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

Ray Munroe

Dear Jason,

The K12' lattice only existed at the TOE - it is now a broken symmetry. The E8 became hyperspace and the H4 became spacetime. Spacetime doesn't seem to be a lattice today - the Big Bang and Inflation probably caused it to disassociate. If the direct lattice disassociated, then the reciprocal one did as well.

Last year, Mohamed El Naschie and I exchanged ideas. I think that fractals could be relevant, but I want to address that part of the problem very carefully. People either love or hate El Naschie's ideas - I don't want to be stuck in such a paradox. My K12' lattice is closely related to El Naschie's E-Infinity. The primary difference is that El Naschie makes a fractal-like approximation that I didn't make. My interpretation is that this fractal-like approximation bridges the gap between a finite K12' and a nearly infinite Universe. In my larger paper "A Case Study...", I may also have a G2 or I(2)_7 centralizing heptagon (or "centralon") that has fractal-like origins.

Have Fun!

Ray Munroe

[deleted]

Hi Ray,

I can certainly understand your caution with respect to fractals; it 's like openinga can of worms that ca never be closed.

What is hyperspace and how does it interact with standard space? Standard space inforces the laws of motion, and all of it's constants. Admittedly it's getting hard to visualize interactions when E8's become involved. Like an Escher painting that gets small and smaller as you logitudinally approach the speed of light boundary, then, there is a layer of nothingness, then there is another Escher space. It's a cool visualization, but doesn't get us any closer. I noticed that Lawrence talks about subgroups inside of a monster group; it's suggestive of a hierarchy of forces, but not definitive. I want to suggest that a spaceship inside of a standard space can move into hyperspace. If this occurs, the two spaces are isolated with respect to the laws of motion. I can't have protons or neutrons take a wrong turn and suddenly find themselves in hyperspace where they immediately begin to decay. Instead, the standard space, which happens to to contain a spaceship, is treated like a hyperspace particle or fermion, complete with a matching boson. The only way the hyperspace boson can interact with the spaceship inside is by deforming the standard space, which creates gravitational fields.

I wish it were possible to describe space itself as a particle so it would be better able to interact with these various forces.

Ray Munroe

Dear Jason,

If space is a particle, it is similar to a Higgs boson, or a Cooper pair of fermions (from BCS Superconductivity Theory). Normally that space between Cooper pairs is pretty small, so I'm not sure how you made it a human-sized bubble.

I am a fan of a hierarchy of forces. If you have read my book, you will see that I expect more forces, and these new forces are contained within these unseen, unknown branes hidden within the former E8 that is now hyperspace.

I'm not necessarily scared of fractals (fractals are a legitimate approach towards renormalization, for instance) - I just want to be sure of them. I don't want to be judged as a "Psuedo-Scientist" because someone thinks I bypassed a mathematical proof (but I also don't want to get trapped in an infinite sea of unnecessary proofs).

Have Fun!

Ray Munroe

Lawrence Crowell

Even the decomposition of the Leech lattice symmetry to (E_8xH_4)^2 is a matter of broken symmetry. This further breaks down to E_8xE_8 which breaks down to ... . I suspect that at the highest energy possible the structure of things is the Monster group, then at lower energy the Leech, then at lower energy ... and on it goes. If we can just work out the Leech system and its lower energy decompositions, such as (E_8xH_4)^2, we would be doing well.

The point of working with J^3(O) is that this is one element of the Leech lattice system. This structure is the automorphism on the Leech. Dang, we might be doing well if we can just figure this part out. I think we can break this into the (E_8xH_4)^2 lower energy system.

Cheers LC

[deleted]

Dr, Ray Munroe,

I would go with a particle of space as being more like a Higgs boson.

This evening I was trying to explain to me girlfriend what tesselation of spacetime really means. We happened to be at a shopping mall. I pointed to the square tiles on the floor. I told her that each of the corners represents a particle; and each of the edges represents a force. Then I told her that we were trying figure out what the tiles really were and what were their properties. In boiling down the tesselation approach in such a simple way, I realized that a standard space could be described as the tiles on the floor. A hyperspace could be described as the tiles on the ceiling. I wanted to build a special surface with both ceiling tiles and floor tiles.

[deleted]

HEADLINE NEWS: Terrible collision on interstellar freeway. Both starships destroyed.

Just outside of the Pleadese hyperspace freeway, two starships drifted within relativistic velocities, less then c, as they intersected. The two vessels, each weighing 100,000 metric tons, collided at an estimated 0.9c. Hyperspace physics law specifically states that intersecting space vessels must maintain a minimum difference in velocity of c (2.998x108 m/s) to avoid relativistic overlap. Failure to do so can, and usually will, result in a violent relativistic collision that will be observable for many lightyears, eventually. There were no survivors. Galactic bureau of investigation is investigating. There efforts may be hampered due to the lack of available debris. Velocity spacing procedures are under review.

Lawrence Crowell

I think a better model for tessellation of spacetime is the stacking of fruit at the grocery market. It also should be realized that nothing is actually tessellating up spacetime! These are Planck units of volume, which just demark the scale limit of observation. The lattice is also transformable by the SL(2,O) group and modular functions. So on one frame there might be a certain tessellation and another frame a different tessellation. The tessellation is just a group theoretic construction which indicates how much quantum information can exist in a region according to a general quantum error correction code --- which is the symmetry of the lattice or tessellation.

Cheers LC

Lawrence Crowell

There would be no debris! At v = .9c the gamma factor is γ = 2.3, or the kinetic energy is a billion electron volts per proton mass. If the two objects collide they would turn into a plasma at a temperature, given by kT = E (equipartition theorem), around a billion K. Anything not utterly vaporized (even nuclei would be vaporized into protons and neutrons) would scatter out at relativistic velocities. As for survivors, fogetaboudit.

Cheers LC

Ray Munroe

Dear Lawrence,

Is it (E8xH4)^2 or G2x(E8xH4)^2 or (E8xH4xG2)? (Or is it I_2(7) instead of G2?) I haven't worked out all of the details of Supersymmetry. I like your J^3 Jordan transformation. It looks like a triality rotation matrix. Does it fit with my "Generaton" Q bosons?

Dear Jason,

Just forget the walls and make unified ceiling/ floor tiles. Can we travel perpendicular to the floor tiles (through nothing?) and jump directly into the ceiling tiles? Lawrence doesn't think so.

Most of my friends would have had their cruise control set at least at 1.1 c, so it probably wasn't one of my friends in that wreck...

Have Fun!

Ray Munroe

Dear Lawrence,

I like the stacked fruit analogy. That is basically a Face-Centered Cubic (FCC) Close-Packing lattice. In my book, I formed an SO(8) (or D4) out of a tetrahedron plus its 24 nearest-neighbors in an FCC lattice.

Have Fun!

Ray Munroe

[deleted]

Lawrence,

I agree with you on two points. First, I figured the collision would result in total annhilation into a plasma explosion; but down to the last atom? Wow!

Second, I agree that tesselation is a model, that nothing is being stacked. I do appreciate the clarification.

For the two colliding spaceships, I want to think of each of their bubbles of standard space, with speed of light c, as a particle-space or a spatial anomaly within hyperspace, similar to a particle. I think of quantum particles as spatial anomalies themselves. Then, each of these space anomalies, with the spaceship inside, have a relative velocity of their own with respect to hyperspace. If I approach the problem this way, can I theorize some hyperspace physics?

Lawrence Crowell

The sphere packing in 3 dimensions is the FCC lattice or tessellated octahedron. In four dimensions it is the 24-cell, in 8 dimensions the Gosset polytope. These are the miminal sphere packing condition, and reflect the most efficient quantum error correction coding possible.

When it comes to the structure of the vacuum state, that involves the F_4 automorphism of the exceptional group and and the role of G_2. Consider the elements e_i as the basis elements of the G_2 so that the three form

Ω = ω^{ijk} e_i/\e_j/\e_k, /\ = \wedge,

defines the G_2 holonomy on S^7 or M^7. The condition dΩ = 0 means that the F_4 valued curvature forms are

F^{ab} = ε^{ijk}e_i(∂_ae_j)/\(∂_be_k).

This then determines sets the content for the relationship between the G_2 holonomy on the OP^1 and the gauge theory content of F_4.

Cheers Lawrence B. Crowell

[deleted]

Lawrence,

Holonomy and these various other concepts talk about information transport from one space to another. But how do constants like c and h fit in? I'm sure they will scale something, but what?

[deleted]

A mathematical example of a holonomy is the parallel transport of a vector around a loop. A classical physics example is Foucault's pendulum. In quantum mechanics the Ahranov-Bohm effect of a phase shift of the wave function of en electron outside a solonoid.

Cheers LC

[deleted]

Dr. Ray B Munroe,

I need your input. When I think of a theory of everything, in so far as theoretical physics is concerned, I think in terms of a single fundamental cause from which all physics related effects emanate. You do not appear to think that way. Could you please tell me something about your perspective on what constitutes a theory of everything. As usual, this is not meant as confrontational even though it may come across that way. It seems it is often hard to ask a question without appearing disagreeable. My impression after a first reading is that you are developing an efficient arrangement for organizing information. In other words, something similar to compressing data for digital transfer or perhaps the folder and file system of a computer. One can always create another folder. That is the way extra dimensions strike me. I will be reading it several times more because that always leads to better understanding. It would be helpful to have your viewpoint on this.

James

[deleted]

For two starships travelling in hyperspace, they not only have relative position with respect to each other, x1,x2,x3, but relative velocity as well,v1,v2,v3. The standard space that each one of them occupies will have a center of mass. That center of mass will have an average velocity. If two spaceships overlap while travelling in hyperspace, they will pass through each other if their velocity separation is greater than c. A If two spaceships overlap with an accidential velocity margin less then c, there is a gamma factor to consider. But somehow, the kinetic energy between two starships moving as particle-spaces in hypespace, has to be transferred in a collision event that involves gamma. This has to be done without violating conservation of energy. Mmm...

[deleted]

To use holonomy to describe a particle traveling in a loop betwen standard space and hyperspace, there is the problem that the particle might not be stable in both spaces. Mmm...

[deleted]

Dear James,

Thank You for your interest and your questions. Please call me "Ray".

I found what I think is an interesting direct comparison between the Tetrahedral Symmetry Classes of Experimental Physical Chemistry/ Solid State Physics versus the Georgi-Glashow SU(5) Boson GUT of Theoretical Particle Physics (Equation 1). This Georgi-Glashow SU(5) Boson GUT contains the gluons of Color Theory, the photon of Quantum Electrodynamics (basically a quantized version of Maxwell's Equations of Electromagnetism), the left-handed Weak force of the Standard Model, and some hypothetical X and Y bosons. This part of the paper is "old-school" theory, and we normally expect the X and Y bosons to be quite massive or else we have to worry about proton decay.

Having received my Doctorate in Particle Physics Phenomenology, I can't help but build bigger (and hopefully better) models. It occurred to me that if the Tetrahedral Symmetry Classes are relevant, then the Octahedral and/ or Icosahedral Symmetries (which are equally founded in Experimental Physical Chemistry/ Solid State Physics) might also be relevant, so I pushed that extrapolation to its natural limit. Ultimately, this led to an SU(11) Yang-Mills Boson GUT (Equation 3) that contains a framework capable of supporting a Quantum Gravity Theory in addition to the rest of the Standard Model of Particle Physics. Along the way, I introduce a couple of new short-ranged forces: Hyperflavor (similar to a more massive Weak force, but with left-, right- and mixed-handed interactions rather than exclusively left-handed interactions), and WIMP-Gravity (similar to massive gravitons that might imply "imaginary mass" = tachyons).

The K12' lattice is a 12 dimensional extrapolation of the Exceptional Groups (G2, F4, E8,...). I called it E12 originally (because of similarities with E8xH4), but the mathematicians did not appreciate my cavalier definitions. So I renamed it K12' because of similarities with the Coxeter-Todd K12 lattice. K12' is my favorite model, but I am playing with other ideas as well. K12' is also a shallow hole in the 24 dimensional Leech lattice, and has an interesting decay channel that breaks into a Super Yang-Mills Boson GUT plus an E8 Gosset lattice Fermion GUT. I call it a TOE because it contains a framework capable of containing all Bosons (gluons, photon, W, Z, graviton, Hyperflavor, WIMP-Gravitation, Generatons, etc.) and all Fermions (up, down, charm, strange, top, bottom, electron, muon, tauon, all neutrinos, all colors, left- and right-handed spins, plus some weird tachyons). I have not yet written all of the Feynman diagrams and Lagrangian components. I think I understand the Supersymmetric extension of this model (In my "A Case Study 3.3.pdf" paper), but Lawrence Crowell and I are still bouncing ideas off of each other. It is a work in progress...

I equate new force charges (or rank or folders) with new dimensions. And I equate broken symmetries with dimensional collapse. If K12' was a 12 dimensional lattice, but we now live in a 3+1 dimensional (non-lattice) Universe, then we had 8 broken symmetries, Hyperspace is the remnants of a broken E8 Gosset lattice, and Spacetime is the remnants of a broken H4 lattice (which comes full-circle back to the icosahedron mentioned above).

K12' is a finite model that is closely related to Mohamed El Naschie's E-Infinity - the primary difference being a fractal approximation. Perhaps the difference between a finite K12' and a nearly-infinite Universe is a simple fractal approximation.

Jason wants to create a hyperdrive, and has been having many discussions as to how we might get into hyperspace.

I hope I have clarified this paper, and why I consider it "A Geometrical Approach Towards A TOE". I don't of this as the Prime Mover/ Prime Cause so much as I think of this as a geometrical Prime Theory that the Prime Mover/ Prime Cause may have manipulated.

Have Fun!

Ray Munroe

Jonathan Dickau

Greetings,

I've downloaded your essay. I will read it, then digest it a bit, and I'm sure I will have questions or comments before long.

All the Best,

Jonathan

[deleted]

Ray,

Here is a hyperspace physics idea for you. Let's say that the speed of light represents a velocity range for all particles that have charges. Even neutralized charges have this velocity range. That results in a space-time in which all of the universes matter, which has charge (neutralized or otherwise), will settle at some average velocity. If this is the case, then the speed of light is a characteristic of the particle, not the space itself.

Here is where we have some fun. I have a propulsion system that is designed around the idea of transmuting protons into hyperprotons by transmuting the charge into a c'>>c charge. The transmutation is one way. When I accerlate the hyper-protons, they give me a thrust of equal and opposite momentum. But this momentum is based on p' = E/c'. While it takes more energy to accelerate them, they can give me FTL momentum because their associated charge is FTL.

I'll work on the idea. Actually, I still need to enshroud my starship in some kind of special space. I'll work on.

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