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

Dear Lawrence,

I always enjoy your comments - you force me to think the problem through to the next step. Gravi-Weak is strange - maybe it is technically Gravi-Hyperflavor. I need a 5-brane to explain my E8 pentality symmetry. I don't think this 5-brane is stable, but I could build a five brane out of the 1) the 3-brane gravity-brane and the M2-brane hyperflavor(weak)-brane, or 2) the 3-brane gravity-brane and the 2-brane generation-brane (which I think is the original 5-brane in the theory).

Yes, the Monster group is huge and a seemingly impossible task.

Have Fun!

Ray Munroe

The veilbein which frames the graviton with another field is

E_M^A =

|e_m^a ψ_m^α bar-ψ_m^α'|

|0 ~~~~ δ_m^α ~~~~~~0 |

|0 ~~~~~~0~~~~~ δ_m^α'|

where the top row consists of the gravitational tetrad (graviton) and the Rarita-Schwinger field or gravitino. This matrix is identified with θ = bar-θ = 0. The framing can be seen with the equation of motion

x^m - -> x^m - i(θσ^m bar-ξ(x) - ξ(x)σ^m bar-θ)

θ^m - -> θ^m ξ^m(x) and HC,

where the general rule is z^m - -> z^m - ξ(z). The coordinate basis in general can be found from E^A = E_M^Adz^M where dz^M obeys these supersymmetry equations of motion.

The key fact is that the frame (these equations of motion and the definition of superfields) here frames the graviton with the 3/2-spin field. We don't know what this field is physically. No fundamental spin 3/2 field have been identified by experiment. This particle is clearly not a gauge field by any stretch. Now the particle might form a composite or be a composite of some sort. The 26 dimensional bosonic string without the two tachyonic vacuum states is SO(24) and the operator Ω^{ab} acts on the vacuum to give Ω^{ab}|0> = |Ω^{(ab)}0> Ω^{[ab]}|0>, decomposed into symmetric and antisymmetric parts. The symmetric part is a spin 2 field or the graviton and the symmetry between the a and b is equivalent to the symmetry between m and a in the veilbein and that the curvature is an eigenvalue of the veilbein DDE^A = E^BR_B^A. The antisymmetric part is a gauge field-like term. So the gauge field might then be some field composite

A_m = (bar-ρ)_αψ_m^α - bar-ψ_m^α'ρ_α'

where (bar-ρ)_α is a fermionic spin1/2 field. So the equation reads spin3/2 - spin 1/2 for a total spin = 1. However, this might be an oddity of sorts. This Dirac field might be the superpartner for a gauge field, a gaugino. Further this might be a component of dark energy, and compose not a gauge field for how matter we understand interacts, but how dark fermions and the like interact.

The monster group is clearly out of hand, and we may never do much with it in physics outside of some almost qualitative description. Of course maybe quantum computers will let us work somehow with all its 8x10^{50} roots. Maybe we will become neurally more connected with cybers and physics of the year 2079 will involve borg-like physicists hooked into a vast network of quantum computers as this collective works to understand some ultra-hyperquantum gravity theory based on the monster group. I have toyed with the idea of a Sci-Fi novel along these lines.

Cheers LC

Ray,

Thank you for your extremely kind words on Grgin's essay page. You can read a more in-depth explanation of his ideas at: http://arxiv.org/abs/0901.0332

I came in contact with his work some time ago due to Hrvoje Nikolic (who is also participating in this contest) and we both agreed that Dr. Grgin is way too modest and Hrvoje challenged me to understand Grgin's ideas and write an overview paper about them (which is the link above). The rest is as they say, history. For the first time I truly understood quantum mechanics and I had the proof of QM's uniqueness in one of Grgin's papers (which I speculated about its existence and I had sought it myself before, but lacked a workable approach).

Form the old GNS construction (theorem) we know that the state space of QM has the Hausdorff's property because complex numbers are commutative. Now quantions are their generalizations in the relativistic domain. Being non-commutative means that the proper way to do relativistic QM is using non-commutative geometry. I knew about non-commutative geometry before quantions, because Connes had already produced an axiomatization of the Standard Model in this framework, but I did not understood a thing about them and the physics intuition Connes suggested was childish at best (Connes is a Fields medal winner mathematician, not a physicist). I had asked around everybody to see if anyone could explain non-commutative geometry to me, but everyone was just as lost as I was. It was not until recently (and after the publication of my paper) that it all started making perfect intuitive physical sense from the quantionic perspective.

Now it is not everyday that the unification of relativity with QM is achieved, and I do stand by by original statement that Grgin deserves the Nobel prize for it. Yes the work continues, but the basic framework is done. Another remarkable thing about this unification is that it is only possible in 3+1 space-time dimensions. Let's only imagine what publicity string theory leaders would have if their theory would predict 4 dimensions and not 10 or 11.

Hi Ray ,

Thanks for the advice ,it's likeable .

Don't worry ,never I am disheartened,never because I know what my theory is fundamental .

Like I said I am here to know interesting people with a beautiful spirituality and that for the sciences center ,probably the name will be Unified Sphere or Sphere Institute .

Like I said too ,I don't wait anything from systems ,it's like that ,I am not pretentious ,just conscient to my discovery .

I am sorry to have discovered that ,I know it's revolutionary thus I have many people against me ,normal ,the jealousy is human like the vanity .

About the essay ,like I said ,it's not important ,I know where I go ,I must have a good administration for the Nobel prize and others .

This week ,I am going to meet a Belgian person here in Belgium to elaborate the international strategy for my Theory .

Of Course I must stabilize all that ,there is too much monney in the short ,middle and long term .

Hope this contact will be well .I am a little parano due to my past .

Like I said all are welcome for synergies with my conditions of course .

Regards

Steve

You know Ray ,

If I must write this paper with two persons ,it's with you and Dr Corda .

I will tell you .....

Steve

Dear Friends.

WOW! This is a lot of information to absorb. This is a first response - there might be another later.

Dear Lawrence,

I know that spin-3/2's particles have never been discovered, but Supersymmetry expects the spin-2 graviton to have a spin-3/2 gravitino SUSY partner. I predicted more spin-2 particles (an entire class of massive, short-ranged tensor bosons related to Gravity that I call WIMP-Gravity), and this should also lead to more spin-3/2 gravitino-like fermions with a one-to-one correspondence of degrees-of-freedom.

Dear Florin,

Emile's ideas are interesting. It will take time for me to process these ideas. Off the top of my head, I expect to need pairs of quantions to rewrite the Dirac Equation in terms of quantions instead of gamma matrices. Still, a pair of quantions is only four dimensional.

Dear Steve,

I would be surprised if relative unknown scientists like you and me even have a Lottery chance's shot at the Nobel Prize, which is why I think you should start with a reasonable goal - with something like this contest. But I would be willing to offer ideas and proof-read your theory. We never know which overlooked idea will evolve into the next great theory.

Have Fun!

Ray Munroe

Dear Dr Cosmic Ray ,

The prizes ,the real prizes aren't a lottery .

When a theory is fundamenatl ,it's logic .It is recognized .

In fact ,I am persuaded what many people have understood my mesage and this theory of evolution towards the Ultim Sphere .

You know Ray ,it's a long,long research for me ,a lot of works .

Thus not necessary to publish here .An intelligent person understand this reality .Quantum spheres ....time space evolution...codes of evolution ...complexification ...cosmological spheres and their ROTATIONS...ultim sphere .

It's not difficult to encircle this very short evident resume .All is linked .

Now let's improve,optimize this reality .

The mass has a cause .....the rotating spheres ,simply.

All is said in fact but of course this theory can be optimized and completed wth pragamatism ,rationality ,logic ,basic ,....never I will insert mathematical extrapolations without physicality .

What I like with you is your spirituality and your facility to play with equations and furthemore your desire to find the real truth .

The future will tell us if we could collaborate .

Sincerely

Steve

I have been giving the matter of quantions some study. I am not entirely decided about their status as yet. My sense is they are an interlinking between two complex number or quaternions in a way which defines norms differently. This might have something to do with S-matrix. So I will outline some aspects of S-matrix theory and black hole complementarity, and then try to make possible links to quantions.

The holographic principle and black hole complementarity are generalizations of the S-matrix. Susskind's treatment of strings falling onto a black hole according to a distant observer treats the S-matrix on a domain which is causally defined on an infinite domain of support according to the tortoise version of the radial Schwarzschild coordinate

r* = r - 2m ln|r - 2m|

The S-matrix requires an infinitely extended domain by which fields are causally related, which is "manufactured" by this coordinate. In these coordinates the string exhibits a range of strange behavior, which I am not going to review again in great detail. Yet the string ends up covering the black hole horizon and is frozen their according to this distant observer. To an infalling observer on a commoving frame with the string none of this is the case, but rather the string enters the black holes with no apparent change and then exhibits tidal forces of an extreme nature near the interior of singularity. The string is a form of S-matrix theory, and the two cases reflect the existence of two S-matrices, each according to state space elements which are incommensurate with each other, or according to noncommutative operators. This is one way of looking at the so called black hole complementarity principle. There is then a superposition of the string in these two bases of states, and for this reason the distant observer may see the string frozen above the event horizon and also "burned up" by Hawking radiation made of quanta scattered from the string according to the infalling observer's frame.

The ordered S-matrix defines each vertex, or particle, and its neighbor. In a linear chain a general state is an S-matrix channel of the form

|φ> = |p_1, . . . , p_i, . . . , p_j , . . . , p_n>

This state or S-matrix channel is related to but distinction from the channel

|φ'> = |p_1, . . . , p_j, . . . , p_i, . . . , p_n>

The particles or vertices p_i and p_j have exchanged their neighbors, which means some "relationship" structure to the amplitude has been fundamentally changed. The S-matrix is written according to S = 1 - 2πiT, so two states or channels |p_1; : : : ; p_n> and |q_1; : : : ; q_n> are related to each other by the S-matrix as

=

= - 2πi:

For the < | the in channel and | > as the out channel p_n and q_1 are neighbors, and neighbors through the T-matrix. This eliminates an open vertex in the chain. The vertices or particles p_1 and q_n are the open elements in the chain and defines an "anchor" for the chain, and are thus defined as neighbors in this manner.

A four point function and the transition matrix defined by vertex operators T = V(p_1)ΔV(p_3) will contruct the Euler-beta function for coherent states of the S-matrix. This is the connection of course between string theory and the old bootstrap or S-matrix theory. Now for two S-matrices, which pertain to the different domains of causality on a black hole this theory is made more difficult. The S-matrix is a braiding operation of sorts between elements of a quantum group G. So we might model this as a commutator structure (braiding) between two elements a and b \in G. So we might denote this as ab --- ba. Now let us assume the states we observe are super-positions of incommensurate states involving two quantum groups G and G'. We will then have a structure of the sorts (ab)c --- a(bc), that exist in an associahedron I_2(5) with a homotopy structure. This homotopy then connects to a K-theoretic field theory, which I discuss in my paper

http://www.fqxi.org/community/forum/topic/494.

I will not belabor this part of the things, until later or somebody takes an active interest in what I am suggesting here.

The black hole complementarity principle. The complementarity is an odd structure, for Hawking radiation is due to a Bogoliubov transformation between basis elements. In this setting the theory of spacetime is classical and the fields scatter off the black hole or spacetime with an event horizon. The response of the black hole or spacetime is a metric back reaction, which is a classical response to a quantum scattering. Yet black hole complementarity has demonstrated that quantum information is preserved for the case of a BZT black hole in an anti-de Sitter spacetime. So a connection between the quantum principles of unitarity (or maybe more generally modularity) and a classical field theory which exhibits thermal physics (black hole entropy and Bekenstein bounds etc) exists within this AdS/CFT setting. Yet we do not as yet understand how quantum information is preserved. We just know that it is.

So the quantumal rules of Grgin seem to segue into the picture here. The permitted multiplication rules

(fαg)αh (gαh)αf (hαf)αg = 0

gα(fσh) = (gαf)σh fσ(gαh)

(fσg)σh − fσ(gσh) = agα(hαf)

Connects the Jordan exceptional algebra to a quantum algebraic system. The associator is then by the homotopy equivalence mapped to a quantum group as a system of permutations (related permutahedra) with one set of norms determined by the underlying permutative rules or associahedra and the other by standard rules of complex conjugation in quantum mechanics. So the associator is [f, g, h]σ = agα(hαf) which induces the map between the octonions and the quantion group. This seems like an interesting problem to develop.

There are so called massive gravitons in N = 8 supersymmetry. These are of course issues with some of these problems. Where in your paper, or the case study 3 paper do you construct massive gravitons?

Cheers LC

The equation that failed, due to a carrot sign, is

(p_1, . . . , p_n|Sjq_1, . . . , q_n> = (p1, . . . , p_n|(1 - 2πiT)|q_1, . . . , q_n>

= (p_1, . . . , p_n|q_1, . . . , q_n> - 2πi(p_1, . . . , p_n|T|q_1, . . . , q_n>:

Cheers LC

Dear Lawrence,

So quantions might be related to your Jordan algebra and my permutahera/ associahedra/ n-simplices? Would a 2-D quantion transformation of an 8-D octonion look like Dray and Manogue's 10-D work, but with a corrected S-matrix?

I denoted the massive tensor bosons as WIMP-Gravitons or "F" for "Fifthons". This idea is more fully developed in References 3 (A Case Study 3.3.pdf - Discussion Section) and 4 (my book "New Approaches Towards A Grand Unified Theory" with a free preview link above - Chapters 5.5 and 7.5).

Have Fun!

Ray Munroe

For the theory of Stasheff polytopes and associahedra take a look at Fomin and Reading's paper

arXiv:math/0505518v3

This gives a reasonable account of the homotopy theory involved here. I have been working on a K-theoretic aspect of this. Quantions seem to be what this would lead to in some general setting. I will try to get back to more of this later. The hour is getting a bit late and my energy levels are dropping.

I will see if I can understand what you are saying about other massive gravitons. There are a lot out there who would not be happy with this sort of development.

Cheers LC

Always full of creativities and technical extrapolations .

I learn in the same time ,thanks the two maveriks .....

Take care

Steve

Dear Ray,

Your essay is very educational to me, which motivates me to read your book.

Besides this generality, a particular detail in your paper will very likely help me get over an obstacle I ran into in deriving the group SU(3) within quantionic math. I've been stuck with it for over a year.

Regards, Emile.

I am sorry, Ray. In the post above I did not mean to be anonymous. E.

Emile,

I would be interested in your problem or thoughts on SU(3) here. As I indicated yesterday I think a JOrdan exceptional model involves G_2 holonomy, and on the algebraic level g_2 = su(3) (3 bar-3). You can respond on my blog space http://www.fqxi.org/community/forum/topic/494 if convenient.

Cheers, LC

Geometry is the beauty of Mathematics and when applied to Physics should certainly help clear the picture. nature is simple but human mind is complex. Sometimes we contribute to make Physics complex through our overuse of Mathematics without first evolving the right concepts through our observation, critical analysis and hard use of our intuitive strength. Silence contains noise too but not viceversa. Entire knowledge resides in the depths of silence. Similarly, order contains randomness and not viceversa. This is the game we are playing in Physics!

Dear Narendra Nath,

Thank you for your comments. I am attracted to the beauty of geometric symmetries and hope they are relevant to our explanation of the natural universe.

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 paridigm 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 Ninteeth Century - thay sure were wrong!

At the end of this 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 Commets, 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.

Have Fun!

Ray Munroe

Ray,

I thought it was a very informative paper. It really gave me a sense of how physicists are approaching a TOE.

On a philosophical note, I think that properties like beauty and simplicity are not goals in and of themselves, but are natural consequences to the way the universe truly manifests. Those who believe that God created the universe are, in my opinion, correct. However, words like "God" and "create" are single notes in the grand cosmic symphony that continues forever.

On a hyperdimensional note, I still think that hyperspace is a 5D space time with a c'>>c and a Planck constant h'>>h. I still think that particles are tiny disruptions in space that ever so slightly curve space-time enough to account for the particle's energy. The tesselation approach demonstrates an important property of space, like a balance or equilibrium of some kind. I think your paper will reveal the answer.

Dear Jason,

Thank you for your comments.

I am a Christian. I believe in a God who desires a relationship with all of humanity, and restored that relationship with the life, death and resurrection of His Son. That belief places me in the minority of scientists.

Nonetheless, it is our duty as scientists to try our best to explain physical phenomena with physical processes, and thus my appeal to beauty and symmetry. On the contrary, I could have equated God with beauty and symmetry and said that God did it all (I believe that God established rules to create the Universe, and God gave us the capacity via language, logic, mathematics and science to understand most of those rules). I know that my belief in God biases me in my approach towards a TOE, and I reject the idea of our Universe arising out of purely random chance.

If Lawrence and I are correct, dimensions 5 and 6 are radically different from dimensions 1 through 4. It would be interesting if these unseen dimensions have different values for "c" and "h", although I am not at a stage of theory development to be able to claim something so fantastic. But what if everything rescales around those constants and continues to thwart our efforts for a hyperdrive? As far as we know, our Universe may be full of isolated pockets of life - with each pocket isolated from the others by our speed of light limitations.

There was at least one other paper about hyperdrives in this essay contest. Did they present any ideas that you have not yet considered?

Your Friend,

Ray Munroe