quantum gravity philosophy or with the basic ideas of Mohamed Elnaschie E-Infinity theory except for not admitting irrational numbers at a fundamental level. Seen in this light, Lisi's theory is not restricted by mathematics used traditionally in this field which is an advantage.
I think people tend to forget that the founding fathers of quantum mechanics were appalled by Feynman's path integral and string theory took even much longer to be accepted. All what I am saying is give Lisi a chance. I am not directing this toward the young researcher but I am addressing the establishment, particularly the strings community.
As for Lisi, my only advice is that he extend combinatoric as the factorial function was extended to gamma function and topological dimension was extended to non-integer Hausdorff dimension. This would be a revolution similar to Einstein bending spacetime and making it curved.
Dr. L. M. C.
I am a lay person, and I have read Brian Greene's book about string theory. String theory does not allow for the existance of singularities and quantum chaos. What implications does your "Exceptionally Simple Theory of Everything" have regarding singularities and quantum chaos.
Maybe I missed something, but I'm confused as to the relationship of this model with time. Maybe I'm being to simple here, but is there any way this model reflects the concept of infinty? The E8 design is a very defined shape that appears to have a definate beginning and end.
Yes of course you have týme ýn Lýsý's E8. It ýs the same sýtuatýon as wýth Eýnsteýn. If Einsteýn's space týme ýs compact and closed, then ýt ýs lýke on a sphere. There ýs no begýnnýng and no end although ýt ýs closed and compact. The E8 you see ýs a projectýon of what ýs close and compact but has ýnfýnýte týme. There ýs no problem here at all. However Lýsý dýd not embed E8 ýn any spacetýme. But he can very easýly. Someone on thýs sýte poýnted out that embeddýng 248 ýnto the 26 bosonýc dýmensýons you get at the end 548 dýmensýons or 4 x 137. It ýs somewhere on thýs sýte. You wýll easýly fýnd Sara.
Dr. Robert Fýsher
Yes of course you have time ýn Lisi's E8. It is the same situation as with Einstein. Ýf Einsteýn's space time is compact and closed, then it is like on a sphere. There is no beginning and no end although it is closed and compact. The E8 you see is a projection of what is closed and compact but has infinite time. There is no problem here at all. However Lisi did not embed E8 in any spacetime. But he can very easily. Someone on this site pointed out that embedding 248 into the 26 bosonic dimensions you get at the end 548 dimensions or 4 x 137. Ýt is somewhere on this site. You will easily fýnd it Sara.
Dr. Robert Fisher
Sorry dear friend but the correct word is Gibov copies. I hope it is only a misprint. There are many similar maladies in the quantum theory of fields. All these problems can be solved by summing over all compact and non-compact harmonic exceptional two and three stein spaces. For an in-depth consideration of this and related problems, see Chaos, Solitons and Fractals in science direct. The paper is titled "The internal dynamics of the exceptional Lie symmetry groups hierarchy and the coupling constants of unification". See also related papers by L. Crnjac, Ji-Huan He, Ayman Okaby as well as the various papers by Garrett Lisi and Lee Smolin.
D. Wong
A mathematical derivation of the mass spectrum using essentially Lisi's E8 theory extended to exceptional family has been given recently. The paper is in an Israeli journal published by Freund in Tel Aviv "International Journal of Nonlinear Sciences and Numerical Simulation". 9(3) pp. 307 - 208 (2008). The paper is called Montonen-Olive duality and the mass spectrum of elementary particles via E-Infinity.
A. Mehra
Dear Garrett,
I think I have worked out the similarities and differences between my ideas and your ideas, and the answer is E12 with a rank and effective dimension of 12 and an order of 684. Of course, several mathematicians just said "There's no such thing", and maybe someone can prove that my "E12" should be defined differently, but that's what I used for my TOE.
Your ideas inspired me so much that I had to write a new Section, reference your work, and publish the Second Edition of my book "New Approaches Towards A Grand Unified Theory". I published this book through Lulu.com, and free partial previews of "Section 7.7 - A Deceptively Simple E12 Theory of Everything" are available through Lulu. Lulu will have the 2nd edition - I'm not sure which edition (if any) the other online book retailers will have this month.
I didn't need any ghost particles - I was able to fill all available particle states with my SU(11) boson GUT and Hyperflavor fermions. I concluded that a Supersymmetric Exceptional group MUST have fermion singlet representations, and that these fermions become the basis vectors for the adjunct Supersymmetric representation. A simple example is your G2 of color, with 2 basis vectors: g3 and g8; twelve roots: 6 gluons, and 6 up quarks/ anti-quarks; and a 2-dimensional fermion color singlet: electron/ positron. In the adjunct Supersymmetric representation, the 2 basis vectors are now: selectron/ anti-selectron; the twelve roots are: 6 gluinos, 6 up squarks/ anti-squarks; and the 2-dimensional singlet is gluino-3/ gluino-8. When we add a 4-dimensional fermion singlet to an F4 group, then our 24-plet of fermions with a 3-fold triality symmetry becomes a 28-plet of fermions with the 7-fold "septality" symmetry that is characteristic of Hyperflavor.
Table 19 is a symbolic E12 TOE. Unfortunately, Lulu's preview software didn't like Table 19, so I excluded it from the preview. Dr. Robert Fisher is correct that we need a Lagrangian, but I have exhausted this month's inspiration...
Any new ideas from you?
Have Fun!
Ray Munroe
such a symmetry...
as it's "everything": there is no more left&right...
how we can more speaking about "symmetry"
is it a "point" symmetrical?
cherio:
e
Garrett,
An article I've read describes E8 as encapsulating the symmetries of a 57-dimensional geometric object and is itself 248-dimensional.
Do these numbers in reality refer to the number of variables in this particualr Lie group and the geometry described by it? Discussing this with a friend, there remains some confusion about how these multiple 'dimensions' relate to the 4-dimensional world we're familiar with. Are these multiple dimensions merely characteristics of this particular mathematical tool used to describe our 4-dimensional world? In other words, are they real-world dimensions or merely the mathematical/geometrical structure of the E8 formalism?
Thanks.
Lou Abshire
Houston, Texas
Some people seemed determined to supress different ideas.
But everybody should have their say whether scientist or layperson.
The snobbery that prevents Garretts own work from being published should not be repeated here.
Rich.
El Nacho es grande