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

Dear Jayakar,

Thank you for your comments. Lambda-Cold Dark Matter ties in closely with Lawrence Crowell's interests, but Lawrence's ideas and mine seem to be merging. I am not familiar with the coherent-cycle cluster-matter model of the Universe, but will read your essay this upcoming week and see what I can learn. Our simplices may be related. My "stringy branes" seem like a cross between String theory and CDT.

If you need a fine-structure constant, I can probably find one. In my book, I used Quantum Statistical Grand Unified Theory to describe the various force coupling strengths (including the fine structure constant). And when I introduced K12' (as E12) last year, Mohamed El Naschie immediately noticed how close it was to his E-infinity, which has an order of five times the inverse fine-structure constant.

Good luck in the contest!

Ray Munroe

Hi Ray.

In reading/considering your essay, I have some very important questions for you:

1) Why is it NOT your position that it is plain and simple common sense that the known mathematical unification of Einstein's theory of gravity (general relativity) with Maxwell's theory of light (electromagnetism) that is achieved by the addition of a fourth dimension of space to Einstein's theory must be plainly and significantly obvious in our direct experience? This, obviously, bears heavily upon the predictive effectiveness of mathematics.

2) Do you agree that the fundamental union of gravity and electromagnetism/light necessarily/ideally involves balancing scale by making gravity repulsive and attractive as electromagnetic energy/light?

3) Do you agree that a key component of unifying gravity and electromagnetism/light would be/is the demonstration/understanding of scale as balanced by representing space as BOTH invisible and visible.

You quote support for the statement "The Genius is in the Generalities and the Devil is in the Details". This is generally true.

You also state:

"Is the TOE just a mathematical model? Mathematics doesn't even like the idea of a TOE!"

Now consider the following:

The ability of thought to describe or reconfigure sense is ultimately dependent upon the extent to which thought is similar to sensory experience.

4) Do you agree with this? If not, why?

Thank you very much for your concern and consideration regarding these fundamental and very relevant questions. Frank

Dear Jayakar,

I read your paper - the many diagrams made it fast reading.

I didn't see any 5-simplices. It looks like you are attacking the multi-body problem as a hierarchy of 3-body problems (which I don't think are 3-simplices - they might be related to 2-simplices). This is different from my ideas, but interesting nonetheless.

Are you familiar with Mohamed El Naschie's work? Your figure on the top of page 3 looks very similar to some of El Naschie's fractal representations.

On page 7, you say "Nothing is always something that is not Zero". You should read Leshan's essay - it is related.

On page 8, you say "In C-M-U the force carrier is the net centrifugal force by the spin of elementary matters that is not particles, whereas in M-U they are Bosons". I am a proponent of the latter (my model has a Super Yang-Mills 444-plet of bosons), but am not opposed to the possibility of some weird interactions via the former (I think that Leshan's paper describes something similar to the Higgs). Further down the page, you said "whereas in C-M-U the dynamics of the C-M is explained in Continuum mechanics with Supersymmetric quantum mechanic similarities". Leshan and I have discussed this, and my opinion is that even nothing must be a quantum, not continuous, effect.

I'm still thinking on your ideas.

Good luck in the contest!

Ray Munroe

Dear Frank,

Thank you for your interest and questions.

1) Look at history. Theodor Kaluza unified gravity and electromagnetism in 5 dimensions, but did not include the nuclear forces.

I equate rank with dimensionality. We see 4 dimensions, and the first four (ranked) charges are 1) color_g3, 2) color_g8, 3) hyperflavor and 4) weak isospin. The first four ranks (dimensions) do not include a quantum gravity charge! That's OK if gravity is just a 4-D curvature effect without a gravitational quantum (such as the graviton), but then a full unification of QED and quantum gravity is impossible.

I also equate dimensional collapse with broken symmetries. We MUST have at least one broken symmetry (I count 8 - perhaps from an octonion of hyperspace or N=8 Supersymmetry) or else we would be living in the TOE universe. Therefore there must be at least 5 (I count 12) dimensions.

I also think that octonions are relevant to GR because an octonion contains the 10 antisymmetric tensors of Einstein's Field Equations.

2) At the Big Bang, there may have been an Electro-Gravity union, but you won't hear me call it that because those are different branes and different spaces (regular spacetime vs. hyperspace). You will see me call the unions Electro-Color (3-D space) and Gravi-Hyperflavor-Weak (hyperspace plus time) for a complete Electro-Color-Gravi-Hyperflavor-Weak union. Sorry - It is a little complicated.

3 and 4) I read your ideas when you started blogging on FQXi. I like bouncing ideas off of interesting people, but got frustrated when you and Georgina kept badgering each other. Your ideas are heavy in Philosophy, Psychology and Language. I need more math or the voices in my head start saying "Blah-blah-blah, blah-blah-blah". Sorry, I'm one of those ADHD people who compensated with a high IQ!

Have Fun!

Ray Munroe

The primary candidate for dark matter is the neutralino. The superpartners of the Z boson (zino), the photon (photino) and the neutral higgs (higgsino) have the same quantum numbers. This means these superparnters can mix, such as in a condensate, to form four eigenstates of the mass operator called "neutralinos". This system is similar to the K-Kbar system Feynman writes about in his lectures, though the mass matrix is a bit more complex. Then of course there are the other super partners, such as s-quarks and s-leptons. Dark matter might in fact compose a whole "zoo" of particles that form a whole dark world which couples to our known world most strongly by gravitation.

There is for the Cl_8 group 256 dimensions with 9-grading for spins in a cycle of -2, -3/2, -1, -1/2, 0, 1/2, 1. 3/2, 2, which appears as

1 + 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1 = 1 + 8 + 28 + 56 + (35+35) + 56 + 28 + 8 + 1, which predict eight Rarita-Schwinger fields and a single graviton. E_8 has a 7-grading 8 + 28 + 56 + 64 + 56 + 28 + 8, where the graviton sector and the scalar and pseudo-scalar fields are removed. The extra-octonionic graded structure 1,0,0,0,3+3,0,0,0,1 indicate that the graviton and the scalars (Higgs & dilaton) are derived elsewhere. Yet in this way the Clifford-8 can embed the exceptional E_8. That the graviton and scalars are not independent in E_8 is why there is the extended CL_{16) system, which embeds E_8xE_8, where now the graviton is due to two copies (in string theory interpreted as due to the handedness of the fields on a closed string) .

In particular, in the J^3(O) the two E_8s are related to each other by the "point" corresponding to one octonion, are dual to lines in OP^2, which are themselves OP^1 --- 7 dimensional spaces. The holonomy for the 7-sphere is the G_2 group, which is centralized with respect to F_4 in E_8. The duality here then describes a graded system on O^2 with dual 8_vx8_s representations. This is then one reason why octonionic gravitation involves the F_4 transformation of the octonionic group which diagonalizes the Jordan exceptional algebra. The action of the F_4 and G_2 groups I indicate in the attached jpg file.

BTW, this is one problem with the Lisi program. The graviton was assumed to be framed with the electroweak interactions. Yet the gauge interactions are internal symmetries, while gravitation is an external symmetry. The intertwining of them is through supersymmetric transformations and the graded structure over Lie algebras.

Anyway back to the issue of dark matter, it is likely a consequence of supersymmetry. Even your structures have these additional fields, some which you label as SUSY pairs. In this we may have a whole classification of structures with masses ranging from the low range of ~ 1TeV for the neutralino to 10^6TeV for SUSY partners for T-quarks. These are extremely weakly interacting fields, and proposals to detect them directly have given null results. The Fermi spacecraft and PAMELA detector have detected some statistically significant production of gamma rays from a weak decay (slow decay rate) of neutralinos, though some controversy exists over these results. Last month I read a physics short about sapphire detectors meant to find the presence of dark matter. There is an ongoing mine shaft experiment in Italy which employs supercold crystalline material which might vibrate in response to a neutralino.

Lawrence B. CrowellAttachment #1: octonionic_curved_space.JPG

Dear Lawrence,

My doctoral thesis was SUSY phenomenology, and I am familiar with much of what you are saying. I concentrated on the potential discovery of SUSY at electron-positron supercolliders, but my graduate school office mate, Mike Brhlik, focused on SUSY discovery bounds based on Dark Matter.

Mike finished his doctorate a year behind me in 1997, and worked as Gordon Kane's post-doc for the next two years. Gordon Kane is one of the essay authors, and his team has analyzed PAMELA data, and decided it is consistent with a neutralino that is primarily a 180 GeV neutral wino (Zino). Although we know that these neutralinos are mixtures of photino, zino, and Higgsino states (and my MSSM is a little rusty - I haven't used it much in over a decade).

When I first found apparently "scalar fermions" in my K12' lattice, I had to determine whether they were sleptons and squarks (as predicted by SUSY) or whether they were something new. But their electric charges seem to be different from that predicted by SUSY, so I think they are new (and we still need to incorporate SUSY sparticles).

Have Fun!

Ray Munroe

There is some controversy over whether Fermi and PAMELA are really detecting neutralinos. These SUSY neutrino-like particles at the low end of the mass scale, about 1 TeV, should have a characteristic gamma ray spectrum. However, and I must confess I can't recall the details, there is some debate over this. Yet there is a rather anomalous glow from the galaxy center that suggests their occurrence.

I have seen some papers on cold dark atoms and cold electromagnetism. The 256 Cl_{8} sequence

1 + 8 + 28 + 56 + (35+35) + 56 + 28 + 8 + 1,

where the left are SUSY pairs and the stuff on the right are "ordinary," there should be gauge-like particles that are SUSY pairs of dimension 3/2 and 1/2 particles. There should be CDM analogues of the ordinary gauge bosons. There might in fact be a sort of weak QCD, say in S-duality, where the gauge-like bosons (squarks) carry family numbers and so forth. If S-duality holds then the SUSY dual of the weak interactions might in fact be very strong, with asymptotic confinement and so forth.

It is curious to think there might exist an alternative world right amongst our own.

Cheers LC

Dear Lawrence,

This sequence is interesting and very close to the Clifford sequence 1,8,28,56,70,56,28,8,1 with maximum rank of eight versus the octonion sequence 1,5,10,10,5,1 with maximum rank of five. I naturally expect spin 3/2 gravitino-like SUSY partners to spin-2 gravitons.

Have Fun!

Ray Munroe

The N = 8 SUSY is of course a supergravity multiplet, with a spectrum of gravitinos. There are also gravitinos in the N = 4 SUSY. These are curious beasts. I have wondered how one would ever detect them. They have no electric charge and they probably have enormous masses. They might show up in exceedingly high energy cosmic ray events.

The supersymmetry naturally comes out of the J^3(O) matrix, The basic matrix is the N = 1 supersymmetry. The extension to N = 2 involves the merging of the hermition and anti-Hermitian J^3(O) with F_4, The N = 4 SUSY involves E_6 and the N = 8 the E_8.

I am working up the analogue of the Unruh radiation in the 26-diemsional exceptional J^3. This will locally describe physics similar to near an event horizon of a black hole.

Cheers LC

Dear Ray,

If I were going to look for other universes whose c and h are different, I would want to take some of these lattices, and the space they represent, and attempt a smooth transition between two spaces. By smooth, I mean that neither space would be curved or compressed in any way that could store energy to reveal it's position. Instead, I would want the speed of light and the Planck constant to adjust accordingly to make the two spaces fit together. Do you have any suggestions for lattices that might be amenable to this?

In truth, I really don't think that the two spaces have a planar wall between them (like a sign that says now entering Florida). Instead, I picture to different spaces that overlap in the same "space" more like two different electron shells or valence and conduction bands. However, if that were the case, I would be asking the tesselation itself to distinguish between universes with different c and h. The problem is that tesselation doesn

t work that way. Even worse, if it did, it robs us of our ability to say that n=1 has energy x and n=2 has energy y...

In the pursuit of a hyperdrive, the different c and h strategy looks like it could work. The problem is trying to manipulate two different kinds of space into some delicate energy balance. I'm not sure how to get two different kinds of space to work within the same framework; other than straining one or both spaces to get them to fit together. And of course straining a space is equivalent to curvature and energy density.

Any thoughts?

Dear Jason,

This multi-dimensional lattice model might have existed at the Big Bang, but has since collapsed due to broken symmetries (such as Electro-Weak Spontaneous Symmetry Breaking etc.) that reduced the number of observable dimensions to four, while preserving the quantum numbers of the original multi-dimensional lattice.

If hyperspace inflated at a different pace than spacetime (I assume that spacetime is much larger than hyperspace, but it could be the other way around?), then hyperspace may still have lattice-like properties, different effective lattice parameters, and different values of "c" and "h". But how could we access hyperspace? What if the entrances to hyperspace are Black Holes?

In optics, we can design lenses with minimal reflectivity by adding a thin film with an index of refraction between that of air and that of our lens. But I wouldn't know how to design such a "thin film" between spacetime and hyperspace. I assume that the boundry between these two types of branes must be as distinct (and fuzzy?) as the event horizon of a Black Hole.

Lawrence Crowell's ideas on Black Holes, branes, and the Cosmological Constant are relevant. I think his Jordan transformation of Octonions is related to some of my multi-dimensional lattice ideas. His AdS space may be my fifth and sixth dimensions. Perhaps he has some useful ideas.

Have Fun!

Ray Munroe

Dear FQXi Friends,

Today, I realized that there is a direct connection between the FQXi homepage and this blog-site topic #520. How fantastic! Please allow me to give you some background information...

This paper defines fermions as lattice points within a multi-dimensional (my best model thus far is 12 dimensional) lattice. At the Big Bang, broken symmetries (such as Electro-Weak Spontaneous Symmetry Breaking etc.) caused the lattice to "break" and collapse down into the four observable dimensions of spacetime. However, I contend that these original quantum numbers survived the dimensional collapse, and are now responsible for the distinct properties of known fermions. This model does predict some new and interesting properties. It is hoped that future Cosmic Ray analysis will probe the properties of these new particles.

This paper also provides a minimal background on a complementary bosonic content (alas - we all had essay length limitations, and I didn't want to crowd too much in) that could contain the Standard Model, a generic Quantum Gravity, and other new and intersting phenomena.

These bosons exist in the Reciprocal Lattice to the Fermions. In this picture, Fermions are points/ sites in the Direct Lattice that are connected via bosons, which are vectors in this Direct Lattice.

If we take the Fourier Transform of our Direct Lattice, then we have a Reciprocal Lattice. In a 3-D crystal, this is equvalent to transforming from a Face-Centered-Cubic (FCC) Direct Lattice into the reciprocal Body-Centered-Cubic (BCC) Reciprocal (or Brilloin) Lattice.

In this Reciprocal Lattice, Bosons are points/ sites in the Reciprocal Lattice that are connected via fermions, which are vectors in this Reciprocal Lattice. This paragraph may be a reasonable way to model a Supersymmetric transform. Thus, we should be able to properly describe Supersymmetry as well.

Critiques are welcome!

Sincerely,

Ray Munroe

Hi Ray,

Thank you for the additional clarity about bosons/fermions/points/struts/etc. This has been needling me for quite a while; particularly, what does it mean that fermions/bosons have this point/strut(connection) relationship for reciprocal/direct lattices? It's like it echoes the delta x delta p >= h; quantum mechanics.

By the way, I assume that the standard model can be (or has already been) set up with this lattice approach. If so, does it predict Higgs particles? I suspect that gravitons might be predicted by a completely different lattice. What do you think?

Hi Jason,

Of course these inverse lattices echo the wave nature of Quantum Mechanics, and the mathematics of the Heisenberg Uncertainty Principle by design. The easiest way to learn about direct lattices vs. reciprocal lattices is to pick up an intermediate-level Solid State Physics book.

My interpretation is that Higgs bosons are introduced at the level of an SU(7) Yang-Mills GUT (equation 2), and the graviton (and related massive WIMP-gravitons) are introduced at the level of an SU(11) Yang-Mills GUT (equation 3).

I studied Particle Physics and Solid State Physics in graduate school. Of course, there is a branch of QCD lattice physics, but I haven't seen many physicists (other than Lisi and I - Alan Schwartz is using crystallography) attempt to describe the Standard Model with a lattice. I did it with a simple 3-D tetragonal symmetry and a Face-Centered-Cubic (FCC) lattice in Section 7.2 of my book. Then I saw Lisi's 8-D E8 Gosset lattice approach and was re-inspired.

Gravitons are different in that they require a higher-ranked sub-algebra because they are tensor, not vector, bosons. However, the graviton still seems to fit into this Yang-Mills GUT. We have to incorporate the graviton into our puzzle in a similar way as the other forces (at least prior to Spontaneous Symmetry Breaking). It might be OK for some massive WIMP-gravitons to reside in a certain brane within the lattice, but if it is a different lattice then we don't have a true GUT.

Have Fun!

Ray Munroe

Have Fun!

Ray Munroe

The AdS/CFT duality of Maldacena is that the boundary of the AdS is equivalent to a conformal field theory on a 5-sphere. The AdS is SU(2,2), and in the large N limit it appears that the duality holds, where AdS_n+1 ~ S^n on the boundary of the AdS. Here the SU(2,2) ~ SO(4,2) is six rank dimensional (15 roots).

I am writing up the work on horizon effect in 26 dimensions and how this physics is given by a Born-Infeld action. This is the entryway into M-theory. I will send this to interested people in the next week or so.

Cheers LC

I was afraid I had asked a stupid question; yes, of course a Higgs particle is predicted. But I do appreciate some of the insight you both have provided into how these problems are set up.

Ray,

So you introduce Higgs bosons at SU(7) Yang-Mills GUT, and the graviton at SU(11) Yang-Mills GUT. You mentioned that gravitons are second ranked tensors, not vectors. Then you say that certain things are introduced prior to symmetry breaking. I respect that you can't just ignore the mathematics as just some detail you'll worry about later. It seems like even the strategy or recipe of how the derivation is set up could suggest some ontological cause, but that could be deceptive as well. I'll keep trying to make some sense out of what is posted here. I'm sure a hyperdrive physics is in there somewhere.

Lawrence,

I would be interested in any information you want to diseminate.

Would it be a big problem if I just referred to space as the Higgs Field? If a Higgs field gives W+/- particles mass, and presumably other particles as well, it does so by regulating the laws of motion on its space-time surface. When planets, stars and blackholes curve space, maybe it's not space that they curve, it's the Higgs field. The Higgs field, which introduces mass, also introduces the very laws of motion. What would KE = 1/2mv2 if there was no associated mass. The Higgs field, which gives mass, is the very thing that interconverts kinetic energy and velocity. Momentum would be zero if not for the Higgs field. Since the Higgs field is a lowest energy field, and higher energies are referred to as tachyons, why not just refer to those fields as hypothetical hyperspaces with Tachyonic-Higgs fields that have not been observed, yet. By doing it this way, we are free to describe a hyperspace as a Higgs field variant with hypothetically different values of c and h.

Dear Jason,

I called my paper "A Geometrical Approach Towards A TOE" and it does include the Standard Model, a generic Quantum Gravity, all bosons, and all fermions. Although the four dimensions of spacetime are closely related to the four charges of (color_g3, color_g8, hyperflavor, weak isospin), I'm not certain if or how spacetime is incoporated into this model. Maybe "TOE" is an overstatement, or maybe it just needs a little more work.

Hans-Thomas Elze is proposing a quantized spacetime. Leshan is proposing "holes" and Jayakar is proposing "clusters" that must all behave like quanta. If spacetime is a quanta, then it may behave somewhat like a Higgs because 1) the Higgs has zero spin (as should spacetime), and 2) any absence of spacetime should attract spacetime, and thus cause spacetime curvature equivalent to gravitation or mass (this is my reinterpretation of Leshan's ideas - English is not his primary language, and his paper did not seem this clear to me). My hypothetical scalar fermions/ tachyons might become lattice defects in the 4-D of spacetime and behave like some of these odd quanta.

Have Fun!

Ray Munroe

Dear Lawrence,

Yes, this SO(2,4) of Hyperflavor is part of my SU(7) Yang-Mills GUT. There are 15 total components that I called C, D, and E in equation 2. These states mix with the Higgs states to become w and z Hyperflavor bosons (in lower-case letters rather than upper-case letters to demonstrate similarities with the Standard left-handed Weak force). A primary difference between Hyperflavor and Weak is that Hyperflavor allows left-handed interactions, right-handed interactions, and mixed left-right interactions. Hyperflavor bosons must be more massive than the W and Z bosons, or we would have already discovered these hypothetical bosons.

Because SU(7) has a rank and dimension of six, it is large enough to contain a four dimensional spacetime plus a two dimensional AdS.

Have Fun!

Ray Munroe