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

This looks similar to the paper you sent to me in August, though more condensed. I will give this a read by tomorrow.

Cheers LC

Hi Ray,

Glad to see that you are participating in this contest. I will read you paper carefully in the following weak. Good luck in this contest!

Hi Dr Cosmic Ray ,

Happy to see your paper on the contest .

It's well condensed your work ,and relevant .

Good luck .

Steve

Dear Ray Munroe,

A theory of everything would endow us with God-like powers, masters of the laws of the Universe. The idea of getting a theory of everything is the idea of the end of fundamental physics [Giovanni Amelino-Camelia]. Thus, if somebody creates TOE, we can close all physics laboratories because we are masters of the laws of the Universe.

Consequently a TOE cannot be created for following reasons:

1. We don't know the nature of space-time, matter, gravitation, inertia, ets. There are a lot of 'holes' in all physics theories. Can we create a TOE using our poor knowledge about space-time and matter?

2. TOE cannot be created because it will be the end of fundamental physics.

Thus I have a question. Why theorists look for TOE if this theory cannot be created by definition? Maybe they must look for less important theories like unification of three interactions. Do you think TOE must be a mathematical model only?

Sincerely,

Leshan

I read your paper. I post in the following from what you wrote:

An important decay route for K12' is K12SU13SO24E8 , where the interpretation is that the SU13SO24of rank 12 and order 444 is a Super Yang-Mills Boson GUT with tensor, vector and scalar boson content - many of which are hypothetical and as yet undiscovered (Ref. [3] has an expansion of the prior Icosahedral example - Equation 3), and the E8 of rank 8 and order 240 is a Fermion particle multiplet. From its Dynkin diagram, E8 has symmetries of 240 82 35, and thus exhibits two-fold "duality", three-fold "triality" and five-fold "pentality" symmetries in an eight-dimensional "octality" space. To the author's knowledge, Lisi never identified the pentality symmetry. Curiously, H4 has the same symmetries of 120 4 ´ (2 ´ 3´ 5) in a four-dimensional "tetrality" space.

This appears to take off from what we communicated about last August. One point which is worth pointing out is that SU(13) ⊂ SO(26), which is a bosonic realization of the 26-dimensional string. Hence the open string with α'M^2 = n - 1 is replaced by α'M^2 = 4(n - 1). The SO(24) multiplet of physical states for the open string are doubled, into SO(24) x SO(24) in the closed string. The gravitational massless state is the symmetric part of |Ω^{ab}> = α^a_{-1}α^b_{-1}|0> in the closed string. The state ½ |Ω^{(ab)}> is a spin 2 field, which is the graviton. The antisymmetric portion is a second rank tensor. The antisymmetric portion will then define the gauge fields.

I will have more comments to follow.

Cheers LC

I have some further comments as I look at your essay again. One problem with Lisi's program was that he framed the weak interactions with gravity. In order to do this and keep within the strictures of the Coleman-Mandula theorem is to use supergenerators or Grassmannians. Supersymmetry was advanced in part for this purpose.

Cheers LC

Dear Leshan ,

You say

"TOE cannot be created because it will be the end of fundamental physics."

I think what a theory evolves ....and the fundamentals show us the road ...

It's the same with the general relativity ,this theory evolves like all .

A real theory permits to evolve and never shows an end road of fundamenatls of physics ,because a real theory inserts the fundamenatls ,simply .

In the extrapolations of Ray ,Lawrence ,Lisi ,Florin,.....it's mathematical and this technic needs limits and fundamenatls .But these extrapolations are interestings for the geometry and the symmetry .

Of course the physicality is not present but if the fundamenatls are inserted and if some realities are considered thus it's relevant .

I think what when the two senses are harmonized ,phys/math,thus it's very relevant .I dlike see a superimposing of these works with a kind of sorting with fundamenatls ,for me the rotating spheres implying mass .

Steve ,The theory of spherisation ,a UTE or GUT of Rotating Spheres ,the physicality is an effect ,the mass .

Sincerely

Steve

Dear Lawrence,

Of course we have been talking about these ideas for at least a couple of months, I referenced your blog comments in the Ref. [3] paper posted above. It is interesting to me that the maximum dimensionality of the bosonic operators keeps coming up one short of the space dimensionality. In my 12-D K12' space, my highest-dimensioned bosons are 11-D. Similarly in your 27-D space, we have an SO(26) with a 26-D bosonic string.

It is good that you found a graviton in the mathematics. I felt certain that this model was large enough to include Gravity, a Gravity-brane , and a related short-ranged WIMP-Gravity force.

I obtained much inspiration from Lisi's paper, but still think that the E8 is large enough for a particle multiplet, but not all of the known interactions as well.

I tried to find the form of a Supersymmetric K12' in Ref. [3].

Dear Steve,

Perhaps the GUT is an evolution process. Perhaps we will never truly know everything. As soon as I work out K12', Lawrence will have J27 ("J" for Jordan?) finished. My simplices would probably get along with your spheres.

Have Fun!

Ray Munroe

The real crux of the matter seems to be with G_2 automorphism over the octonions. This determines a holonomy which for N fixed points or Killing spinors determines the number of supersymmetries in the theory and the conformal structure of holographic principle.

Cheers LC

At the bottom of page 3 you write:

These geometrical constraints may be related to Clifford bivectors and the first-class constraints RB Munroe Jr, What is Ultimately Possible in Physics - A Geometrical Approach Towards a TOE 4 of BRST formalism (Becchi, Rouet, Stora and Tyutin) [9]. Note that antiparticles could simply be the inversion operator applied to these particle states, thus yielding a nested dual tetrahedron.

I am intrigued by this comment and I was wondering if you had further developments on this.

Cheers LC

Hello ,

Dear Ray or Lawrence ,

Could you explain me what is this holographic principle ,please ?

Regards

Steve

Dear Lawrence,

Is it a G2 or an I2(7)? See the supersymetric part of the discussion section of Ref.[3] - attached above as "A Case Sudy 3.3.pdf".

These two nested tetrahedra collectively comprise a cube (diagram and basis transformation in Ref.[3]). BRST and/ or Faddeev-Popov "ghosts" are relevant to this geometry - they comprise the "fifth point" in the E8 Pentality symmetry.

Dear Steve,

I haven't worked directly on the holographic principle, but a reference is here.

Dear FQXi Friends, OUCH! It is ironic that all of my scores have been 8's, 7's or 1's. I guess people either "love" or "hate" my ideas. Please "hate" them in moderation - I'm not the only person with "crazy" ideas in this contest.

Have Fun!

Ray Munroe

The isometry of G_2 is on 2-planes tangent to C^5. There are 10 possible such planes and given any choice of basis, and up to 10 possible Killing spinors which can exist accord to the holonomic action of G_2 with dΩ = 0 on a system of Pfaffian forms. The holonomic action of G_2 is then set by dK = 0, or equivalently above dΩ = 0. The condition means Ω is covariantly constant, which is a condition it being a Killing spinor, and the existence of additional covariantly constant field-form restricts the G_2 holonomy so the Killing spinor equation has more than one solution and the 4 dimensional field theory has extended N > 1 supersymmetry. So the G_2 as the automorphism of the octonions in J^3(O) is what determines the supersymmetries.

The I_2(7) is a discrete group identical to the Fano plane. This is a different structure entirely that determines the multiplication tables (168 of them) for the octonions.

This sort of segues into one possible problem with your program. Again you have this matter of the gravi-weak sector. It appears to be a framing of the SO(4) P-S electroweak theory with SO(3,1) gravitation. On page 4 your write:

"Curiously, H4 has the same symmetries of 120 4 2 35in a four-dimensional "tetrality" space. Table 2 represents these E8 component symmetries as products of Simplices within a 12-dimensional K12' lattice. We already reviewed the 3-Simplex of Electro-Color, and learned that this sub-theory implies that leptons possess the neutral Strong Color charges of white and anti-white. The next new physics is revealed in a study of the 4-Simplex of "Gravi-Weak"."

which might give you a way out. The H_4 is a 5dim octahedral (octahedrachoron) which can tessellate AdS spacetime. This gravi-weak sector might then be a multiplication of the EW fields with quivers of quaternions in this spacetime tessellation. This all of course pertains at a higher energy than standard string theory. The whole point of this with the Leech lattice is that strings are skymrion field effects due to quantum error correction codes or sphere packings. The (H_4xE_8)^2 is an intermediate energy state of affairs between the Leech lattice (penultimate symmetry) and E_8xE_8. At the string level the gravitons are framed according to supersymmetric graded structures with spins (3/2, 2).

I use the term penultimate symmetry, because the Leech lattice or Mathieu M_{24} is the automorphism group over the Fischer-Greiss group. I dare not try to go this far, for this is huge, but it is the ultimate set of symmetries for the 26 dimensional space of Lorentizian symmetries (the good ole fashioned bosonic string). A monster group theory of fields might in 50 to 100 years be seen as the ultimate theory of physics.

Lawrence B. Crowell

Dear Lawrence,

G2 has the right symmetries for supersymmetry. I expect a five-fold symmetry to yield 5 particle multiplets: 1) scalar bosons, 2) matter fermions, 3) vector bosons, 4) gravitino fermions, and 5) tensor bosons. On the other hand, the 168 of I_2(7) is also interesting - it is half of Klein's Chi(7) (order 336), and a quarter of the K12' roots (672).

These symmetries are all relevant. The 672 roots of K12' appear as shallow holes in the Leech lattice four times (Conway & Sloane, "Sphere Packings, Lattices & Groups" 3rd ed. pp.517-520). If the TOE is the Monster Group, it will take a very long time to understand all of the symmetries and physical implications. The TOE may be an evolution of ideas.

It seems that we started at opposite ends of the problem. I wanted to "fix" Lisi's seemingly simple ideas, and ended up with something that might be related to 11-D M-Theory. You started out with the Leech lattice and 26-D String Theory and tried to work out that end of the problem. I refuse to say that one is right and one is wrong because I think they are related - my view may be a simplification or a transient decaying solution of your view.

I like your "Quiver of Quaternions" and did refer to this in Ref.[3].

Have Fun!

Ray Munroe

Hi Ray,

The TOE may be an evolution of ideas.....super .

You are two genius ,a pleasure to read your extrapolations .I learn in math with both of you .

Thanks for that .

Take care

Steve

Ray,

Your scheme is rather complex in some ways. I think the framing you have of gravitation with electro-weak interactions is a bit which meeds to the thought out a bit more. The Leech lattice has in terms of Tacobi theta function s 3 E_6's and so the breakdown to two copies of H_4xE_8 might reflect a framing of gravity with gauge fields ir EW according to a Bloch wave function defined by the 120-cell lattice.

Your connection between K12 and I_2(7) above is interesting. When I get the chance I will try to think about this more.

You might want to consider how this vast zoo part fields or particles you have are an aspect of dark matter. Dark matter is probably in part supersymmetric pairs of matter we understand fairly well.

When it comes to the monster group, we hardly have the techniques to understand this outside of rather superficial aspects. A physical theory based on the Conway groups and the F-G monster is far beyound our abilities right now. The Mathieu and Leech lattice systems are the automorphism groups over the monster and provide a formidable challenge to work with now in the early 21st cnetury.

Cheers LC