A Geometrical Approach Towards A Theory of Everything by Ray B Munroe

MAthematics is simply a reality of physics, and it is not going to get more elementary. Newton had to invent calculus in order to advance his laws, and calculus is a senior high school subject these days. Einstein used Riemannian geometry to formulate general relativity, then a 60 year old mathematical topic, supersymmetry takes us into topology, a mid-20th century mathematics, and on it goes. Clearly mathematics is not physics, but a decent knowledge of modern mathematics gives you a better tool box to work with.

In Ray's K12 or H_4xE_8 I am trying to figure out what the physical basis for this is. The 120-cell tessellates an AdS spacetime. There is also an interesting duality between AdS_3 and QCD. The automorphism of the Jordan algebra is the exceptional G_2 group, which contains as its maximal subgroup SU(3). So this breakdown seems to suggest some sort of duality between AdS structure of spacetime and QCD. I think this holonomy is some sort of extended idea similar to quantions.

So to pursue physics it does require that one have advanced mathematical concepts at hand. There seems to be no escape from this.

Lawrence B. Crowell

Dear Lawrence,

Mathematics is one of the cornerstones of physics.

Regarding the use of mathematics in physics, I used math in my own ideas. I am not opposed to Emile and Florin's use of quantions - I simply have not yet been convinced that we cannot accomplish similar things (even though I know that the mathematical structures are different) with Pauli and Dirac matrices, but I scored both of their papers well, and remain open-minded regarding their ideas. I truly would like to see a quantion theory with interactions.

K12' has a G_2 of color buried deep within (see Lisi's paper or Ref [11]). Regarding the G_2 holonomy, Gordon Kane also referred to this mathematical structure. I was originally distracted by the similarities between K12' and Klein's Chi(7), and thought I was working with an I_2(7) seven/fourteen-fold symmetry. But now I realize that I may be working with a Lambda_{10}, and NOT a Chi(7). If it is a Lambda_{10} (Conway & Sloane "Sphere Packings, Lattices and Groups" - Laminated Lattices), then it would have the same five/ten-fold symmetries as the G_2 holonomy. I think this five-fold symmetry is important to Supersymmetry, where we might expect five fundamental particle multiplets: scalar bosons (spin-0), matter fermions (spin 1/2), vector bosons (spin-1), gravitino fermions (spin-3/2), and tensor bosons (spin-2).

Have Fun!

Ray Munroe

Dear Lawrence,

Another oberservation:

If I understand quantions properly, they are an effectively two dimensional algebra in competition with the Pauli sigma matrices. Just as we can build twistors (an equivalent to Dirac gamma matrices) out of pairs of Pauli spinors, we should be able to build relevant 4-D structures out of pairs of quantions. That should be relevant for 4-D spacetime.

BUT, WE are also dealing with an AdS 2-D M2-brane (my fifth and sixth dimensions). Is the rule of algebra in these dimensions based on quantions or on Pauli matrices? We also anticipate anyons in these bizarre dimensions. Would one algebra be more likely to yield this feature than the other?

What are your thoughts?

Ray Munroe

Dear FQXi Friends,

Most of my scores have been 8's or 1's. Recently, more of the scores have been 1's. If you think you have found an error in my logic, please point it out. Constructive critisism would be greatly appreciated if you can spare the time (I understand that we are all under time constraints to read these papers this month).

Thank You!

Ray Munroe

I noticed that I too am getting a string of ones, as are I think a number of other papers. It is worth noting that the highest score is now less than 5, and I suspect that a few people with low scores are trying to supress other scores. Almost all the scores have decreased in the last week or so. Some of the papers with very low scares are honestly rather marginalin their intellectual value, and I wonder if some of the writers of these are trying to drag the whole process down. There are a number of pretty good papers here with scores in the 3 to 4 score level, which honestly should be in the 6 to 7 score level.

The anyonic nature of the M2-brane is mirrored in the lagrangian for the whole Jordan exceptional algebra. The diagonal terms define a simple Chern-Simons Lagrangian, while the rest of the Lagrangian (from the determinant of the matrix under triality maps) shares this feature as well. The M2-brane is S-dual to the D5-brane (black brane) in the NS sector. The world sheet for this is a 6-volume.

More later, when I find the time.

Cheers LC

As I left you page here and went to the main page I just noticed everyone's score appears to have dropped, including mine. So I racked up another one, as did most everyone else I think.

LC

Perhaps someone is reaching for the prize money using a tactics other than intellectual prowess. Is there any way to tell whose score did not rack up a "1" during this time period? It would not be a definitive way to pinpoint the source/intent, but it might help to take a look.

If this is happening, and honestly I hope not, it is mostly likely not somebody raching for prize money, but rather someone who thinks, "Well if I'm going down with a score of 1.4, then dammit I'm gonna take you down a notch as well." It is probably hard to prove something like this is happening anyway.

LC

Dear FQXi Friends,

While I think of scores of 1's and 10's as being statistically unlikely, many of the voters obviously think of this as a way to make their votes count more heavily. Perhaps this strategy will mostly average out and the best papers will win anyway. Perhaps it is good that they think highly enough of me and Lawrence as competitors that they want to take us down.

But seriously, I would go back to the drawing board and rethink or give-up on this entire Geometrical Approach Towards A TOE if someone could prove me wrong.

I welcome constructive or destructive criticism. All I ask is that you read the entire paper first.

Have Fun!

Ray Munroe

The scoring is funy in some ways, and it seems to lead to this general suppression of scores. I have noticed in the last several days how a whole list of papers with various scores will in a day be reduced by about the same amount. I agree that people should take the trouble to read papers before scoring them. I have actually only scored a few, which have been some that I thought were really good and conversely bad. I am waiting to cast most scores until close to the end.

LC

Lawrence,

I had this idea of some evil genius somewhere with an evil plot to take over the contest money. They might even be a supervillian! Actually, I have a hunch who it might be. If it really is the person I'm thinking of, they are capable of succeeding with honest intellectual hard work.

Ray,

Scores of ten are not that statistically uncommon; it depends upon the reader. I gave at least one ten to the papers I've read. I could tell a lot of work went into it, and it was potentially useful.

Dear Dr Cosmic Ray ,

Your approach hasn't false in fact .Personally I noted 8,I have voted perhaps 10 times,and always I read a paper , and it was sincerely because you and Lawrence are two mavericks and your extrapolations are very relevant even if I don't agree with some ideas like multiverses ,extradimensions ,strings ,higgs ,Lie algebra.All that isn't sufficient and too much mathematical without the real limits .Now of course all can be synchronized with the physical laws .

I have learned a lot with both of you since I have known FQXi.

My vision of your work is simple ,the imaginaries and the extrapolations must be physicals .The thermodynamic is essential in my opinion .

The complexs too need limits ,without limits ,it's infinite and the physicality don't need that .

About the contest ,I am surprising by some comportments ,like a game ,it's sad .But it's not important in an universal point of vue ,but on Earth indeed ,some systems are bizarres .If the strategy becomes a machiavellism like a play of chess ,it's sad .There I don't understand this human nature .

My conclusion about these contests ,

in resume 15 per cent of fundamentals and conscious

30 per cent in the imaginaries

40 per cent with a mix of fundamenatsl and theories where???

10 to 90 hihih per cent of business practices

5 per cent of jokes

HIHIH dear Ray you you are in the two first lines ,with 85 per cent in the first line and 15 in the imaginaries

Best Regards

Steve

In your works ,similars ,of course You ,Lawrence ,Florin ,Emile ...has some rivairies indeed ...perhaps it could be well if you work together in team for your researchs and works .

The team with a good mind can make interesting things in complemenatrity .The machiavellian mind falls always ,it's the real equilibrium of our universe .

Always the bad falls.

Best Regards

And good luck for this competition too

Steve

Dear Steve,

Thank you for your support.

Truly, I do not care about the money. I just love physics.

My purposes for entering this contest were: 1) to make new contacts with interesting people (checked box), 2) distribute my ideas in a larger forum (checked box), and 3) attempt to gain FQXi membership (unchecked box thus far).

It is funny to me that the concept of a TOE draws instant criticism or appeal - there seem to be few unbiased perspectives between these extremes.

It is OK - I welcome criticism. The cowardly and silent 1's bother me more than legitimate criticism.

Have Fun!

Ray Munroe

I agree that the prize is not what I am after. I will confess I would be unhappy if my paper fell towards the bottom of the heap. Yet the real purpose is to increase communications of new ideas with people and potential collaborations.

Cheers LC

You are super Dr Cosmic Ray ,don't change never ,

And don't forget ,your faith is welcome for the humanistic sciences cenetr .It will be a real honor for me .The faith and the skills ,waawwwww it's the solution ...

Take care

Steve

Ray,

(I submitted this on Abhijnan's blog area)

This problem is related in some ways to Perleman's proof of the homotopy equivlanece of homology spheres. I have been doing some background reading on this problem and am in many ways suspect this has some very deep mathematics to it. If you take a toy balloon and twist it up into various shapes it will smapp back into a spherical shape. I assume the surface is perfectly frictionless so that tying it up does not clamp it into shape. This Hamilton flow is such that it is always guaranteed to bring the space back to its minimal configuration. If you look at Perelman's paper you will see how he assigns entropy functionals to this! So a three sphere is guaranteed to evolved by the Ricc flow

dg_{ab}/dt = -2R_{ab} ...

This idea is carried over to higher dimensional spaces, and this evolution is conidered according to Turing machine logic. Look at the Novikov theorem quoted in Abhijnan's paper. So the logic is whether one can compute the minimal configuration of a space by Turing machine logic and assertain whether it is the same space as a known space in its minimal configuration. This is important for understanding all these strange Calabi-Yau spaces and whether one can compute them distinctly from each other.

The one thing which needs to be done is to carry this from homological theory to K-theory. K-theory is a much more powerful approach to topology, and it has connections to noncommutative geometry. So this is a vast domain which has many areas left unexplored. I am still patiently trying learn the foundations which Abhijnan quotes in this summary paper.

It is too bad this is not receiving a higher score than what it has garnered so far. This is one of the better papers in the whole lot submitted here.

Cheers LC

Dear Lawrence,

Abhijnan's paper does contain more physics than most of the papers in this competition. In my opinion, too many of these papers contain more philosophy than physics. Philosophy is certainly important to physics ("natural philosophy"), but we are past the days of Aristotle - we do have real knowledge and data to work with as well. I am tired of reading modern "hand-waving" arguments about how TOE's do or don't exist that rely exclusively on previously existent theorems such Godel's Incompleteness Theorem or the Turing Machine. I prefer the Nike slogan "Just Do It!".

Although Abhijnan's paper does contain a lot of physics, his goal of computing the string ground state is absolutely impossible with modern computers in the absence of a real breakthrough in our understanding of strings or TOE's. He indicates the possibility that patterns might simplify the computation. Perhaps my lattices ARE the patterns he needs! My alliance with Mohamed El Naschie last year led me to think that the difference between the finite K12' minimal roots and the nearly infinite Universe can be represented with a fractal approximation. My papers emphasized the minimal roots of K12', which are our nearest-neighbor lattice points, but this lattice could also have next-nearest-neighbors (similar to the long roots of K12, and also similar to the hyperflavor leptons and quarks in my book), next-next-nearest-neighbors, and so on to infinity. This is the physical reason why a fractal approximation may be appropriate.

I have been rereading your Jordan paper. You combine some interesting mathematical structures in your paper. Your 27 dimensional Jordan transformation is the natural extension to Dray and Manogue's 10 dimensional transformation. I think your physical interpretation is different from mine, but I'm not certain of myself either - I'm still considering the problem, and how it might tie into Supersymmetry or Feynman diagrams.

Have Fun!

Ray Munroe

A fair number of these papers are more philosophical than physial. Some make references to results. Wolfram has entered the fray. He does make a statement which occurred to me some years ago. In effect there is an equivalence of computational complexity in systems. The thought occurred to me years ago that if I miz cream in my coffee that the system is computing the complex folding of the cream by hydrodynamic means. We don't normally think of this as complexity as such, such as with an organism or a computer. Yet a part of the problem is one of perspective. We don't set up the motion of cream in coffee to extract some output.

I am working on a problem involving octonionic black holes, or a way to use the heavenly phere structure of the Jordan exceptional algebra as local systems of 26 dimensional Lorentz spaces. The identification between the three octonions by the triality operation and the light cone structure of the diagonal elements reduces this to 10 and 11 dimensions. The J^3(O) is locally diagonalized by the F_4 group. The F_4 group is the Hurwitz quaternion "1154" representation of the 24-cell. The 24-cell has B_4, D_4 and F_4 representations and the quotient F_4/B_4 determines a short exact sequence between spin(9) and the Moufang plane OP^2. This local Lorentzian system is then given by connection coefficients on this system.

The Jordan algebra of a vector space V, which can be O, is ~ V\oplus R according to the mixed product

(u, α)*(v, β) = (αv βu, (u,v) αβ), (u,v) = \langle u, v\rangle

but the inner product gives

(u, α)*(v, β) = (u,v) - αβ,

which is the Lorentz metric. Thus the diagonal entries of the J^3(O) set the three copies of the octonions in a Minkowski geometry. The diagonalization of the Jordan matrix is the defined locally with a "gauged F_4," which defines both the Minkowsi structure and the quantum algebra locally and constructs connection terms between local charts (local inertial frames).

Forget quantions, this stuff is much more general and powerful.

Lawrence B. Crowell