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

Ray Munroe

Dear Narendra,

Please do not pity me. I chose family and money over career, but I still get to play with Physics as a hobby. Somehow, it seems that I may have the best of both worlds.

I appreciate your supportive comments. Yes, I think crystal defects are very relevant. And I think that gravity arises from hyperspace phenomna that are trasfered to spacetime via General Relativistic curvature (thus the different nature, and the apparently "older" or "deeper" nature of gravity).

I have read your paper through once quickly already. I will read it again and make comments before the end of the week.

Thank You!

Ray Munroe

Jonathan Dickau

Hello again Ray,

This post was composed off-line, then pasted, so I'll have to get to any comments above later. I wanted to tell you I liked your paper greatly, once it sunk in. I thought it was a lot to digest, but you do seem to tie a lot together. I shall have many suggested readings for you, as your essay touches on a lot of work with which I'm familiar, and seems to provide some of the missing pieces for work I've been playing with for 20 years now (Cosmology and the Mandelbrot Set).

It seems you are trying to connect the limits of complexity with the corresponding simplicities afforded by geometry, and I like that idea. You have made some complicated ideas simple, or should I say simplicial? I like simplices a lot myself. I also find Causal Dynamical Triangulation interesting and relevant to this discussion. The Wikipedia entry - written mainly by me - may offer some useful insights. Buckminster Fuller liked triangles as a structural element as they offer the greatest possible strength and rigidity from a given material. Triangles also define an area, which seems to be the conserved quantity at the Planck scale (Planck area rather than Planck length).

There do appear to be connections thereby, between the preferred working spaces of Loop Quantum Gravity and String Theory/M-theory. Have you read the paper on Integrability and the 10-j symbols, by Baez and Barrett? I'll find the arXiv reference and include that in a future post. It seems to me that the 4-simplex could be a 2-way door of sorts, between higher and lower dimensional spaces. If it represents the graininess at the Planck dimension, by a restriction of possible angular displacements, this could indicate that we must re-define orthogonality at that scale. The projections from each of the 10 faces of the 4-simplex can then be viewed as independent 'dimensions' as they are mutually exclusive directions in space. CDT says space-time is 2-d at or below the Plank scale, but this 2-d space is said to evolve into a 4-d space-time. Maybe a dual 2-d/10-d space becomes a 4-d/8-d space, or something like that.

In any case, Ray, your paper has gotten me thinking again, about stuff like that. Your theory appears very complicated, despite the fact of using geometry to simplify things, but it may be a necessary level of complication, to fully explicate the solution you propose. And I like the idea of working inward from the maximal complexity and minimal simplicity, to define the middle ground. Your methodology shows great promise. It looks like the theory still needs work, but you have apparently gotten farther than Lisi did. Good work!

All the Best,

Jonathan

[deleted]

I really am not able to spend a lot of time writing here. J-invariants, or Klein's modular forms, play a major role in the Jacobi theta functions for the Leech lattice. The Leech lattice in 24-dimensions is with two additional dimensions the 26-dimensional Lorentz group automorphism of the Fischer-Griess group. There is a correspondence that Borcherds discovered between the Virasoro algebra, which cuts off the "anomaly" at 26 dimensions, and this automorphism group.

Cheers LC

Ray Munroe

Dear Eckard,

I enjoyed reading your essay. It started out as an essay about the science of hearing, but turned into a detailed discussion of the properties of numbers and transforms. I am surprised that your paper is not more highly rated. Was Bio-Physics too far off the average reader's interest?

In your paper, you said "Thus Hilbert-space is the straightforward generalization of Euclidean space if one considers the vectors as the essential notions. Now we begin to believe that it is not the vectors which matter but the lattice of all linear (closed) subspaces." - If you study my essay, you will see that fermions are direct lattice points, and bosons are the vectors (the reciprocal lattice) that allow us to connect direct lattice points.

Your essay also said "Introducing analytic geometry, Descartes hesitated to usa negative as well as positive xyz. He strived for as little arbitrariness as possible. Disdain of a natural origin like r=0 implies the need to arbitrarily choose a point of reference." - In my model, negative x, y and z correspond to anti-particles. And the origin seems to be a lattice defect remnant of a collapsed higher dimensionality.

A legitimate question is "How does a finite model such as K12' connect with an infinite (or nearly-infinite) Universe?" If K12' is the "Wigner-Seitz cell" of a 12-D lattice that extends out to infinity in all directions, then 1) it represents the topography of Unification, and 2) perhaps the difference between a finite K12' and an infinite Universe may be modeled with a fractal approximation such as El Naschie's E-Infinity (which has an order of 1 fractal larger than K12').

On JCN Smith's blog site, you said "We may ascribe events to particular points on a scale that refers to a chosen point. The only natural reference point is the very now. So it cannot be fuzzy. It is distinct by definition, i.e., by our choice. Whether we then prefer a continuous in the sense of Peirce's definition" - Which is distinct by definition...

"or discrete scale for all other points of elapsed time does not matter" - Which may be "fuzzy" by Heisenberg's Uncertainty relation:

[math]\Delta E \Delta t \approx h/2 \pi[/math]

I understand that this interpretation may be irrelevant in the example of a non-quantum ear...

"in practice because we do anyway not have any chance to define and measure the absolutely exact distance of a second point. In this case rational numbers are sufficient." - Are you appealing to Cantor's paradise or experimental error? ...

"I do not hide my reluctance to swallow the common belief in spacetime as a 4th dimension of space, and I am also not ready to share believe in further dimensions as long as there in no agreement how many dimensions correspond to reality." - Any realistic multi-dimensional model must explain why we see 3 space plus 1 time dimensions. With the essay length limit, I did not have the luxury of showing these details. I think the K12' disintegrates into a 4-D H4 Quaternion of Spacetime and an 8-D E8 Octonion of Hyperspace. Broken symmetries cause dimensions to collapse and disappear from our perception resolution scale (Planck's constant, h)...

"When G. Cantor found out that a cube has not more points as compared with the line he reiterated the likewise ridiculous conclusion by Albert von Sachsen (1318-1390). Actually it is nonsense to ascribe a number of points to something with more than zero dimensions. Even a 3D structure that consists of a finite number of points is zero-dimensional." - I agree with you so far. My lattice points represent 12-D worth of quantum numbers (or fundamental charges). In the massless, point-particle model, these would appear to be 0-D points that possess intrinsic spin - a concept we normally ascribe to objects of size. There is a paradox here. First, realize that our 12 Dimensions have collapsed. Second, realize that the concept of a massless point particle may be a fallacy - neutrinos aren't massless, photons aren't pointlike...

"I appreciate that you wrote "my presence". Accordingly I do not see it a complicated concept and something intangible and therefore inapt for physics. It always refers to an object under consideration, and it must not play any role as a state: |sign(x)|=1 for all x without exception for real numbers. In order to avoid theoretical problems we need real numbers here." - I wasn't certain if your meaning was physical or philosophical. Even our "physical presence" changes with time. I shed dead skin, hair, etc. Does time travel consist of a physical transposition of my atoms (that also exist in the destination time) or a transposition of the information that is identified as "Ray"? It may depend on the technology used...

Good Luck in the contest!

Ray Munroe

[deleted]

This is an interesting article in ways. I am not sure I absorbed everything. I read it rather quickly. I would not lose too much sleep over Cantor transfinite numbers. I am not sure what these have to do with physics, at least physics we currently understand or likely in the near future. Iwrote a bit on Eckard's site about this.

Cheers LC

Ray Munroe

Dear Narendra Nath,

I knew I had read your paper once before. On Oct. 2nd, I posted the following review on my blog site:

"I read your short essay. Some points could have been explained better (such as baryonic vs. non-baryonic and the strong nuclear force/ color confinement). I don't think that quantum mechanics "evolved" out of classical physics - QM really represents a paradigm shift so tremendous that it disturbed one of its founding fathers, Einstein. Oddly enough, the first three pages seem to indicate that we know nearly everything. Prominent physicists thought the same way at the end of the Nineteenth Century - they sure were wrong!

At the end of your 3 pages of Significant Developments, you said "Physics of the early universe may require some radically different approach conceptually!" This is what Lawrence Crowell and I are working on. Can we extrapolate back to that early time and deduce what physics must have been like then, and explain why (via broken symmetries and dimensional collapse) we observe the present laws of Physics? I don't think that someone flipped a switch on to create the Big Bang, and then flipped that switch off to create the present Universe. The theories must blend into each other in a predictable manner.

In Overall Comments, you said "What physics cannot hope to do? Some expectations outlined above may never get fulfilled." I understand that we may be near the observation limit, but I hope that mankind will continue to ask these questions and push towards answers."

Those were last month's comments. I didn't score your paper last month. The following are this month's comments (after a second read).

You said "It may well be advisable to attempt instead conducting more accurate and precise space experiments in order to understand more and more of what transpired cosmologically in the early universe - a challenge too!" I agree. The LHC center-of-mass energy is sufficient to probe Weak-scale phenomena, but not Gravity-scale phenomena. We need to use every experimental trick available to us. Although we have studied cosmic rays for decades, I think this could be the source of our next major experimental breakthroughs. It is a shame that experimental techniques lag theoretical speculation which lags science fiction... It was relevant to mention "Star Trek".

You also said "We hardly expect to arrive at any finality of understanding." My essay is "A Geometrical Approach Towards A TOE". I think it lays down framework for a possible unification of the four fundamental forces, all fermions, and all bosons. In this respect, I think it is fair to call it a TOE of Particle Physics. Would that make it a TOP (Theory Of Particle Physics)? But I agree that we should be suspicious of any claims that we have arrived at a finality of understanding. In another paper, Frank Martin DiMeglio claims that the Dream unifies Gravity and Electromagnetism. The irony is that humankind might understand more about Gravity and Electromagnetism than we understand about the Dream/ Mind/ Soul. We can't understand everything as long as we don't understand the Dream/ Mind/ Soul.

You also said "For Physics to grow, let us leave the psychology of absoluteness/perfectness and instead adopt ways and means that are free from bias and consider 'freedom of thought' supreme." I agree that biases are a problem. I received many scores of 1's in this contest with few critiques against my work. Did they object to my paradigm or my math or my presentation?

I think it was a good introduction to a paper - it was just way too short. It introduced many good topics for possible essays, but never delved into any of the ideas very deeply. Many of the contestants (me included) chose overly ambitious ideas and wrestled with the length limitations. I could have made my paper exactly 10 pages plus a reference page long, but decided that it had enough detail in it.

Good Luck in the contest!

Ray Munroe

[deleted]

Dear Ray,

i see that i visited your essay site twice. I forgot to respond to your posting that you reminded me on my essay site. i have now posted my response there today. I sse that your essay got the due attention. Just ignore the rankings these are hardly a certificate for your originality and innovation. Just keeo doing what you feel intersted, many abig anmes got the recognition well after they left the world. People ar like that and they have hardly anything common with the spirit of Physics that they engage in as a profession. In old days, it was fascination and curiousity that guided the profession. Today it is a kind of glamour more than merit/deep interest that rules one's professional activity. That is why the quality is at a disadvantage. This is happening in all spheres of human activity and let us not disheartened with such a scenario. Such is the nature that changes its shapes/sounds. Underneath the stratum remains unaffected and even unseen

[deleted]

Dear Ray,

I see you moved up in the ratings. Good for you. I do not understand how essays by serious physicists with their PHD's can garner all these low ratings. It is your's and their's participation that makes this a quality, international, important contest. I believe it is good to accept participation by others; however, it exists because of those who have established credentials.

James

Ray Munroe

Dear Jonathan, Narendra and James,

Thank you for your gracious comments. I joined this essay contest to connect with other intellects who were interested in the fundamental questions of physics.

Jonathan - You gave me new material to read and think about.

Good Luck to you all!

Ray Munroe

Dear Jonathan,

I found arxiv articles by Baez and Barrett from 1999 and 2001 (both attached). Both of these articles tie in the 4-simplex, which is the key to E8 pentality symmetry. I want to better understand the fifth vertex of the 4-simplex because this seems to be the origin of tachyons. The older article has 4 j's, but not 10 j's. I would be interested in similar articles.

Thank You!

Ray MunroeAttachment #1: 9903060v1.pdf Attachment #2: 0101107v2.pdf

Lawrence Crowell

It turns out I have the first of these, which I guess I read a long time ago. I will need to read it again. This might have some bearing on the Dirac monopoles recently discovered. Further, I presume these methods could be used for any polytope in space.

Cheers LC

Jonathan Dickau

Hello again Ray,

(comment also appears in my forum)

Ah yes. Or should I say whoops? A quick review of my file collection reveals that while the Baez-Barret paper on integrability (arXiv:gr-qc/0101107) is foundational to that work (and to CDT I imagine), the paper on the 10j symbols is by Baez, Christensen, and Egan arXiv:gr-qc/0208010. Somewhere in the back of my mind, I must have labeled the Baez-Barrett paper as essential reading for understanding the asymptotics of 10j symbols paper. I take an ambling course sometimes, in getting to an understanding about a subject of interest.

Hopefully it will aid your understanding. I have a lot more papers I selected, when I was trying to understand the basis for CDT - and I'll look through them. I am still curious about how things will shake out, given the Fermi results. It was the addition of a causal constraint (where the timelines of adjacent simplices have to match) that made the CDT formula work in the first place, so if this violation of Lorentz symmetry near the Planck scale is ruled out - it is not a workable model. I still have the distinct impression that the notion of time has a very different meaning on that level of scale, compared to what we see on the macroscopic level, but I guess it remains to be seen just what that is.

I do not believe that time is linear and unchanging at the microscale. I have imagined that it is more like breezes down there, and becomes like a steady wind for object-sized or cosmic events. I tend to feel that there is an illusion of time's constancy, that arises from the steady motion of the planet through the cosmos, but that is largely intuitive as I have no clear reasoning to explain why that should be. Perhaps it is related to decoherence, or if Darryl Leiter is correct to the way particle-particle interactions are colored by their mutual measurement of each other. I wonder if MC-QED still flies, in light of the Fermi results. I imagine it might.

But I digress. Thanks again for your interest in this thread - I'll pass on any further references that seem relevant.

All the Best,

Jonathan

Jonathan Dickau

Hello again Ray,

I just wanted to point out that the idea presented in my essay has a geometrical basis in tetrahedral geometry too. If matter, energy, space, and time are the vertices of a tetrahedron, then space-time and matter-energy are edges that are separated by other edges, and rotated by 90 degrees from each other. They never touch, and their relationship to each other is established by the remaining links.

Pretty cool, huh?

All the Best,

Jonathan

Ray Munroe

Dear Jonathan,

I see your point. Rather than calling the tetrahedral vertices (red, green, blue, white), we could call them (matter, energy, space, time). The vectors that connect these vertices define an SO(3,1)xSO(3,1) 12-plet of operators including: matter-anti-energy, matter-anti-space, matter-anti-time, energy-anti-matter, energy-anti-space, energy-anti-time, space-anti-matter, space-anti-energy, space-anti-time, time-anti-matter, time-anti-energy, and time-anti-space. The edges would be exactly your six fundamental combinations: matter-energy, matter-space, matter-time, energy-space, energy-time, space-time.

Have Fun!

Ray Munroe

Jonathan Dickau

Thanks Ray,

Exactly!

Jonathan

[deleted]

The vertices are quaternions or spinors, or maybe quivers of them according to some internal symmetry. This might all work in a way similar to the paper I attached on Dirac strings or monopoles.

Cheers LC

Ray Munroe

Exactly. Norman Cook is using a tetrahedral FCC close-packing lattice. Jonathan could use a tetrahedral foundation. My K12' has a tetrahedral component and related simplices. My book uses a tetrahedral FCC close-packing lattice of Hyperflavor leptons and quarks. The paper on Dirac strings/ monopoles has tetrahedra. We just can't get away from certain geometrical structures, can we? Is Nature trying to tell us something?

Have Fun!

Ray Munroe

[deleted]

Cook has some interesting stuff there. I have to make this a bit brief, but nature has a self-similarity or recherche structure to it. The lattice systems in crystals or in nuclei appear in other guises, such as the underlier for field theory.

Cheers LC

[deleted]

Dear FQXi Friends,

This stage of the voting ends in less than an hour and my community vote is tied with Lev Goldfarb for 5th and 6th. I would like to thank everyone who participated in constructive critiques and who voted my essay into the this upper tier. May the judges be as kind...

Good Night!

Ray Munroe

[deleted]

Well my paper ended up in the upper third or so of the lot. We can of course keep communicating. I am a bit intriqued by how one might consider the physics in the perspective article by Gingras I sent a few days ago. The spins in the lattice can be generalized to quaternions or icosians.

Cheers LC

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