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Essay Abstract

In 2007, A. Garrett Lisi published “An Exceptionally Simple Theory of Everything” (TOE) in which he presented a geometrical approach towards TOE based on E8 and the Gosset lattice. Although Lisi’s approach has been very well received by FQXi members and pop culture, it has received some serious physics critique – most notably from Prof. Jacques Distler of the University of Texas. Distler’s fundamental complaint is that E8 is not large enough to properly contain three chiral generations. Still, it seems appropriate to consider Lisi’s geometrical approach a reasonable way to model an approach towards a TOE – a “toy model” TOE as such. The author recently posted “A Case Study of the Geometrical Nature of Exceptional Theories of Everything” and published a book on “New Approaches Towards A Grand Unified Theory”. These two papers present the possibility of a geometrical approach towards a TOE. Geometry enters into this approach to TOE in two different ways: 1) Yang-Mills Boson GUT’s are derived by recognizing similarities between certain crystal symmetries and certain SU(N) Lie Algebra symmetries, and 2) Particle multiplets are constructed from Simplices, and the product of these Simplices builds representative multi-dimensional lattices. It is anticipated that this geometrical approach may be an axiomic breakthrough that allows us to bypass the apparent complications of Gödel’s Incompleteness Theorem and ask the question “What is Ultimately Possible in Physics?” – A Geometrical Approach Towards a TOE.

Author Bio

Dr. Ray B. Munroe, Jr. received all of his degrees in Physics from Florida State University with a Ph.D. in High-Energy Physics Phenomenology in 1996. He is currently CEO-in-waiting of his family's retail business.

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Dear Readers,

This "What is Ultimately Possible in Physics?" essay refers to two papers with limited availability. Both files are rather large, and may load slowly. They are posted here as Ref.[4] and Ref. [3] (attached below).

Sincerely,

Ray Munroe

attachments: A_Case_Study_3.3.pdf

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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

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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!

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Hi Dr Cosmic Ray ,

Happy to see your paper on the contest .

It's well condensed your work ,and relevant .

Good luck .

Steve

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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

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Dear Lawrence,

You have the old version of Ref. [3]. This is a condensed version with a different theme and presentation. I enjoyed your contest paper. Now I need to read your larger “Jordan” paper. Good luck in the contest!

Dear Florin,

I enjoyed your contest paper. Could a geometrical approach to a TOE bypass Gödel’s Incompleteness Theorem? Good luck in the contest!

Dear Sphere-keeper Steve,

Thank you for the good wishes.

Have Fun!

Ray Munroe

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Dear Leshan,

Your perspective is an interesting one. Truly, I despise the implications of “TOE”, but follow industry-wide nomenclature regarding a unification of matter and interactions.

Even if we understood everything/ nearly everything, we may still have limitations such as the speed of light and Planck’s constant. So the gap between human-like vs. God-like may be the gap between...

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Dear Leshan,

Your perspective is an interesting one. Truly, I despise the implications of “TOE”, but follow industry-wide nomenclature regarding a unification of matter and interactions.

Even if we understood everything/ nearly everything, we may still have limitations such as the speed of light and Planck’s constant. So the gap between human-like vs. God-like may be the gap between knowing how something works in theory vs. being able to apply that knowledge in a practical manner. I don’t consider this knowledge God-like. If I did, I probably wouldn’t share it with anyone else.

Regarding “closing all physics laboratories”, I worry that our great experiments such as the LHC are getting so expensive and expansive that we may not be able to (easily) trump the last great experiment. For the sake of all future Supercolliders (my thesis modeled phenomena for the International Linear Collider ILC that hasn’t been built yet), I hope that the LHC discovers something – the Higgs would be nice…

I think that the form of an SU(11) boson GUT is large enough to contain any Theory of Quantum Gravity – even though we do not currently have that Theory. I referred to the need to enumerate Feynman Diagrams and Lagrangian components in my “What is Ultimately Possible” Conclusion. Furthermore, I think that the form of an SU(13) boson GUT is large enough to contain the effects of Fermion Generations, and the CKM Quark and PMNS Neutrino Mixing Matrices (more details in the attached Ref. [3]) – even though we may not yet fully understand all of these effects either.

In other words, I don’t have all of the answers, but maybe I have the right framework and maybe WE (humanity) can work together to flesh out the details. As they say “The Genius is in the Generalities and the Devil is in the Details”.

As a Particle Physicist, I love symmetries. If these symmetries lead to THE TOE, then that is wonderful. If we can’t find THE TOE because of philosophical or mathematical (Gödel’s Incompleteness Theorem) limitations, then hopefully it will bring us closer to a full understanding of particles and interactions. Why do physicists chase grand theories? Why do dogs chase cars? It is part of our nature that we must always ask the difficult questions and keep pushing at the horizon.

The unification of the three strongest interactions has been done: Standard Model and Georgi-Glashow SU(5). We need to unify Gravity with those three forces, and we need to unify boson and fermion particle content. I think my Geometrical model is large enough to accomplish these goals.

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

Good luck on your essay!

Sincerely, Ray Munroe

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

An important decay route for K12’ is K12SU13SO
1480;24E8 , where the interpretation is that the SU13SO24=
472;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

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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

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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...

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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

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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

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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

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Hello ,

Dear Ray or Lawrence ,

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

Regards

Steve

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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

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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,...

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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

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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

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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

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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

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Dear Steve,

Do not become disheartened. Your spherical ideas may be related to my simplices. I understand that English is your fourth language, but you probably should have submitted an essay for this contest. Then you could talk about spheres and be relevant to your blog site. Of course, the FQXi overseers would expect you to have a properly themed paper.

You and I have had our ups and downs, but you can e-mail me anytime (please remember that certain words are more taboo in English than in French).

Have Fun!

Ray Munroe

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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

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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...

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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.

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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

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You know Ray ,

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

I will tell you .....

Steve

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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

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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

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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...

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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

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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

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Always full of creativities and technical extrapolations .

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

Take care

Steve

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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.

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

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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

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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!

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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

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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.

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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

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Hi Ray,

I read the paper by Barcelo. There is no doubt in my mind now. Whatever is necessary to achieve FTL, the physics community doesn't have it or know it. Just from my ponderings, I can see that we would have to have access to a yet unproven hyperspace. If that hyperspace had a Planck constant of 10^+34 J-s, about 68 orders of magntitude larger, we might be able to use what I call the "particle-space" relationship. A particle-space relationship says that particles are just manifestions of energy stored in space, itself. With a very large Planck constant and a very large speed of light, c'>>c, it might be possible to describe our universe as a quantum particle in hyperspace.

The other property that we would need would be the existence of negative energy. In hyperspace, if a universe-anti-universe pair can spring up, the idea is that the negative universe would have negative energy, and therefore negative curvature.

I think those discoveries might be enough to allow the possibility to achieve FTL travel. But there are other strange features that would have to be worked out. We have to acquire the ability to scale (c,h) in such a way as to keep the mass very low. Also, as I've mentioned before, we need to create a pair of pocket universes of small radius, and large energy/neg energy stored in curvature, to create the effect of a battery. Then, we need to figure out how to generate gravity waves in such a way as to transmit momentum, equal and opposite, to the direction we want to travel.

We're not going anywhere FTL for quite a while. In my optimistally biased opinion, someone already has this technology. But if they're are not willing to share it, then we won't be able to achieve it for many thousands of years. We're like a village of Pygmies who want a computer, but don't even understand the Shotkey diode.

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MAthematics is simply a reality of physics, and it is not going to get more elementary. Newton had to invent calculus in order to advance his laws, and calculus is a senior high school subject these days. Einstein used Riemannian geometry to formulate general relativity, then a 60 year old mathematical topic, supersymmetry takes us into topology, a mid-20th century mathematics, and on it goes. Clearly mathematics is not physics, but a decent knowledge of modern mathematics gives you a better tool box to work with.

In Ray's K12 or H_4xE_8 I am trying to figure out what the physical basis for this is. The 120-cell tessellates an AdS spacetime. There is also an interesting duality between AdS_3 and QCD. The automorphism of the Jordan algebra is the exceptional G_2 group, which contains as its maximal subgroup SU(3). So this breakdown seems to suggest some sort of duality between AdS structure of spacetime and QCD. I think this holonomy is some sort of extended idea similar to quantions.

So to pursue physics it does require that one have advanced mathematical concepts at hand. There seems to be no escape from this.

Lawrence B. Crowell

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Dear Lawrence,

Mathematics is one of the cornerstones of physics.

Regarding the use of mathematics in physics, I used math in my own ideas. I am not opposed to Emile and Florin's use of quantions - I simply have not yet been convinced that we cannot accomplish similar things (even though I know that the mathematical structures are different) with Pauli and Dirac matrices, but I scored both of their papers well, and remain open-minded regarding their ideas. I truly would like to see a quantion theory with interactions.

K12' has a G_2 of color buried deep within (see Lisi's paper or Ref [11]). Regarding the G_2 holonomy, Gordon Kane also referred to this mathematical structure. I was originally distracted by the similarities between K12' and Klein's Chi(7), and thought I was working with an I_2(7) seven/fourteen-fold symmetry. But now I realize that I may be working with a Lambda_{10}, and NOT a Chi(7). If it is a Lambda_{10} (Conway & Sloane "Sphere Packings, Lattices and Groups" - Laminated Lattices), then it would have the same five/ten-fold symmetries as the G_2 holonomy. I think this five-fold symmetry is important to Supersymmetry, where we might expect five fundamental particle multiplets: scalar bosons (spin-0), matter fermions (spin 1/2), vector bosons (spin-1), gravitino fermions (spin-3/2), and tensor bosons (spin-2).

Have Fun!

Ray Munroe

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Dear Lawrence,

Another oberservation:

If I understand quantions properly, they are an effectively two dimensional algebra in competition with the Pauli sigma matrices. Just as we can build twistors (an equivalent to Dirac gamma matrices) out of pairs of Pauli spinors, we should be able to build relevant 4-D structures out of pairs of quantions. That should be relevant for 4-D spacetime.

BUT, WE are also dealing with an AdS 2-D M2-brane (my fifth and sixth dimensions). Is the rule of algebra in these dimensions based on quantions or on Pauli matrices? We also anticipate anyons in these bizarre dimensions. Would one algebra be more likely to yield this feature than the other?

What are your thoughts?

Ray Munroe

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Dear FQXi Friends,

Most of my scores have been 8's or 1's. Recently, more of the scores have been 1's. If you think you have found an error in my logic, please point it out. Constructive critisism would be greatly appreciated if you can spare the time (I understand that we are all under time constraints to read these papers this month).

Thank You!

Ray Munroe

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I noticed that I too am getting a string of ones, as are I think a number of other papers. It is worth noting that the highest score is now less than 5, and I suspect that a few people with low scores are trying to supress other scores. Almost all the scores have decreased in the last week or so. Some of the papers with very low scares are honestly rather marginalin their intellectual value, and I wonder if some of the writers of these are trying to drag the whole process down. There are a number of pretty good papers here with scores in the 3 to 4 score level, which honestly should be in the 6 to 7 score level.

The anyonic nature of the M2-brane is mirrored in the lagrangian for the whole Jordan exceptional algebra. The diagonal terms define a simple Chern-Simons Lagrangian, while the rest of the Lagrangian (from the determinant of the matrix under triality maps) shares this feature as well. The M2-brane is S-dual to the D5-brane (black brane) in the NS sector. The world sheet for this is a 6-volume.

More later, when I find the time.

Cheers LC

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As I left you page here and went to the main page I just noticed everyone's score appears to have dropped, including mine. So I racked up another one, as did most everyone else I think.

LC

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Perhaps someone is reaching for the prize money using a tactics other than intellectual prowess. Is there any way to tell whose score did not rack up a "1" during this time period? It would not be a definitive way to pinpoint the source/intent, but it might help to take a look.

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If this is happening, and honestly I hope not, it is mostly likely not somebody raching for prize money, but rather someone who thinks, "Well if I'm going down with a score of 1.4, then dammit I'm gonna take you down a notch as well." It is probably hard to prove something like this is happening anyway.

LC

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Dear FQXi Friends,

While I think of scores of 1's and 10's as being statistically unlikely, many of the voters obviously think of this as a way to make their votes count more heavily. Perhaps this strategy will mostly average out and the best papers will win anyway. Perhaps it is good that they think highly enough of me and Lawrence as competitors that they want to take us down.

But seriously, I would go back to the drawing board and rethink or give-up on this entire Geometrical Approach Towards A TOE if someone could prove me wrong.

I welcome constructive or destructive criticism. All I ask is that you read the entire paper first.

Have Fun!

Ray Munroe

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The scoring is funy in some ways, and it seems to lead to this general suppression of scores. I have noticed in the last several days how a whole list of papers with various scores will in a day be reduced by about the same amount. I agree that people should take the trouble to read papers before scoring them. I have actually only scored a few, which have been some that I thought were really good and conversely bad. I am waiting to cast most scores until close to the end.

LC

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Lawrence,

I had this idea of some evil genius somewhere with an evil plot to take over the contest money. They might even be a supervillian! Actually, I have a hunch who it might be. If it really is the person I'm thinking of, they are capable of succeeding with honest intellectual hard work.

Ray,

Scores of ten are not that statistically uncommon; it depends upon the reader. I gave at least one ten to the papers I've read. I could tell a lot of work went into it, and it was potentially useful.

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Dear Dr Cosmic Ray ,

Your approach hasn't false in fact .Personally I noted 8,I have voted perhaps 10 times,and always I read a paper , and it was sincerely because you and Lawrence are two mavericks and your extrapolations are very relevant even if I don't agree with some ideas like multiverses ,extradimensions ,strings ,higgs ,Lie algebra.All that isn't sufficient and too much mathematical without the real limits .Now of course all can be synchronized with the physical laws .

I have learned a lot with both of you since I have known FQXi.

My vision of your work is simple ,the imaginaries and the extrapolations must be physicals .The thermodynamic is essential in my opinion .

The complexs too need limits ,without limits ,it's infinite and the physicality don't need that .

About the contest ,I am surprising by some comportments ,like a game ,it's sad .But it's not important in an universal point of vue ,but on Earth indeed ,some systems are bizarres .If the strategy becomes a machiavellism like a play of chess ,it's sad .There I don't understand this human nature .

My conclusion about these contests ,

in resume 15 per cent of fundamentals and conscious

30 per cent in the imaginaries

40 per cent with a mix of fundamenatsl and theories where???

10 to 90 hihih per cent of business practices

5 per cent of jokes

HIHIH dear Ray you you are in the two first lines ,with 85 per cent in the first line and 15 in the imaginaries

Best Regards

Steve

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In your works ,similars ,of course You ,Lawrence ,Florin ,Emile ...has some rivairies indeed ...perhaps it could be well if you work together in team for your researchs and works .

The team with a good mind can make interesting things in complemenatrity .The machiavellian mind falls always ,it's the real equilibrium of our universe .

Always the bad falls.

Best Regards

And good luck for this competition too

Steve

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Dear Steve,

Thank you for your support.

Truly, I do not care about the money. I just love physics.

My purposes for entering this contest were: 1) to make new contacts with interesting people (checked box), 2) distribute my ideas in a larger forum (checked box), and 3) attempt to gain FQXi membership (unchecked box thus far).

It is funny to me that the concept of a TOE draws instant criticism or appeal - there seem to be few unbiased perspectives between these extremes.

It is OK - I welcome criticism. The cowardly and silent 1's bother me more than legitimate criticism.

Have Fun!

Ray Munroe

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I agree that the prize is not what I am after. I will confess I would be unhappy if my paper fell towards the bottom of the heap. Yet the real purpose is to increase communications of new ideas with people and potential collaborations.

Cheers LC

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You are super Dr Cosmic Ray ,don't change never ,

And don't forget ,your faith is welcome for the humanistic sciences cenetr .It will be a real honor for me .The faith and the skills ,waawwwww it's the solution ...

Take care

Steve

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Ray,

(I submitted this on Abhijnan's blog area)

This problem is related in some ways to Perleman's proof of the homotopy equivlanece of homology spheres. I have been doing some background reading on this problem and am in many ways suspect this has some very deep mathematics to it. If you take a toy balloon and twist it up into various shapes it will smapp back into a spherical shape. I assume the surface is perfectly frictionless so that tying it up does not clamp it into shape. This Hamilton flow is such that it is always guaranteed to bring the space back to its minimal configuration. If you look at Perelman's paper you will see how he assigns entropy functionals to this! So a three sphere is guaranteed to evolved by the Ricc flow

dg_{ab}/dt = -2R_{ab} + ...

This idea is carried over to higher dimensional spaces, and this evolution is conidered according to Turing machine logic. Look at the Novikov theorem quoted in Abhijnan's paper. So the logic is whether one can compute the minimal configuration of a space by Turing machine logic and assertain whether it is the same space as a known space in its minimal configuration. This is important for understanding all these strange Calabi-Yau spaces and whether one can compute them distinctly from each other.

The one thing which needs to be done is to carry this from homological theory to K-theory. K-theory is a much more powerful approach to topology, and it has connections to noncommutative geometry. So this is a vast domain which has many areas left unexplored. I am still patiently trying learn the foundations which Abhijnan quotes in this summary paper.

It is too bad this is not receiving a higher score than what it has garnered so far. This is one of the better papers in the whole lot submitted here.

Cheers LC

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Dear Lawrence,

Abhijnan's paper does contain more physics than most of the papers in this competition. In my opinion, too many of these papers contain more philosophy than physics. Philosophy is certainly important to physics ("natural philosophy"), but we are past the days of Aristotle - we do have real knowledge and data to work with as well. I am tired of reading modern "hand-waving" arguments about how TOE's do or don't exist that rely exclusively on previously existent theorems such Godel's Incompleteness Theorem or the Turing Machine. I prefer the Nike slogan "Just Do It!".

Although Abhijnan's paper does contain a lot of physics, his goal of computing the string ground state is absolutely impossible with modern computers in the absence of a real breakthrough in our understanding of strings or TOE's. He indicates the possibility that patterns might simplify the computation. Perhaps my lattices ARE the patterns he needs! My alliance with Mohamed El Naschie last year led me to think that the difference between the finite K12' minimal roots and the nearly infinite Universe can be represented with a fractal approximation. My papers emphasized the minimal roots of K12', which are our nearest-neighbor lattice points, but this lattice could also have next-nearest-neighbors (similar to the long roots of K12, and also similar to the hyperflavor leptons and quarks in my book), next-next-nearest-neighbors, and so on to infinity. This is the physical reason why a fractal approximation may be appropriate.

I have been rereading your Jordan paper. You combine some interesting mathematical structures in your paper. Your 27 dimensional Jordan transformation is the natural extension to Dray and Manogue's 10 dimensional transformation. I think your physical interpretation is different from mine, but I'm not certain of myself either - I'm still considering the problem, and how it might tie into Supersymmetry or Feynman diagrams.

Have Fun!

Ray Munroe

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A fair number of these papers are more philosophical than physial. Some make references to results. Wolfram has entered the fray. He does make a statement which occurred to me some years ago. In effect there is an equivalence of computational complexity in systems. The thought occurred to me years ago that if I miz cream in my coffee that the system is computing the complex folding of the cream by hydrodynamic means. We don't normally think of this as complexity as such, such as with an organism or a computer. Yet a part of the problem is one of perspective. We don't set up the motion of cream in coffee to extract some output.

I am working on a problem involving octonionic black holes, or a way to use the heavenly phere structure of the Jordan exceptional algebra as local systems of 26 dimensional Lorentz spaces. The identification between the three octonions by the triality operation and the light cone structure of the diagonal elements reduces this to 10 and 11 dimensions. The J^3(O) is locally diagonalized by the F_4 group. The F_4 group is the Hurwitz quaternion "1154" representation of the 24-cell. The 24-cell has B_4, D_4 and F_4 representations and the quotient F_4/B_4 determines a short exact sequence between spin(9) and the Moufang plane OP^2. This local Lorentzian system is then given by connection coefficients on this system.

The Jordan algebra of a vector space V, which can be O, is ~ V\oplus R according to the mixed product

(u, α)*(v, β) = (αv + βu, (u,v) + αβ), (u,v) = \langle u, v\rangle

but the inner product gives

(u, α)*(v, β) = (u,v) - αβ,

which is the Lorentz metric. Thus the diagonal entries of the J^3(O) set the three copies of the octonions in a Minkowski geometry. The diagonalization of the Jordan matrix is the defined locally with a “gauged F_4,” which defines both the Minkowsi structure and the quantum algebra locally and constructs connection terms between local charts (local inertial frames).

Forget quantions, this stuff is much more general and powerful.

Lawrence B. Crowell

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Dear Ray B Munroe,

In Lambda-CDM model of cosmology, the existing generations from gauge group axioms provides geometrical approach on Yang-Mills Boson GUT to resolve constrains on the scalar transformation of large distance scale with the plank length for evolving background to construct TOE, in that E8 lattice may have importance. But the particle multiplets in Simplices and building of multi-dimensional lattice representations may be limited within quantum level and chirality expressions for structural determination is constrained.

In Coherent-cyclic cluster-matter model of universe, as there is no fine structure constant, string theory along with gauge theory is much applicable, in that 2-Simplex and 3-Simplex may be gauge representational for symmetry transformation between cluster-matters as branes, in that helicity and chirality may be expressed. As 3-Simplex representation is descriptive on the relativity of a cluster-matter with its coherent super-cluster-matter and 5-Simplex describes its sub-cluster-matters, combinations of branes is much applicable for this model and this geometrical approach provides good environment to evolve principles and phenomena on this model, thank you ..

With best wishes,

Jayakar

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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

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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

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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

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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

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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,...

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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. Crowell

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attachments: octonionic_curved_space.JPG

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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

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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

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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

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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

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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?

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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

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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

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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?

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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

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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

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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.

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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.

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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

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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

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Spacetime may in some ways be a condensate or due to a phase transition which is induced by Higgs-like behavior. I would not call spacetime the Higgs field. In fact the Higgs field is only somewhat related to the scalar field induced inflationary field, or inflaton.

Tachyons are vacua configurations on two of the 26-dimension of the bosonic string. These are "removed," so to speak by flying off to infinity in the big bang, or they appear associated with black hole singularities. The Cumrun Vafa work on tachyon condensates does illustrate some parallels with the Higgs field. My paper discusses tachyon condensates with black hole interiors and complementarity. They are involved with transitions between string types. I discuss this in my essay:

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

Cheers LC

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You might see if your model can be expressed according to a Born-Infeld action that has M-theory content. The AdS-CFT duality is one of the major developments of the 1990's which was advanced further into the BTZ-black hole or AdS-black hole result outlined in Susskind's book "Black Hole Wars."

These results are of course not the end of the story. The duality appears to exist and this indicates that quantum information is preserved in quantum gravity. As yet we don't know how this conservation takes place, where I think it involves quantum error correction codes.

Cheers LC

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Lawrence,

The idea of "space" reall comes out of geometry. But geometry only has to be enforced by the postulates from which it's built. On the other hand, the "space" that General Relativity and the Einstein equations refer to is subject to a speed of light constraint and a stress-energy curvature/compression relationship; gravity atually alters the path of light within this 'cosmology' space. 'Cosmology' space, and the causality that must exist, are subject to a path-of-light natural law that doesn't appear anywhere in 'geometric' space. It's like the two things that we call space are different. I'm not an expert on Minkowski space, but I'm pretty sure there isn't a postulate that says that causality cannot occur above a velocity c. 'Cosmology' space, the thing that satellites/planets/stars/etc. exit in, has built into it the Laws of Motion, a speed limit c, and all the other laws of physics. Some people even say that gravity waves can distort it. But geometric space has none of this. A Higgs field supplies the mass, which immediately invokes the laws of motion via momentum (conservation of momentum)/kinetic energy/etc. Ricci curvature describes the deviation from Euclidean space. But that is simply because the path of light is forced to change because of gravity. It's as if 'cosmology' space is occuring on some kind of a surface/brane/Higgs field or something, which provides for all these things (light path, QM, laws of motion, mass, ...), but can, itself, be distorted by gravity. These are my reasons for wanting to call it something other than space; a Higgs field comes closest to describing this 'surface'.

Ray,

I think space-time, which should be called a Higgs field IMO, is quantized. But if it is, does the standard Planck constant, h=6x10-34J-s, supply enough energy-time to fit it? The fact that you have to "fit in" gravity really makes me think that gravity won't fit at all. Electromagnetism operates by photons which seem to define and limit the brane. Gravity which operates by gravitons, seems to be off of the brane. Gravity is more than capable of distorting space (e.g. black holes). It's as if gravitons are tachyonic. I disagree with the idea that tachyons "fly off to infinity"; maybe Lawrence actually watched them fly off, but it sounds like a mathematical simplification. I think that gravitons are hyperspace forces that can distort 'cosmological' space. Gravitons, I think, are vibrations in a different lattice. I think that's why QM and GR can't be unified.

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What happens if I explain it this way. You and I sitting/standing in two overlapping spaces: gravity-space and QM/electromagnetic-space. Here are there properties:

QM/EM-space: c = 3x10⁸m/s and h = 6.6x10^-34J-s.

Gravity-space: c'>>c, h'>>h.

There are two sets of quantum waves that handle position and momentum. When a high enough density of mass occurs, due to QM/EM oscillators or defects/oscillations in QM/EM-space, it causes the gravitons (c' and h') to vibrate. This effect causes QM-EM space to distort.

Is that a clearer picture? The Higgs field would have to be a manifestation of QM/EM space. We might also be talking about either two different tesselations, or one tesselation fitting inside of another tesselation.

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Dear Lawrence,

Simply counting dimensions: I have four dimensions of spacetime, a 2-D M2-brane (with an SO(2,4) algebra) on dimensions five and six, a dual 5-brane (with an SO(5,1) ~ SO(2,4) algebra) on dimensions eight through twelve, and the odd-man-out seventh dimension may be a second time dimension. Some of these algebras may look similar to the AdS_5/CDT_4 Maldacena duality.

Dear Jason,

It may be that a quantized spacetime has similarities with the Higgs boson, but I am not ready to equate them. You said "Electromagnetism operates by photons which seem to define and limit the brane. Gravity which operates by gravitons, seems to be off of the brane. Gravity is more than capable of distorting space (e.g. black holes)." I agree. I consider dimensions eight through ten to be a Gravity-brane that contains massive WIMP-Gravitons. Gravitons travel freely on the seventh dimension, and are external to our observed 4-D spacetime, but affect spacetime via geometry.

If we look at the current scenario, we have different branes with different properties, and we should not expect to be able to unify the Standard Model and a quantum General Relativity in four dimensions. But I think unification is consistent in twelve dimensions. Obviously, we do not live in twelve dimensions, so these dimensions have collapsed and introduced the Spontaneous Symmetry Breaking that prevents us from clearly seeing the original lattice.

The space-brane and the gravity-brane are two different tessellations with potentially different values of h and c. Would the vacuum expectation value (vev) also be different? Or is the Higgs field a property of the space-brane, and the gravity-brane has a different sort of Higgs? If you look at my Ref [3], you will find many "Higgs" type particles (with corresponding fields) in my Super Yang-Mills 444-plet.

Have Fun!

Ray Munroe

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Hi Ray,

I think we have some agreement. The terminology is pesky, I'll try to refine that. I'm drawing a distinction between two kinds of space: Photon-space and Gravity-space. Photon-space, alternatively EM-space or even "Higgs+" space. Photon space, with standard c and h, is responsible for light, electromagnetism, and particle mass via whatever Higgs mechanisms are discovered. Curvature or compression of photon space has energy relationships which are part of the Einstein equation. Kinks in photon-space are hadrons, leptons, and of course photons. Photon-space provides the connection, mass m, between particles, and the laws of motion. Photon-space also gives rise to QM. The tesselation of photon-space using standard c and h is proceeding normally, whatever the right geometry is, we'll eventually figure it out.

Gravity-space has a tesselation that is based on c'>>c and h'>>h. Curvature (compression) in photon-space due to gravitationally significant objects, translates (haven't quite solved this part) into charge in gravity space. Negative energy expands space as if it were a negative charge. Positive energy compresses space (black holes) as if it were a positive charge. I'll continue devleoping this idea.

By the way, you mentioned a scalar fermion. I'm curious how you arrived at that. A scalar fermion might be interpretated as a vector with identical components, x = [x x x x=ct]. Our universe which expands at the speed of light might be a scalar fermion.

Gravity-space particles, such as a gravity-Higgs, are unknown at this time. I'll develop that, along with "gravity-space".

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Dear Jason,

What you are calling "photon space" and "gravity space" are probably the same as what I call the space-brane and the gravity-brane. I don't know for sure that these branes have different values of c and h, but I wouldn't be surprised if they do. My "scalar fermions" are the sf in Table 3, and the paragraph below Table 3 clarifies their basic properties.

Have Fun!

Ray Munroe

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Hi Ray,

Physicists release their grip, their garantee that physics still works, at the event horizon. When the acceleration is high enough to stretch the photon-space (space-brane?), odd things start to happen. I'm so tempted to just rip the Einstein equations and conservation of energy apart; but I'll be good. The black hole surface area is proportional to its energy content, right? ...

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Hi Ray,

Physicists release their grip, their garantee that physics still works, at the event horizon. When the acceleration is high enough to stretch the photon-space (space-brane?), odd things start to happen. I'm so tempted to just rip the Einstein equations and conservation of energy apart; but I'll be good. The black hole surface area is proportional to its energy content, right? But the event horizon is just the point where the space-brane can't keep up with the acceleration. Yet, all I want is a hyperdrive; but I don't want to have to supply the energy of 50 universes to do it. I really need to work with more energy, but I don't want to blow up the universe. Lawrence, and others, have already said that quantum mechanics becomes unstable in the high acceleration zones of the Alcubierre drive; I guess that's where we get to blow up (intentional pun) the Planck constant. Whatever it takes to get into hyperspace, it doesn't seem to be calling attention to itself; let's invent a warp-boson and see what happens.

Warp bosons are like energy charges +E and -E. Let's imagine that they come in pairs; they are attached by a spring that extends between them; for now, we'll say that the spring is a displacement in the "mysterious" dimension. Since springs go with energy, and our charges are also energy (+E/-E), let's say that these special warp particle/forces are meant to satisfy the requirements for warp drive, only. They can't blow up the universe, but they can, with a very reasonable amount of spring energy, expand (-E) and contract (+E) space. But let's say that it comes at the expense of the Planck constant. Just for fun, let's say that are found naturally occuring as little bubbles of uncurved space, just floating around. Wouldn't you know it! When two of them combine, they just become a larger bubble. If you take alot of them and combine them, the bubble becomes large enough that you can step inside of them. Now you ask, well, don't springs, especially springs in particle physics, oscillate? Answer: do you know of any oscillation gravity fields? OK, maybe you can get them to oscilate, but they dampen out rather quickly. Now these springs that I mentioned, they exist in a "mysterious" dimension. But, wouldn't you know it, they just happen to line up with magnetic fields. What are the odds? Now Ray, your brave, right? You go inside of one of these warp bubbles with an electro magnet, and a battery. Your so brave! What happens? Let's say you want to visit me in Portland. So, you orient the magnet in the NW/SE direction (the N and S poles are oriented along the path from Florida to Oregon). The spherical bubble begins to change into an ellipse. You bump your head. This was just with the electromagnet unplugged. And, oh Ray! You brought a 9v battery. You slowly accelerate across the lawn. Go back and get a bigger battery. Now, as anybody with ADD/ADHD would do, you went and came back with a fifty thousand watt generator, a chair, and a crash helmet. Good thinking, Ray! So, you get inside of the bubble, an inertial frame unto itself, and here is what happens.

Lawrence and Steve walk up, and watch everything. You throw the switch and energize the elextromagnet. Lawrence is good at watching things fly off to infinity. He watches as the +E and -E warpspace charges begin to dipole. The -E warp-charge builds up behind Ray (space expands), and the +E charge builds up in front, causing space to contract. Sorry Ray, I don't know whose dog that was, but it got sucked into the black hole in front of you. Now, with Lawrence's keen vision, he watches the dog get translated along the surface of the ellipse, from the black hole front, along the sides and out the back of the expanded space. Amazingly, Fido is ok! He pukes.

Next, Lawrences observes the photon-space (space-brane) start to move along the blackhole-ellipse center-white hole pathway creating equal and opposite momentum. Then, Ray flies off to infinity in his home made hyperdrive. Sorry Ray, you flew right past Portland. I didn't see you fly by, my vision isn't that good. But USAF watched you leave Florida at .5c. After that, there were funny lights and you went off radar. Do you know how to navigate from outerspace?

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Corrections:

Physicists lose their grip on physics inside of the boundary of a Schwartzchild sphere (a surface of a Planck size black hole).

That was a 50 thousand watt DC generator. Don't ask me where Ray got that!

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Dear Jason,

Poor Fido. I used to teach Astronomy - maybe I could navigate by the stars if I gain control of the craft before I get too far from Earth (did I survive the ionosphere and the cold vacuum of space?). I hope I packed lunch! It would be fun to visit Portland for the weekend, but it sounds like Lawrence and Steve have the easier jobs. I melted too many things when I was an experimentalist - you really don't want me to handle the 50 kW generator.

I'm not sure what these warp-bosons are. I think you need a Black Hole. Ask Lawrence if you can borrow his foolish observer.

Have Fun!

Ray Munroe

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Dear Lawrence,

Einstein's equations cost energy if you want to compress space. If you want to expand space, then you need negative energy, right? Warp bosons, which is a cool name, is actually a particle pair. One particle is a contracted space that wants to expand, like our universe. The other is a contracted space that wants to expand in the -R (-radius) space. It might look like gravity. But for a delicate balance between them, they will want to exchange space-brane (photon space) until they neutralize each other. By sheer coincidence, the space that they exchange travels along the surface of the "bubble". If you're inside of the bubble, your safe. This flow of this photon-space/space-brane has to (will hopefully) engage the space of our universe so that the laws of motion are consistent.

There are some things I'm uncomfortable with. This method, which was inspired by the Alcubierre drive, seems to assume that space will have friction enough to create velocity.

On an interesting note, it is important that Fido land at the same speed he was moving when he got sucked up. If he went shooting out the back, then more energy would have to go into the system, possibly 10 universes worth. Mmm...

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The Maldacena duality is AdS_6 ~ S^5, where the SO(4,2) ~ SU(2,2) gives the extended AdS. There is of course the AdS_5, which is the original AdS spacetime with group SO(3,2). That whole gemish AdSo+S^5 sits in 11-dimensions.

I am working up this paper, but trying to to haste it along too much. The FQXI paper is really a sketch with some of this. Having advanced some of this in areas I might now work up a paper here on the Jordan algebraic structure of this, which includes how to do the AdS physics here.

Cheers LC

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Dear Ray,

The last essay was addressed to you, not Lawrence, sorry.

Given a spatial and reciprocal lattices that describe both position and momentum, the model suggests that acceleration occurs with quantum leaps from one momentum eigenstate to the next. Since there must be a net zero momentum, one must apply an equal and opposite momentum (like a jet plane thrust) in the other direction. When gravity warps space, it does so in all directions, unlike a gravity based hyperdrive that has to push off of the crystal or push off of the space-brane itself.

It is still a mystery to me why accumulating mass/energy is responsible for Newtonian gravity. Yes, the Einstein equations say it does; they say that curvature (compression) creates energy density as either mass, momentum, or a gravity field. What happens if the tesselated lattice just has too many vibrating lattice strings in the same place? Does it overwhelm the crystal lattice? DOes it make the lattice sag?

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The horizon area is proportional to the entropy of the black hole.

The paper by Barcelo and co. in this FQXI area illustrates how the Alcubierre warp drive results in Unruh-like radiation which makes it unstable. I really doubt for a number of reasons these things will happen.

To be honest we may simply never really move out into space much. It is great for astronomy and science. The Hubble repair mission 2 months ago worked out great, and I can see men in space facilitating that sort of thing. Maybe solar power satellites in geo-sych are possible which might require human maintenance. Maybe service trips to facilities at Lagrange points or the moon are also possible as well. But frankly, space is lethal and very dangerous, and very energy intensive and expensive.

Cheers LC

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Dear Friends,

As usual, Lawrence is the voice of reason. Space is very dangerous. This is a serious problem that has kept NASA from sending people to Mars. But I can also relate with Jason because I hate to say that something is impossible. I'm tired of hearing that a TOE is impossible (and reading mountains of Philosophy to support why). Still, I wouldn't be surprised if the Universe is full of pockets of life that are separated by the "speed of light" barrier. If the speed of light can be cheated, we should have aliens here (unless we are that boring).

Is there a trick with AdS/CFT boundaries? Could we use this physics to jump into another brane and hope c is different? How do we cross the boundary? Is it a Black Hole horizon?

Have Fun!

Ray Munroe

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No, unfortunately we can't jump across branes. We might think of open strings which connect D-branes for cosmologies as corresponding to wormholes, or quantum wormholes. The string has two D0-brane (partons) connected by a type of flux tube. So to get a macroscopic wormhole we generate a gas of these partons and merege them into some sort of large tube. The problem is that this runs into huge stability problems, similar to trying to maintain a stable large N quark-gluon system.

I answered a question of yours on my blog area.

Cheers LC

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I was considering the idea that tesselating space with a position/momentum lattice might imply that there are position/momentum eigenstates. High energy density might result in only very high position/momentum states being available. I'm simply trying out a Pauli Exclusion Principle approach. Inside the black hole, the gravity field is so large that everything that can move has to move within the rarely used tachyonic energy levels. But in a black hole, who cares about Unruh radiation.

My warp-boson idea was kind of based on what is needed for the Alcubierre drive to work. But I think that conservation of momentum might kill the idea. Just because you have a black hole attached to the front of your space ship, and a white hole on the back of your space ship, it doesn't mean that you are going to fly across space FTL. The whole problem is that you need to supply have equal and opposite FTL momentum. Of course, FTL momentum is an oxymoron because it implies that your pushing off of a crystal that doesn't support FTL velocities.

It is true that even the tesselation idea is, itself, hypothetical. We don't know if there really are Schwartzchild hyperspheres whose outer surface is space itself. Then again, if these Schartchild spheres did exist, to what degree would they imitate the atomic structure, using space for bands, instead of electrons. Are they forced to be hard shells like bowling balls? If they're more like atoms, are there n=1,2,3... shells? Are the shells on the outside or on the inside?

Ray,

I agree with you; I don't like the word 'impossible'. But if Unruh radiation is part of the problem, ... I'm getting a headache. I'll be sitting in my naturally occuring warp-boson, thinking about it.

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Doesn't the Big Bang theory squash the tessellation of marbles (Schwartzchild spheres) theory?

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The Planck volumes or spheres are minimal volumes that can carry a quantum bit, and if excited with enough energy are elementary black holes.

There is a distinction between the warp drive and tachyons. Tachyons have imaginary mass-energy, while warp drive bubbles involve negative mass-eneergy. So a tachyon might be thought of as the "square root" of the warp bubble. I am not saying I think this is the case, but it might be worth working out.

Cheers LC

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These Planck volumes/spheres sound like they have energy bands of space or space-time. A level n>=2 represents a black hole. Going back to solid state, there are valence bands and conduction bands. Valence/conduction bands comes from neatly arranged atoms; atoms are made of positive and negative charges. These positive/negative charges also have electric fields. Does this mean that Planck spheres with conductions bands of space can be thought of as having charges of positive/negative space with fields that can move/accelerate space? Do I get to have a tractor beam, too? Cool!

Seriously, these excited Planck volume states look like they could provide a hyperspace region for us. But falling out of hyperspace (or black hole space) requires that we prevent our energy from leaking out. Maybe warp-bosons simply remain in the n=2 state unless a certain amount of energy is supplied to get them to drop down into n=1. I'm just kicking around ideas.

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Dear Jason,

According to my models, there is a K12' "neatly arranged" lattice at the Big Bang, but much of it has collapsed due to broken symmetries. Instead of "bands", we have branes. Is hyperspace a lattice? I don't want to think of spacetime as a lattice - that causes aether problems.

Dear Lawrence,

Yes, we have the difference between negative and imaginary mass. In my book, I proposed that WIMP-Gravitons might allow interactions between these odd types of masses.

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Ray,

I wrote on your suggestion about so(12) on my area.

There are band-like structures, or Fermi surfaces, which also have braney content to them. For example strings are Skymrion knots which occur in a way analogous to knotted flows in some solid state problems. D-branes are also emergent from Fermi-like surfaces with certain topological (K-theory or homotopic) properties.

Cheers LC

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Ray,

Maybe I'm being a little imaginative here, but using the crystal metaphor to describe space suggests the existence of positive space and negative space, like charges. Electrons orbit around protons, not the other way around, typically. But that doesn't mean we can't play around with our Planck spheres. Of course, the planck CONSTANT prevents us from changing the size of our Planck spheres. I think I'm going to need a Planck Scaling field, after all.

While lattices cause aether problems, I think of it more as a tool to help us understand what we can't really comprehend. On the other hand, Ray, maybe you go for picnics on branes and admire the scenergy. Who knows?

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The "atoms" here are the roots of "half an E_8," so we might think of these "atoms" as having the analogu of charges, but these are for larger Lie groups.

Cheers LC

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Dear Lawrence,

I don't think it would be too dumb to ask, what is a "root of half an E_8"?

Ray,

Where is the %$#! hyperspace freeway? Do you have the map turned upside down?

I've been trying to find an easier way to represent QM in my mind. What does Psi* ? Psi mean anyway? Well, while at work, I've been troubleshooting a circuit. After I chase the signal into the FPGA, I usually get frustrated. I know a complex conjugate just means the imaginary part is inverted. Somehow, we have an operator that acts on the NOT-inverted part, Psi, then, like it's a sandwich, we take the inverted part and apply that, take the square root and wammo, we have a chance to find a particle. I just started to wonder if any of that could mean that quantum space exists as connections between the two halves of some circuit. Just a silly thought, I guess.

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Dear Jason,

I think Lawrence is talking about an H4 with 120 roots versus an E8 with 240 roots - the same fundamental duality, triality (Lisi's great accomplishment) and pentality symmetries in a 4-D (quatrality) space instead of an 8-D (octality) space. But I am used to Lawrence explaining himself better.

Psi is our quantum wave function. It has complex components. By integrating over Psi Psi*, we get the "magnitude/ length" of our complex vector. When properly normalized, the square root gives probabilities.

Have Fun!

Ray Munroe

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Dear Ray,

I remember roots polynomial roots from high school algebra. For something like H4 and E8, those roots probably mean something like vertices? I'm guessing it's some kind of F(x1,x2...xn)=0 situations. Of course that could imply maximas and miminas for 120 parameters.

Dual lattices I know about. You talk about triality, quadrality and pentality, and I start to get a headache. I had considered that other 4D space-times might coexist inside of something as complex as an H4 or an E8. I think that is what you mean by n-uality. But if we're looking for the hyperdrive onramp, he won't find it there. I'm sure we have to think in terms of what the boundary between two kinds of space would be like, each with there own c and h. They might even be overlapping. I'm not entirely sure how tesselations of that could be set up. I'm not even sure if an energy boundary between them is sufficient. If n universes, each with their own set of c_n,h_n can exist together, how would they be arranged? Suddenly, we have a c axis, an h axis and probably an energy axis. Quantum Mechanics suddenly becomes awkward. I'm quite sure that humans cannot think like this without becoming complete social imbeciles. There might even be homeless people who walk the streets muttering, "damn you E8xE8!! You ruined my life!!"

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I know how we're going to deal with Unruh radiation. The energy can't escape if it has no where to escape to. Space-time itself, outside of the boundary of your spaceship has to be dampened out. Space itself is conducting Unruh radiation. Space itself has to go away.

You might ask, how do where steer if we can't see where we're going? Why do we need to see? Doesn't momentum still operate even if there is a gap of space between the spaceship and the rest of space? Isn't conservation of momentum garaunteed no matter what? Just like conservation of energy, it exists whether there is space or not. But if conservation of momentum requires there to be space, then isn't it possible to violate conservation of momentum by playing around with space? Ultimately, it is the quantum waves that decide where they will or will not go. They see the universe as transmission lines.

If a wave runs into a lack of space, it just bounces off of it, right? Why would it be absorbed into the nothingness? That would result in a violation of the conservation of energy.

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The roots of a Lie algebra are related to roots of polynomials. The Cartan center of a Lie algebra defines eigenvalues of the symmetry. Finding the eigenvalue of a matrix can requires one solve polynomial equations. The techniques for Lie algebras are a bit more advanced that this, but it does all harken back to Galois theory on the roots of polynomials.

Unruh radiation is a manifestation of event horizons. The Alcubierre warp drive has such horizons, which curiously make it impossible to control the warp bubble. Quantum fields across horizons don't maintain entanglements, and this can include the vacuum state as well. As a result the vacuum state as observed outside the warp bubble is equivalent to a vacuum plus a thermal bath of radiation inside. Because the warp bubble requires negative energy to construct this produces a bit of noise which destroyes the warp bubble.

As a rule with any technology it it has zero fault tolerance it does not work,

Cheers LC

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An event horizon occurs when gravity causes standard space (standard model space) to be stretched beyond the light cone. Particles which only exist in standard space are forced to travel faster than light. They have to give off Unruh radiation in order to try to slow down. According to the tested and established physics, Alcubierre drives and FTL travel is impossible.

If hyperdrives are to exist, they have to rely upon physics that we have yet to observe. I believe the first requirement is that we are going to need to discover the existence of a hyperspace. By definition, a hyperspace has a c'>>c; my hunch is that for such a space to exist, the Planck constant has to be very large as well, h'>>h.

Second, we are going to have to discover that a hyperspace and a standard space can form some kind of a bilayer; a std 4D space-time plus a hyperspace space-time interconnected in some invertible hyperD bilayer. I'm working on the details.

At sub light velocities, the spaceship, which always sits in the standard space of, let's call it a warp boson. A warp boson is an idea under construction that incorporates these two spaces as one object. At sublight speed, the standard space of the warp boson can come into contact with the rest of standard space. Presumably, the hyperspace region of the warp-boson is somehow inverted, and on the inside where it's isolated from the rest of hyperspace. As the velocity of the spaceship inside of the warp boson approaches the speed of light, the warp boson begins to invert. The standard space, with the spaceship inside of it, moves to the inside of the warp-boson where it is safely protected from the quark destabilizing conditions of hyperspace. On the outside of the warp-boson is the hyperspace. This hyperspace is in contact with the rest of hyperspace; assuming we can find it. The warp boson is allowed to have a velocity v>c because v

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I think part of my post got clipped. Here is the rest of it:

The warp boson is allowed to have a velocity v>c because v

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The editor is acting funny; my apologies.

Whatever the propulsion system is like, I'm sure it will have to obey action/reaction forces, inertia, conservation of momentum and energy for both standard space and hyperspace.

Like I said earlier, it is becoming apparent that with what we know, presently, about physics, the hyperdrive is impossible. There will have to be some significantly major discoveries before hyperdrive becomes possible. Maybe these OMG particles that strike the upper atmosphere are a clue?

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Dear Jason,

We can think about roots as polynomial solutions or as lattice sites. My education in both Particle Physics and Solid State Physics introduced me to different applications of similar looking symmetry groups that have lattice analogies from Solid State Physics, so I use lattices.

The triality symmetry is important in two physical applications of Particle Physics. In Color Theory, we have 3 colors (Red, Green, Blue) that are represented by a lattice of equilateral triangles (2-simplex) in the 2-D gluon space formed by (g_3, g_8). An operator with a triality symmetry, T, would be such that Green = T(Red), Blue = T(Green), and Red = T(Blue). In the 2-D gluon space, these T operators may be represented by 120 degree rotations, or by translation vectors. There are 6 different rotations or vectors, and this yields the other 6 gluons (with color-anti-color charges). If we include anti-colors, anti-Red = Cyan, anti-Green = Magenta, and anti-Blue = Yellow, then we also have a triality symmetry between these three anti-colors, and we may form a G2 Lie algebra out of these 8 gluons + 3 colors + 3 anti-colors = 14 degrees of freedom. I didn't make a big deal about this triality symmetry because I added a fourth color, and converted it into a quatrality symmetry.

The other relevant triality symmetry was Lisi's generational triality between down, strange, bottom. These can be represented the same way as the prior example, and this becomes the K12' triality symmetry.

I think Lawrence meant "As a rule with any technology, if it has zero fault tolerance it does not work."

Have Fun!

Ray Munroe

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Ray,

I've been thinking about trying to implement a standard space-hyperspace dual hypersphere. I want it to be invertible. I want the space ship to always be in the standard space (so it doesn't disintegrate). A Mobius strip is 2 dimensions, I think. I think the idea of a Mobius strip might work if extrapolated up to an invertible dual hyperspace.

I've been thinking about how it might be possible. The first question is, what tests would we have to run to determine that space is flat? Do we shoot some pool and measure all the angles with bank shots? Do we shine a laser around? What do we do? In my line of work, I configure and troubleshoot MPEG equipment which transmits QPSK, CFDM, ISDB-T signals, etc. I know about things like Shannon error coding. What I am wondering is this: is it possible to take superstrings (super membranes, super vibrating stuff) and construct the real space and momentum space necessary to simulate "space-time"?

Let's simplify this. Let's take a one dimensional loop. Imagine the Bohr atom. Forget the proton. You have one wavy electron. Next, forget it's an electron. Let's just call it space. Let's give it two properties, postion and momentum. This string has to supply both. Next, we take lot's and lots of them until we fill up all of 1 dimensional spatial and momentum eigenstates. This gives us a rubber band or loop made of superstrings that provides all of the eigenstates for momentum and and position. Anything moving it it just excites these eigenstates. It's a lot like transmitting audio and video using 8PSK or ISDB-T complete with Shannon Error coding. Using mathematics that only Lawrence understands, I can extend it to a plane, a 3D space, and up to a 4D space time. The universe is not a crystal. It's an endpoint to enpoint collections of vibrating strings that provides all of the states necessary for momentum and position. You and I are just collections of so many of thing strings in excited states; are you excited yet?

I know I have one universe. Can I squeeze a second universe into this? Can I have regions, using shannon error coding, with additional stable universes that we don't even notice? I haven't quite solved the standard space/hyperspace intervible dual-space, but I'm working on it.

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Dear Ray,

I think I like the idea of using a Mobius strip idea to construct a dual space. If an H4 with a 120 roots represents these Schwartzchilde sphere, maybe using a Mobius strip idea to construct a deliberate Mobius defect in an E8, we can squeeze in there a standard space on one side and a hyperspace on the other. I'm trying to accomplish that dual space that I mentioned earlier. I'm not entirely sure I agree with the crystal interpretation. Why can't a Bohr atom interpretation work just as well? The lowest energy waves actuall cross the entire universe, the n=2 waves cross half way across the universe, etc. By doing it this way, we get away from the awkwardness of tesselation for a Big Bang. The Big Bang is more suitable for hugely energetic events which is completely different from tesselation. Tesselation implies unchanging orderliness. By using a Bohr atom idea where the waves actaull cross the entire universe at the lowest energy level, the universe is allowed to expand or contract as it must. There would be no need for descibing an explosion using H4 or E8 bricks to describe some kind of masonry or crystal.

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Triality with exceptional groups occurs with the Jordan algebra. In that case you get three 8's, one for the vector term and the other two for the SUSY representations and their conjugates. This is sort of what got Lisi under some degree of criticism. There is no triality in E_8.

There is the issue of the Atlas collaboration to classify the roots of E_8 according to the Lusztig-Vogan polynomials for exceptional groups. This was a massive effor to find the 696729600 distinct representations of the E_8. The matter of associating particles to roots of a Lie algebra is to find the irreducible representation of the algebra.

The E_8 contains 248 roots, of which we can assign the 120 dimensional subalgebra so(16) with generators J_{ij} and the Weyl-Majorana algebra of generators L_a of spinors spin(16). The so916) obeys

[J_{ij}, J_{kl}] = δ_{jk}J_{il} - δ_{jl}J_{ik} - δ_{ik}J_{jl} + δ_{il}J_{jk}

[L_a, L_b] = γ^{[i}_{ac}γ^{j]}_{cb}J_{ij}

and the cross commutators between the two are

[J_{ij}, L_a] = (1/4)γ_{[i}γ_{j]}_{ab}L_b.

The point in mentioning this is the E_8xE_8 is under M-theory mapped to the SO(32) for open strings. The J^3(O) model I am setting up here is for closed string which is the N = 8 supergravity multiplet. The duality which maps the closed string to open, eg T-duality or the physics I start out with in my paper on string in black holes, is a transformation of the supergravity multiplet to gauge-Dirac field multiplets. It is here that you end up with the quarks, gluons and ... .

Cheers LC

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Hi Ray.

The unification of gravity and electromagnetism/light occupies the center (and best) position with regard to improving our understanding of physics in general. I agree with the geometrical approach -- the mathematically proven outcome in a fourth dimension of space -- as it has unified gravity and electromagnetism/light.

To unify gravity and electromagnetism/light fundamentally and comprehensively, balancing/unifying scale by demonstrating gravity as repulsive and attractive AS electromagnetic energy/light is required. It is critical to demonstrate electromagnetic energy/light as gravitational space. The unification/balancing/inclusion of both invisible and visible space is central to:

1) Balancing/unifying scale and...

2) Balancing attraction and repulsion in conjunction with space manifesting both gravititationally and electromagnetically. Think wave/particle.

These ideas need to be applied to atomic structure/interactions, and to electromagnetism/light and gravity generally. How space manifests as electromagnetic/gravitational energy is a central and very valuable physical idea.

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Dear Jason,

Your ideas are interesting, but you have pushed beyond my understanding of the warp drive problem. I don't understand how spacetime and hyperspace interact. At the TOE, these two different types of space were united, but the Big Bang and Inflation "collapsed" their common lattice. If the original 12-D strings disassociated into branes, and formed closed loops of strings within...

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Hi all ,

Jason the creative ,sure with your creativity ,you are going to find many interesting things .

Your creativity is instantaneous .Surprising and relevant .

Personally,let's imagine if w could become light ,and after we repolarise the gravity system with its codes .It's perhaps the secret ,becoming light and re encode the systems at the chosem place ,thus the most important is the topology and the coded since 13.7 billions years .

An other idea before the check of this technology is a spherical field system .Two systems one for the propulsion and one for the spherical shield with a balance of gravity thus ,the forces must be balanced .

The spherical field is the key thus for physical travel .But like say Lawrence ,it's lethal and expensive at this moment ,furthermore our technology is so young .But some roads are possible .

Thanks all for your imagination and ideas .

Don't stop .

Best Regards

Steve

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Steve,

Thank you for your encouragement. It really does help.

Ray,

I've been looking at that heterotic E8xE8. Lawrence believes we can get by with just E8 or even H4. I'm fine with that. I just don't see how they can be stacked like a crystal, like atoms. It just doesn't fit the Big Bang picture.

I want to give you a better idea of how standard space and hyperspace interact. It still is a good idea to have a real/reciprecal crystal to account for position and momentum. Just to kick some ideas around, what happens if we say that the entire universe is a single E8 or H4. Can it be like a fractal in which the whole universe is duplicated at smaller scales? Just some ideas. I'll try to come up with something a little better in the next day or two.

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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

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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.

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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

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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

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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.

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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.

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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

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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

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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

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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

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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?

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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

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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?

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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

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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

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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...

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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...

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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...

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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

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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

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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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Dear Jason,

My theory might allow the existance of tachyons. If both real and imaginary masses exist, there might be something similar to the Kramers-Kronig relation that allows us to relate real charges (masses) to imaginary charges (masses) and vice versa. If we could transform a collection of real masses into a collection of imaginary masses (at any energy below the Planck or Infinite scale) then we could travel faster than the speed of light, and would need the reverse transform at the end of our trip. I know its a crazy sounding idea, but I don't know how to beat the speed of light.

Have Fun!

Ray Munroe

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The K-K relationships between the real and imaginary parts of an analytic function would apply for quantum tunneling states. It really tells us, even in classical settings, that the entire analytic function can be determined by either the real or imaginary parts. Classically the imaginary part can correspond to the attenuation of an EM wave in some conducting medium.

I had not thought about it, but these could potentially involve the relationship between instantons and tunneling states with physical states.

Cheers LC

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What if a hyperdrive is actually simple in the following way. What if all of the particles we have ever encountered have a characteristic velocity range of c. It doesn't matter how much propellant we use, it will never let us travel faster than c because the fastest it can travel is c.

Consider a 100 metric ton test rocket. There is a proppellant container labelled: TOP SECRET/Property of Area 51/c'=10,000,000c/10Kg/hyperspeed proppelant. You read the propulsion system specifications. The propulsion system is a simple rocket designed to achieve a non(c')relativistic backwards momentum thrust of v = 0.01c' = 10,000c. It's a mysterious substance with the strange propert that it has a velocity range of c'=10,000,000.

Assuming that we don't care about how many g's the test craft can take, Ray, who just now navigated back to earth, agrees to be our test pilot. He get's inside the rocket, turns the ignition key, and blasts off into space again. Considering only equal and opposite momentum, Ray burns through the whole propellant canister in two seconds. Ray is as flat as a pancake due to accelleration. But something strange occurs.

Conservation of linear momentum: mass of rocket M = 10,000Kg, initial velocity v=0, mass of c' propellant = 10Kg proppelled at v=10,000c(non c' relativistic). Momentum p = Mv = m(10,000c). Velocity of rocket v = (m/M)(10,000c)=(10Kg/10^4)(10,000c)=10c = FTL. Once again, USAF watched Ray until he reached about .9C, then their radar, which can only bounce off him at the speed of light c, started to lose track of the rocket. As Ray hit the speed of light barrier, c, he vanished into hyperspace. After Ray got a brief suntan from all of the photon radiation as he passed the speed of light barrier, he discovered their was nothing above the speed of light, no stars, and no radiation above c. Ray got bored, so he pulled out his Gameboy and started playing. This was unfortunate because of the chunk of mysterious material with a velocity of c', now called Munroe propellant, happened to be floating along Ray's trajectory.

Is it possible that GR only applies to mass-energy with a characteristic velocity c? What if there are particles with a characteristic of c' that exist. What would our interaction with them be like?

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Hypothetically, you could have two identical rockets, both moving at 0.5c. The first one hits the moon; because it used c'-propellant, it has c' momentum. When it hits the moon, there os only a thud. The second rocket used good old fashion c propellants (fission rockets). When it hits the moon, there is a white flash, the ground shakes, and the moon cracks in two (ok, that's a slight exaggeration).

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Quickly, Jason! Grab some of Lawrence's instantons and convert yourself into tachyons!

I don't have a Gameboy. I probably wouldn't spend as much time on this blog site if I had one.

Ray did the little "4G Space Shot" ride at the U.S. Space & Rocket Center. A space shuttle only gets up to 3G. I don't know about this c' propellant...

What's all of this with crashing rockets into the Moon? Are you still trying to discover water ice on the Moon?

Have Fun!

Ray Munroe

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The lunar space people are going bonkers over water on the moon of late. Having found traces of it on the surface, apparently replenished by solar hydrogen, and now the LCROSS impact, the moon is seen as a target for human habitation. I think the whole thing is rather silly. Humans have been visiting Antarctica for over a century. So far the human population here is a few hundred at any given time. Why? Basically the weather and c climate suck at Antarctica. The moon is worse.

Cheer LC

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Hi Ray,

You made it back! Hurray!

I want to approach the hyperdrive from this perspective. Every particle ever measured has a speed of light velocity range of interaction. In other words, we can't directly measure particles that have a velocity range faster than light. The reason is that the photons can't reach it to do a measurement, it moves to fast. Gravitons fit this category. Gravitons, which might have a velocity c', they can interact with standard model particles, but standard model particles can't find these gravitons because they move to fast. The speed of light is built in to the standard model particle itself.

The other idea is that these FTL particles (we could call them tachyons) carry momentum and obey conservation of momentum as well. Since mass gets a little tricky now, we have to be careful. I'll take a look at instantons to see if they can interface between real and imaginary mass. In my view, tachyons might be able to avoid travelling into the past (which is IMPOSSIBLE), by spreading out there effect over many kilometers. By the way, gravity sort of works like that.

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Dear Lawrence,

I like Florida just fine. Sometimes the Summers get a little hot, but I wouldn't want to live in Antarctica during the months of May through August. Its too dark and too cold. The Moon would be worse. The Moon only makes sense as an outpost on a trip to Mars or the Galilean Moons. If we can find water on the Moon, then we can replinish our supplies (It costs >$10K per pound of payload on the space shuttle, so water is strictly recycled), and separate out Hydrogen and Oxygen for more rocket fuel.

Dear Jason,

If you are correct in your assumption, then we might never find my scalar fermions = tachyons. We might confuse their signatures with the missing mass and missing energy of neutrinos or Neutralinos. If we can't verify the existence of tachyons, then it will be difficult to design equipment that utilizes them for propulsion or cloaking.

Have Fun!

Ray Munroe

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Dear Ray,

I am surprised by the scores. Even Dr. Crowell's essay is just barely rated above mine. Now I admit that when I read most of these modern theories, that I find them somewhat like the twilight zone. However, I do not lose sight of who is the expert and who truly represents today's quality physics theory. I find participation in these contest to be educational. It is from others like yourself that help lift up participants like myself. I have waited to give out ratings for almost all of the essays, hoping I could read through them all and perhaps even properly understand them. I am still reading your essay. I am glad to have this chance to learn. I have asked questions and challenged others. I do have my viewpoints and I don't mind being challenged back for them. However, in personal conversation there is a lot more communicated about a person's attitude than through print. That's why smiley faces and other emoticons are necessary on the Internet. Anyway, my point is this: I appreciate being able to read your essay and talk with you about it. It is a rare opportunity to be able to converse with experts like yourself. I think that your rating should be higher and I think Dr. Crowell's rating should be higher. Whether or not I agree or understand is not the criteria that I use. I am going to begin giving out some ratings that I think will help lift some of these ratings up closer toward where they deserve to be, including yours.

James

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Thank you, James!

If you have any Twilight Zone questions, please don't hesitate to ask. If you have a question about my work, then I'm certain that someone else must have a similar question.

Good Luck in the contest!

Ray Munroe

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The score distribution is a bit odd. Essay by people like Borcelo et al, Ellis, Corda and other are lower than I think they should as well have higher scores.

Cheers LC

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I checked out Rej's blog area, though he seems to be MIA. I responded to your post dated Oct 10 with:

I would agree there needs to be some additional physics which selects for an outcome on the so called landscape. That is why I think this is in part determined by a quantum phase transition. The part in my current paper with G_2 basis elements determined by a Dirac field are a part of the physics for this quantum critical point.

So far the outcome on the landscape is similar to finding a microstate on a microcanonical distribution. Some additional physics is required to give a distribution which has low entropy determined by a phase. With standard phase transitions as temperature decreases the decrease in entropy is associated with an increased ordering in the lattice configuration of molecules or atoms in a solid state. Similarly a quantum phase transition should indicate how the "needle" was able to land on a unique low entropy configuration for the early universe.

Cheers LC

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Dear Ray,

Why do you interpret a scalar fermion as a tachyon? As for interacting with tachyons, I still maintain that gravitons are tachyons. My reasoning is that something that moves FTL can't be detected as a localized event like a point-like particle. I'm also trying to avoid any causal violations by spreading out the tachyon in space. It can impart momentum, but has to do so over a wide area.

I'm a little unsatisfied with this imaginary mass interpretation for a tachyon. Imaginary numbers are associated with light, electromagnetism and oscillation. I'm using black holes and gravity as tachyon-like objects, but they do not oscillate. If they do, it's because of their charge. I do believe that tachyons can impart a real momentum. But I think there is a different relationship between tachyon mass and standard mass. I think that photons/standar model particles that are at the same place, can only interact if they're relative velocity is c or less. If it is more than c, they don't have enough time to interact and will miss each other. For tachyons, they will interact with other tachyons at the same point if the're relative velocity is c' or less, where c'>>c. Then how does a tachyon interact with a photon? The tachyon sees a slow moving particle or photon to interact with. The photon doesn't see the tachyon, but nevertheless is subject to the changing conditions of space that alters its path.

As for living on the moon, if it's inexpesive, easy and safe, I'll consider it. I'll need a glass dome, trees and artificial gravity. ...and internet access to earth with high bandwidth and FTL response time.

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Dear Lawrence,

I would like to see Rej push his ideas forward. But he clearly needs to make simplifications and approximations. It would be awesome if we could give him the pattern that works, or vice versa if he could tell us the pattern that works. Does your G₂ triality operate on an AdS₃ of Gravity-brane (my dimensions 8 through 10)? This would be a gravity-related mirror-image of the G₂ triality of color (red, green, blue) in the three dimensions of space.

Dear Jason,

These "scalar fermions" are a wierd species. They belong to a fermion multiplet, and SHOULD be fermions, but their spin projection in the first 6 dimensions is zero. Their intrinsic spins are not properly defined until we reach an 8 dimensional theory. So how do these "scalar fermions" behave in 6 dimensions or less? Are they lattice defects that cannot be defined or supported in so few dimensions? Are they tachyons? Are they related to Supersymmetry? Of course, I calculated their expected electric charges and they do not agree with our expectations from Supersymmetry.

I am open to ideas...

Have Fun!

Ray Munroe

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Dear Ray,

I didn't know there could be fermions that need 8 dimensions just to exist. How cool is that? If it inly exists in 8D, can it project an electric field? If so, does this electric field span 8D as well? Is it particular about which 8 dimensions? Can I pick the 8D of my choice? Probably not.

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Dear Jason,

They are my sf fermions in Table 3 and the paragraph below. They live in dimensions 1 through 8. They do have electric charge, but electric charge is a property of the space 3-brane, so I don't expect that Electric field to reach into hyperspace.

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Dear Ray,

"They are my sf fermions in Table 3 and the paragraph below. They live in dimensions 1 through 8. They do have electric charge, but electric charge is a property of the space 3-brane, so I don't expect that Electric field to reach into hyperspace."

Quoting from above:

"...They live in dimensions 1 through 8. ..."

Aha!! So you admit they live!!

Ray, please accept this in the humorous manner that it is offered.

James

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Dear James,

If it lives, maybe it feeds too. Maybe it feeds off of bad jokes. :-D

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Dear Friends,

Does this explain the emergence of life?

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There is the part I have about how G_2 fixes vectors in S^7. This is involved with a Hopf fibration which tells us how 7 dimensional sphres are knotted in 15 dimensions. This determines a discrete structure to the vacuum. Now g_2 has su(3)+3+3-bar. This can be seen since g_2 is 14 dimensional (compex dimension = 7) and there is the 8 for su(3) and 6 for the 3 and 3-bar. The 3 and 3-bar are a color-like index to the system and there is the SU(3), which is the AdS_2 in the 8 real to 4 complex dimension reduction to SU(2) or SU(1,1). That determines the AdS_3.

Cheers LC

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Dear Lawrence,

I understand the Color analogy and how G₂ breaks into an SU(3) of gluons plus 3 plus 3-bar of quark-quark-bar. However, the 3 and 3-bar are vectors. If we are playing with Gravitons or WIMP-Gravitons, we will need tensors. So is it really a rank-1 times rank-1 SO(3)xSO(3)~SU(2)xSU(2) 3 plus 3-bar, or is it a rank-2 SO(4) 6-plet? Quaternions contain an SO(4) 6-plet of tensors.

Your paper is getting more interesting. I wish I understood more than half of the math...

Have Fun!

Ray Munroe

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Hi Dr Cosmic Ray ,all ,

ahaha yes Jason they eats the hopes of our dreams .

They live our particles in turning ,and always turning in the mind of our fundamentals and their languages are the rotations and their music of frequences .They think thus they live,they dream ,they live ,they sing and dance ,they build ,they continue ,they write on the book of the life ,like the spheres of the sphere.They shall eat our errors and they shall drink our hopes ....fortunally .

Regards to all

Steve

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I don't know what the 3 and 3-bar are really. There are two automorphisms in the exceptional J^3({O}). One is F_4 and the other G_2. The two are centralizers in E_8. So we might of them as independent vectors spaces. The F_4 diagonalizes the J^3, and contains the gravitational physics. The F_4 has a root space which is the 24-cell that is the minimal sphere packing configuration of four dimensions. So we mith think that this holds in a local region, say a local frame in the 19-11 dimensional superspace, or the large Lorentzian space in 26-dimensions. So a local gauge action on g-2 involves a local coordinate frame transformation of F_4.

The g_2 is a holonomy on the 7-sphere in M^4xS^7. The gauged action of g_2, thinking of the M7 as a local 7-sphere in a curved 11 dimensional manifold, results in a similar coordinate shift on M_4, which is where gravitational physics exists.

Cheers LC

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I don't know if you have read George Ellis' paper. I just posted a comment there which might be of some interest

http://www.fqxi.org/community/forum/topic/558#

I am writing up this paper as I complete various calculations, or subset of the matter. There are some AdS-like aspects to this. The g_2 algebra has SU(3) subalgebra, which has AdS-like content. AdS_5, with the group SO(4,2) ~ SU(2,2). So this is on the Dynkin digaram o--o--o and if we remove a o we get the SU(3) or SU(2,1) o--o. So from the g_2 there does appear to exist a correspondence with QCD here and quantum gravitation and M-theory.

Cheers LC

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Dear Lawrence,

I was a little confused last night. I was mixing up the direct and reciprocal lattices.

If we are dealing with gravitons (massless gravitons would have a spin projection of 2, -2, but massive gravitons could also bring in spin projections of 1, 0, -1) and gravitinos (of spin projection 3/2, -1/2 - anti-matter would bring in the missing spin projections of -3/2, 1/2) and three charges (call them Cyan, Magenta, Yellow = (C,M,Y) - I know it isn't original). Then our 6-plet hexagon of gravitinos might be:

12 o'clock - spin 3/2 C gravitino,

2 o'clock - spin -1/2 Y-bar gravitino,

4 o'clock - spin 3/2 M gravitino,

6 o'clock - spin -1/2 C-bar gravitino,

8 o'clock - spin 3/2 Y gravitino, and

10 o'clock - spin -1/2 M-bar gravitino.

The problem I see with this particular model is that adding anti-gravitinos introduces more degrees of freedom than a normal G_2 would contain. Do we need a G_2xG_2? Its just an idea. You're welcome to use it if it works.

Dear Steve,

I hope those evil tachyons aren't eating your hopes and dreams. It would be far better if the good tachyons are supplying your hopes and dreams.

Have Fun!

Ray Munroe

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dear Ray hihihi all is possible,but you know I don't consider them like evil ,they live where these tachyons ,in Las Vegas hahahah bip bip let's see our tachyons bip bip zzzzzzzzzz ahahah bip bip is a tachyon ,impossible to take it ahahah bip bip zzzzzzzzz

An other solution Bip bip is the light ,

In all case interesting thread and likeable .Let's dream and hope dear friends ,

Regards

Steve

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Hi Ray,

I've made some progress on the hyper-drive. If it's possible, then some assumptions are necessary. First, hyperspace and standard space overlap. In other words, anywhere in the universe, I can cross. Second assumption, gravity works the same in both spaces, so G is the same; this makes the math easier. Third, momentum is conserved in both standard space and hyperspace. Fourth, energy is exchanged 1:1 between these two spaces. Fifth, hyperspace has a c'>>c; Planck constant for hyperspace is unknown. Sixth, hyperspace also has a 4D space-time; I don't know if anything scales.

I have a starship that can cross into hyperpsace. When it crosses, it either uses or else creates a spatial anomally, a space-time bubble. Inside of the bubble, standard space -time exists. At the boundary, all the interesting stuff happens. The standard space inside is not considered to be curved or compressed in spite of the bubble. Artificial gravity will come later. Conditions for creating such a bubble are still vague.

Since conservation of energy is upheld, I want to solve the Einstein equation for the stress-energy tensor. To keep it simple, I'm neglecting complicated curvatures in space, so Rmu,nu=0. I'm neglecting the Cosmological constant, for now, so NU=0. That leaves me with (-1/2)g_mu,nu(space-metric)R = (8piG/c^4)T_mu,nu(stress energy tensor). Solving for the stress energy tensor, I get,

T_mu,nu = -c^g_mu,nuR/2*8piG.

If energy exchanges 1:1 at the boundary between standard space and regular space, then the energy stress tensor can be the same at the boundary. So,

T_mu,nu = T'_mu,nu.

So after I drop the minus sign, 8,pi,2,and the gravitational constant, I assume is the same, here is what I get, R*c^4*g_mu,nu = R'*c'^4*g'_mu,nu.

At first, I thought that R and R' are the same for a sphere. But now I'm not sure.

Does it look like I'm approaching the problem in the right way? At this point, I'm not sure what to do with the metric-tensor. I'm assuming a zero gravity environment for right now. I'm also thinking about bringing back a G and G' if I can't get the spatial anomally to behave itself.

Any thoughts?

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Mr. Munroe,

Please feel free to correct me if I'm speaking in error, but I have a nagging suspicion that you're playing just a wee bit fast and loose with the essay evaluation criterion which states, "Accessible to a diverse, highly-educated *but non-specialist* audience, aiming in the range between the level of Scientific American and a review article in Science or Nature." [My added emphasis.]

But I don't want to be a nit picker. FYI, I'll refrain from rating your essay, because I lack sufficient knowledge of the topic to do so meaningfully. Judging by the many associated posts, however, I gather that you're probably on the trail of a good idea here. Good luck with it!

Cheers

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Dear J.C.N. Smith,

Thank you for your candid comments. I will try to read your essay next week. My friend, Jason Wolfe, is interested in trying to beat Relativity via spacetime travel at super-c speeds. Your essay on the impossibility of time travel probably follows the same line as his reasoning. I do believe in cause and effect, and don't see how a future that doesn't yet exist can change the present that does exist. But I should read your essay...

I apologize if my paper has too much math. Most of the math is just geometry. But there is a lot of geometry (with Tables and Figures to help reinforce ideas) Truly, I've seen more difficult math in a few of these essays.

Dear Jason,

Lawrence is the GR expert. I'll have to work with your ideas some.

Have Fun!

Ray Munroe

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Hi Ray,

This is my hyperdrive idea. I want photons/speed of light, c, to be part of the space-time brane. To move faster than c, you have to break off your piece of space-time/brane, and make it move faster, within hyperspace. If light defines motion in space-time, what defines motion within hyperspace? Gravity operates in both standard space and hyperspace. Do space and time exist in hyperspace? Is there a hyperspace speed of light, c'? Are there 3 flat spatial dimensions? Mmm...

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Mr. Munroe,

You wrote, "I do believe in cause and effect, and don't see how a future that doesn't yet exist can change the present that does exist. But I should read your essay..."

To which I will only add a hearty Amen! If you can find time to read my essay I believe you'll find that we're in agreement on many things. And I'd definitely welcome your comments on it. Thanks in advance for at least expressing a desire to do so. I've already read all 113 of the other essays and commented on quite a few, so I understand the insufficiency of time, however one chooses to define it.

Cheers

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As an addendum to my previous post I'd like to quote here from one of my posts to the FQXi blog 'On the Shutdown of the LHC' by Kevin Black, which may be found on the FQXi main community page. I believe you'll be in agreement with me on this?

"Kevin Black wrote (way back on August 5,2008), 'How could you ever design an experiment that would disprove future causal influence on a current condition? I just can't imagine how one could do that, but I am open to suggestions. Any ideas?'

"At the risk of appearing to talk crazy, I'd like to suggest that it is not necessary to design such an experiment. Moreover, I'd like to go on record here as proposing the following as a basic axiom of physics: Anything which does not exist cannot influence anything which does exist. A crazy idea? Maybe, but crazy enough to be true? Time will tell, or not.

"The future does not exist. Therefore it cannot influence the present, which does exist. For a fuller discussion of this, please read my current FQXi essay, 'On the Impossibility of Time Travel,' which may be found here, and also my essay 'Time: Illusion and Reality,' which may be found here. Then let's talk."

Cheers

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Ray, on the three color issue with the gravitino, I guess I am not sure about there being a spin 1/2 gravitino. The 3 plus 3-bar, which with su(3) gives g_2, are some "color" indexed system with a holonomy gauge-like structure. Within M-theory the duality between open string types with closed string types will have an S-dual relationship with QCD.

Cheers LC

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Lawrence and Ray,

When I try to hypothesise a hyperdrive physics, it doesn't seem like travelling faster than light is the magor obstacle, other than we don't know how. If I do want to go FTL, I have to move my starship out of space-time into hyperspace. Transmitting information faster than light doesn't send you to the past or create causality violations. That's not the real problem.

The real problem is conservation of energy and gravity. If my voyage through hyperspace causes my starship's mass to avoid gravity, then I've violated conservation of energy. Not to mention that hyperspace, which appears to contain real space, leaves me confused on how momentum is conserved. Whether I take a rocket to Alpha Centauri at 0.5c or a hyperdrive at 100c, when I get there, I'll still have to slow down again from whatever momentum I had, I'll have to apply a reverse momentum. In essense, if I try to hide the mass of my starship from the laws of motion, changes in the gravity field insist that either I can violate conservation of energy, or I can't hide my mass. So, if gravity is going to be a pain in the neck like that, then I might have to say that at velocities exceeding the speed of light, the gravitational constant is going to have to change so that I don't violate conservation of energy.

I know, who could have an opinion of this crazy stuff.

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Dear Lawrence,

Certainly, it depends on how we define these particles. If these gravitinos or gravitino-like spin-3/2 matter particles are massive, they could have spin projections of 3/2, 1/2/, -1/2 or -3/2. The only part of the Standard Model remotely close to this idea is the massive Z boson with spin projections of 1, 0 or -1.

Have Fun!

Ray Munroe

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I suppose if you consider the projection of m_z as a particle state this might work.

Cheers LC

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Dear Lawrence,

Of course, in the Standard Model, the longitudinal Z (0-spin projection) degree of freedom (dgf) is supplied by a complex scalar doublet (4 dgf's) which yields the longitudinal Z (1 dgf), 2 longitudinal W's (2 dgf's) and a Higgs boson (1 dgf). Supersymmetric models introduce at least two complex scalar doublets. It doesn't seem natural for our fermions (even if they are spin 3/2's) to mix quantum numbers with a scalar boson, so we need to explicitly include these spinor states at definition - just like Dirac spinors for spin-1/2 fermions. If these spin-3/2 fermions are massless, then we only need to worry about spin projections of 3/2 and -3/2, but we don't have any spin-3 bosons that could connect these two spinor states, so it disintegrates into a simple (and probably uninteresting) problem of two independent spinors.

Have Fun!

Ray Munroe

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Of course often in gauge theory longitudinal modes are removed by Ward identities. When it comes to Rarita-Schwinger fields of spin 3/2 we might not have that luxury, though it might be of some interest to see whether that is the case, so there might be a problem analogous to a longitudinal Z mode. Clearly the interaction of a spin 3/2 particle with a gauge field knocks it into a spin 1/2 state. I attach a drawing of this in the attachment. So a Ward identity analogue might then posit that a gauge interaction with the Rarita-Schwinger field must be accompanied by a gravitational interaction (graviton labeled G) which "pops" field RR field from some unstable configuration in spin 1/2 to a spin 3/2. The positive and negative signs on the spins are assumed.

Who knows, this might have something to do with M-theory. Gravitons are associated with closed strings and gauge fields with open strings. The RR gauge or gravitational interaction might mean there must be some relationship between open and closed strings.

Cheers LC

attachments: Rarita_Schwinger_fields.GIF

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Dear Jason,

I am sorry. I have been stumped by your problem. But I think I got a piece of an idea from Frank. Yes - I hate to admit it because that guy bugs me...

The Universe is not (3+1)-Dimensional as Frank and so many others claim. It is (3+1+fractal)-Dimensional. Now where does the fractal come from? Frank centers everything around the Dream. But the Dream is an experience of the Brain/ Mind. In turn, the Brain has "wrinkles" or cortical folds of sulcus and gyrus. This gives the Brain a (3+fractal) equivalent dimension, thus allowing the Brain to experience (3+fractal)-Dimensions, where the fractal dimension is a partial projection of hyperspace into our space. This is the overlap between space and hyperspace - this fractal dimension that our Brain can tap into. Are there other ways to tap into the fractal dimension? I'm not sure...

And tomorrow, I'll go back to saying that Frank is off base, and I'll claim that someone counterfeited this post!

Have Fun!

Ray Munroe

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Dear Ray,

I'll have to think about Frank's wrinkled brane; it's not the first time I've heard of fractal space.

I'm toying around with the idea that there is a c-velocity brane that governs the laws of motion as we know them; next, there is a 2c brane with similar laws of motions, then a 3c brane,...n*c branes. The idea is that these surfaces are stacked. Standard particles move around the c-brane. Gravity has its effects on multiple branes. Right now, it's a mathematical construct that gives me a way to describe a hyperspace. Then, I wanted to play with the idea of using surface-fields or hyper-fields. These fields would be able to deform, slightly multiple surfaces. Next, by somehow deforming these fields in the right way, it might be possible to induce a net velocity on these c-brane surfaces. Doing this way, I might be able to pursue, again, the idea of positive/negative energies (space-time curvatures) as being some kind of charge with the possibility of electro-magnetic similarities. The idea would just assume that only 3D of space are necessary. Space-time, or time, is just the abilility of each brane to transmit information. A 2c brane can transmit information twice as fast as a 1c brane.

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Hi Ray,

I've been looking at black hole entropy trying to get some some ideas. I figure that the event horizon can represent the c_1 brane (speed of light for standard space). At the event horizon, the brane has a maximum information content for its surface area. I'd like to hide my c_2 brane, c_3, etc inside of the black hole. A c_2 brane with a speed of light c'=2c, should be able to contain the same information content inside of a smaller surface area, right? Or, at the c_1 surface area, the c_2, c_3... have lots of information content to spare. I'm guessing it might be possible to calculate the surface areas at which these branes becomes black holes. I have to assume that the Boltzman's constant remains unchanged. I expect the charge might scale with the speed of light, but I haven't worked that out yet. For the Planck length, G and h are there. I'd like to scale one of them to see what happens.

I'll let you know if I discover anything really interesting.

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Dear FQXi Friends,

I am concerned that some of you may think my essay is too complicated. This is a short explaination that I have reposted from James Putnam's blog area.

In my conclusion, I said "One version of Occam's razor says "Plurality ought never be posited without necessity."... Are Beauty and Symmetry necessary reasons to trump Simplicity? If Simplicity always trumps Necessity, then we should be satisfied with the "ugly but practical" Standard Model and a separate General Theory of Relativity, and we need to stop talking about such "foolishness" as Theories of Everything or Not Everything."

I know that my ideas look complicated, but I think it is analogous to finding the least common denominator (LCD) so that we can add fractions. If you wanted to add

$1/2 + 1/3 + 1/6$

you would find the LCD = 6, so that

$1/2 + 1/3 + 1/6=6/6=1$

and the apparently complicated is simplified. Likewise, if we want to unify the four known forces properly into one algebra, then that one algebra must be at least as large as the sum of its individual components. It looks more complicated because it is bigger and predicts new stuff, but the overall picture is simplified - the fundamental forces are placed on a compatible foundation.

Does a 12-dimensional model seem like "overkill"?Garrett Lisi's 8-dimensional E8 TOE seemed to be a reasonable approach, but Jacques Distler shot holes in it. If E8 isn't large enough, then we need to look for something larger. I have played with 8-, 10-, 12- and 14-dimensional models and the K12' presented in this essay is my favorite model.

Critiques are welcome!

Have Fun!

Ray Munroe

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Are you really using a conceptual LCD approach to unification of the four forces, as in, what do each of these forces have in common?

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Its an analogy. They share Lie Algebras of different rank and dimensionality.

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Hello Ray,

I just finished the first read-through of your essay, earlier today. I am impressed by how you seem to link the limits of complexity with the limits of simplicity in geometric construction. I agree that the simplices hold the key to understanding a lot of the underlying order we see. I'll have to give your essay a more thorough read to comment much further, as it does get pretty deep and a bit complicated. I admire the fact that you seem to have paved a road where Lisi ran into a roadblock. That's really very cool.

Despite Occam's razor, I think we must invoke Einstein's quote here "Make things as simple as they are, but no simpler." If you are homing in on how nature uses the available symmetries found in Math, then E8 has to be involved somehow, and your construction shows great promise.

All the Best,

Jonathan

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Dear Ray,

Has there been any feedback from the physics community, or anyone participating in this contest, about your book?

James

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News flash: I kept saying these ideas of frequency dependencies, such as from LQG, on the speed of light were wrong. Well read ‘em and weep

http://www.nasa.gov/home/hqnews/2009/oct/HQ_09-254_Fermi
_anniversary.html

http://arxiv.org/ftp/arxiv/papers/0908/0908
.1832.pdf

String theory makes a nice prediction that the quantum foam which produces this effect is valanced or renormalized out from observable physics.

I have been having long hard arm wrestling sessions over this. This makes me absolutely giddy! Bye bye loop quantum gravity breaking of the Lorentz group at small scales — YIPEEE!!! There are litterally thousands of theory papers now which are worth less than toilet paper. God it feels good. :-)

LC

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Dear Lawrence,

I tried both links. The NASA link brought me to the NASA website, no further. Ther arxiv.org link gave me an error. I'd like to know what you're excited about. Are you saying that loop gravity is dead? What exactly killed it?

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Dear Jonathan,

My larger paper, "A Case Study" posted on 9-22, shows similarities between K12' and E8xH4 (Lawrence coined "A Quiver of Quaternions" and his Jordan transformation is about twice as big). And of course, E8 is an important subset (the fermion multiplet) of K12'.

Dear James,

My book has received very little attention, and I have been talking about K12' rather than Quantum Statistical Grand Unification (my older, neglected child).

Dear Lawrence,

Congratulations. It is good to stick to your guns and not follow every trend. Jason is having trouble with your links.

Have Fun!

Ray Munroe

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I googled the link. So the speed of light is constant over billions of lightyears over a range of frequencies from gamma rays up to, I guess visible light or something. I think that kills Double Special Relativity. The article I found talked about two neutron stars slamming into each other. In any event, congratulations, Lawrence.

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I didn't really accomplish anything, other than to work and argue from a stance in opposition to these ideas.

This pretty much does rule out some quantum gravity theories. Various models of quantum gravity, except string/M theory , have spacetime broken into struts and links near the Planck scale. This results in the breaking of Lorentz symmetry (spacetime symmetry of relativity) at very short scales. These models include LQG and Dynamical Triangulated Causal Nets and so forth, have these features. The one alternative to string theory which fly through this problem is twistor theory, which in what I am working on with string/M-theory does emerge. These various models are going to have to be either seriously revised or scrapped.

Loop Quantum Gravity is not dead though. In fact I have been working, rather unsuccessfully to be honest, on how LQG could be a system of constraints which exist in a map from the string/M-theory AdS_5 spacetime to the physical (the real universe) de Sitter spacetime. String theory works on the anti-de Sitter spacetime, but that is not the universe. It maps to the de Sitter spacetime under a Wick rotation. A BTZ black hole on AdS spacetime makes this rotation-map difficult, but I think the BPS charge of that black hole maps to the LQG constraints on physical spacetime. This problem has proven to be abominably difficult though. But I think something like this has to happen. String/M-theory stuck forever in the AdS domain does not do as much good for understanding this universe.

Lawrence B. Crowell

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Lawrence,

A Wick rotation refers to imaginary time. Are you considering the idea of imaginary time inside of the black hole?

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Well one can think of the radius becoming a time direction and the time direction becoming a spatial direction beyond the event horizons. There are some funny problems with thinking this way though. However, there is no Wick rotation of one coordinate alone.

Cheers LB

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Dear Lawrence and Jason,

Regardless of whether we change the metric signs on time or space, we still have at least one imaginary dimension. I'm not sure what the 7th dimension is. What if the 7th dimension is imaginary time and we need to consider the possibility of complex time? The other 11 dimensions in my model seem consistent with M-Theory configurations.

I think Causal Dynamical Triangulation has some structural similarities with my simplices. Is it dead? Or does the symmetry-breaking mechanism need to be revised?

Have Fun!

Ray Munroe

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It is refreshing that progrss is being made in experimental physics. The LHC is supposed to be fully operational in November. Maybe we'll get a Higgs particle for Christmas!

http://dvice.com/archives/2009/10/large-hadron-co-
6.php

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Tessellations of 10 or 11 dimensional superspace is somewhat different than what Fermi has found. For one thing the tessellation is a system which defins a quantum error correction code. It is not something which is hard and physical. In fact it can't be, because a tessellation is only valid in a certain frame bumdle or gauge choice. What has happened is that loops or struts in spacetime time which violate Lorentz symmetry, common in LQG and with some CDT ideas, has been falisified.

Lawrence B. Crowell

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Ray,

I have been doing some back reading on issues of journals I have let stack up. This is a "Perspectives" write up of two articles in AAAS "Science" October 16. You might find this interesting. It involves the formation of a Dirac monopole in certain condensed matter systems. If you want I can send the main articles.

Cheers LC

attachments: 375.pdf

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Dear Lawrence,

Thank you for the paper. They were also using tetrahedra!

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I attach an image from a part of one of these articles. The spin vertices of the tetrahedra have two pointing in and two pointing out. This gives the Pauling model for the entropy of "cies." Yet a defect on one tetrahedra and the opposite defect on the other tetrahedra results in a Dirac sting. I suspect this can apply to octahedral sphere packing as well. The B_4 representation of the 24-cell is an 8-tetrahedral and 16-cell structure. This is in a way similar to how the Skyrme fermionic field in what I am working with generates flux tubes which are what we call strings, as well as higher structures.

Cheers LC

attachments: Bfield_on_tetrahedra.JPG

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Dear Ray,

it is a pity that your Physics training finally comes to managing your family retail business. There is so much potential in the geometrical approach in evolving Physics, as nature has symmetries and basic simplicity in its structures. However, just like crystal defects we have breakdown of symmetries that are also significant, as these provide the variety in Nature that we observe too. Somehow, we are not bale to solve several mysteries of the universe, specially the ones that arose since early universe, like dark matter/energy and somewhat later the black holes of both large and small size. The anamoly of Big Bang birth results in such anamolies as we are unable to obtain experimental data about that period through cosmological measurements. t is my feeling that if we are able to discern these secrets we shall resolve many of the problems in Physics. There is also a hiddden secret behind the emergence of four force fields in a sequential manner, gravity being oldest. The other three evolved as strong nuclear, electromagnetic and weak nuclear in accordance witht the logic of evolution. There is thus an undercurrent of gravity in all the other force fields that we have not been able to isolate. That may helpm unify the overall picture.

Lot of postings on your essay makes me feel, you have a good task ahead in Physics for which you may sacrifce some of your commercial activities! If time is available, i will value your comments on my essay on this forum.

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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

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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

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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

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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...

view entire post

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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

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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...

view entire post

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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

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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

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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

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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 Munroe

attachments: 9903060v1.pdf, 0101107v2.pdf

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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

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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

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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

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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

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Thanks Ray,

Exactly!

Jonathan

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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

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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

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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

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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

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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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Dear Lawrence,

I enjoy corresponding with you. It is a shame that more don't appreciate your genius. I apologize for my lack of follow-through lately. I have been preoccupied by this blog site, and haven't had a creative burst of my own in a few months. I am impressed with your progress on the "Jordan/ Exceptional Black Holes" paper. I am a huge fan of Dirac and somewhat familiar with S duality, but wasn't sure if the Magnetic Monopole would ever be discovered. Its sort of like the Higgs - you expect it but wouldn't be surprised if it never turns up.

Have Fun!

Ray Munroe

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I too have been a bit lax of late. I have been doing a bit of reading though. I am doing some work on the M-theoretic aspects of a gauge theory based on the Jordan matrix. The work is leading to an M-theoretic approach to black hole complementarity.

I was looking at your paper on hypercolor. The connection to g_2 is interesting and this suggests a parallel structure between QCD and its family structure and the g_2 which acts along with F_4 as the centralizer of the exceptional algebra J^3(O).

Cheers LC

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Hello Ray ,

Happy for your result .

Best Regards

Steve

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Dear Lawrence,

I hope that my ideas help inspire you and your ideas help inspire me. I run hot or cold on ideas. Hypercolor was one of those ideas that I thought was great when I first put it on paper, but then it didn't mean as much to me anymore. I primarily did it to show the 2 dimensional triangular close-packing lattice equivalent of my 3 dimensional Hyperflavor FCC close-packing lattice. But it helped me better understand G2 and the relevance of the reciprocal lattice.

Dear Steve,

Thank You for your good wishes and your vote. If the community vote is the primary score, then I finished in the top eight and earned FQXi membership. As you know, membership in FQXi and exposing my ideas to a larger audience were my primary goals. There is, however, sufficient confusion about judges votes and public votes, that I won't celebrate until I receive the congratulatory e-mail.

Have Fun!

Ray Munroe

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Of course these discussions can continue. I suppose technically the time blogs are still open for discussion, though I think they are a bit cold by now. I do have to sit down and crank a number of calculations.

The G_2 and F_4 are centralizers and the F_4 ---> B_4 or D_4 decomposition describes the extended Lorentz group. So local gauge-like transformations of G_2 determines different "slices" of F_4 in the J^3(O). The G_2 group action, which is a holonomy on the S^7 is then directly linked with transfomration of the extended Lorentz group, in particular the embedding of B_4 ~ SO(9) in SO(9,1).

Cheers LC

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Hi Ray. How do you plan on getting around all of this?

Since dreams make thought more like sensory experience (including gravity and electromagnetism/light) in general, the idea of "how space manifests as electromagnetic/gravitational energy" is not only demonstrated in dreams (as I have shown), but this idea is then ALSO understood to be NECESSARILY central to an improved understanding of physics/experience IN GENERAL.

According to Jonathan Dickau, my idea of "how space manifests as electromagnetic/gravitational energy" is "right on" as a central and valuable idea/concept in physics.

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Dear Frank,

In my opinion, you are appealing to a Dream/ Mind/ Soul that may be more complex than the Gravitational and Electromagnetic Fields that you are trying to describe.

I am simply trying to unify the four forces - Strong, Electromagnetic, Weak and Gravitational - and the three generations: up, down, electron, charm, strange, muon, top, bottom, tau, and all neutrinos - in a seemingly consistent geometrical manner.

If you can also tie your ideas regarding Psychology and Dreams into a TOE then that is wonderful. As I have said, I think you should examine Klingman's techniques and see if any of those models can be reapplied to support your ideas. I compared your essay with Klingman's because you were both using a Dream/ Consciousness that may be more complex than the gravity that you are attempting to describe. Creative modeling is the point where Klingman's essay beat yours - PERIOD! How can you win First Place if there is obviously at least one better paper? No one else did anything quite like my paper, so I can't be eliminated by one essay so easily. I like Jonathan Dickau's ideas, but I think he was being polite to you.

Have Fun!

Ray Munroe

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Hi Ray.

According to Jonathan Dickau, my idea of "how space manifests as electromagnetic/gravitational energy" is "right on" as a central and valuable idea/concept in physics.

Since dreams make thought more like sensory experience (including gravity and electromagnetism/light) in general, the idea of "how space manifests as electromagnetic/gravitational energy" is not only...

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Hi Ray.

According to Jonathan Dickau, my idea of "how space manifests as electromagnetic/gravitational energy" is "right on" as a central and valuable idea/concept in physics.

Since dreams make thought more like sensory experience (including gravity and electromagnetism/light) in general, the idea of "how space manifests as electromagnetic/gravitational energy" is not only demonstrated in dreams (as I have shown), but this idea is then ALSO understood to be NECESSARILY central to an improved understanding of physics/experience IN GENERAL.

The core theoretical/actual application and manifestation of the wave/particle duality is evident when thought is more like sensory experience in general. Wave/particle duality occurs in dreams. Dreams make thought more like sensory experience in general.

The theoretical/actual basis of the known mathematical union of Maxwell and Einstein's theories (with the addition of a fourth spatial dimension to Einstein's theory) IS dream experience.

Since dreams involve a fundamental integration AND spreading of being, thought, and experience at the [gravitational] MID-RANGE of feeling BETWEEN thought AND sense, dreams make thought more like sensory experience (including gravity and electromagnetism/light) in general. Indeed, how space manifests as gravitational/electromagnetic energy is a central and very valuable concept in relation to physics (and experience) in general. Dream experience offers an expanded (yet relatively unified) perspective in relation to experience (and physics) in general.

The significance of the following, in relation to the above, to physics, experience, being, thought, and to a better understanding of genius as well is not to be underestimated:

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

The integrated extensiveness of thought/thinking is improved in the truly superior mind (and in the highest/ideal form of genius).

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Hi Ray.

The theoretical/actual basis of the known mathematical union of Maxwell and Einstein's theories (with the addition of a fourth spatial dimension to Einstein's theory) IS dream experience. I proved the three to one (one third) relation in BOTH space AND time in my essay as well -- consistent with BOTH general relativity AND said union of Maxwell and Einstein's theories.

We are, in fact "outsmarted" in the dream, as dreams make thought more like sensory experience in general.

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Dear Frank,

I probably already told you this, but I have personally had an 'out-of-body' dream-like experience that I related to my religious background. I agree with the power of the Dream/ Mind/ Soul, and think it may be more complex than Gravity or Electromagnetism (the power of being and understanding is greater than that of mere force fields). I feel that you need to understand that professional physicists expect some modeling and mathematics. Klingman's modeling and mathematics might be valid or might be garbage. The point is that he tried to bring his ideas closer to the expectations of mainstream physics. Is it easier to repeat yourself hundreds of times - until people get tired of arguing with you or politely agree with you, or is it easier to conform to the expectations of the profession? I'm trying to challenge you into improving your ideas by supporting them with mathematical models and/ or equations. If you accomplish this, I would be glad to review and critique the new ideas.

Have Fun!

Ray Munroe

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Hi Ray.

Think of how genius, dreams, memory, and art are possible. Now think of this in keeping with this enormously important fact:

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

Emotion, thought, feeling, and sensory experience are all fundamentally interactive. Dreams add to (or improve upon) what is the integrated extensiveness of being, experience, and thought. Dreams conceptually/actually unify gravity and electromagnetism/light. It is that simple.

Note the transparent space/sky around the larger and red [setting] sun.

(Telescopic/astronomical observations make the objects larger, or they could not be seen at all.) Importantly, isn't the increased transparency/invisibility of space, in relation to the blackness of night/outer space, the requirement of seeing farther?

LARGER OBJECTS, IN A RELATIVELY SMALLER SPACE -- COMPARABLE TO THE EARTH -- WOULD HAVE HIGHER GRAVITY, WOULD THEY NOT -- CONSIDERING THAT THE INVISIBILITY/TRANSPARENCY OF [THE SPACE] IS INCREASED?

Of huge importance, isn't the increasing transparency/invisibility of space the reason for the redshift?

How would you account for this? Do you not agree that telescopic/astronomical observations are "activating" -- similar to dreams -- what would otherwise be the waking/ordinary visual experience of the stars?

FQXi -- stop deleting my posts, or I will not participate at all at this site.

I'm very serious.

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Dear Frank,

I won't delete your posts. We are all trying to say something that is important to at least us. I am glad to see you are still alive. I hope you are doing well. Tonight, I will be cheering for one of my college football teams, the Texas Longhorns. Although all of my degrees (BS, MS, PhD) are in High Energy Physics from Florida State University, I attended grad school at Texas in the 80's and also studied Solid State Physics and Plasma Physics.

Have you ever listened to a train whistle or an emergency vehicle siren, and noticed that the frequency is slightly higher when the vehicle is approaching, and is shifted to a 'lower note' after the vehicle has passed you? This is the Doppler effect for sound. It is caused by the fact that sound waves have a certain speed in Earth's atmosphere. The normal assumption is that red shifts in stellar spectra are due to stars moving away from us (light also has a certain speed, so a similar Relativistic Doppler effect can occur for light waves) and blue shifts in stellar spectra are due to stars moving towards us. I used to teach these concepts in a freshman-level Introductory Astronomy class at the local Community College.

I have my biases, and think that you should study those theories that you hope to overthrow or modify, and then use the appropriate type of modeling and/ or mathematics to support your idea. The 'old ideas' work to a degree. New ideas are more likely to be wrong than correct. You should try to follow the physics profession's expectations.

Have Fun!

Ray Munroe

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Dear Frank,

The nature of your comments causes me to question your knowledge of spectra. If you know everything in this current post, then I apologize for talking down to you. If not, please consider this a friendly lesson in spectra.

There are two fundamental types of emission spectra: discrete (like a neon light bulb) and continuous (like an incandesant light bulb). At a fundamental level, all light emission is caused by electrons transitioning from one quantum state to another and releasing photons to counter-balance energy conservation. This leads to discrete spectral lines that allow us to uniquely identify elements. If we crowd a large number of these atoms together in a very small space, then this discrete spectrum gets smeared out into a more continous spectrum. In the case of a star, its heat is generated at its core by thermonuclear fusion. That heat makes its way to the stellar surface by radiation and convection, then produces a Blackbody Radiation spectrum that uniquely defines the star's surface temperature. Thus the color of a star indicates its surface temperature. Blue stars are hotter than red stars (and blue stars burn out quicker than red stars because they are so bright). Spectral lines indicate the abundance of various elements in the stellar atmosphere. It is these elemental spectral lines that get red-shifted or blue-shifted by the Relativistic Doppler Effect.

Likewise, there are two fundamental types of absorption spectra: discrete and continuous. If we have interstellar dust, it will absorb lines that are characteristic of its elemental make-up. It re-emits this energy in a variety of directions (not perfectly alligned with the original solar radiation that excited its spectral lines), and removes certain lines of color out of the original stellar spectrum.

Why is the sky blue and the sunset red? This is an example of a continous absorption spectrum. Rayleigh scattering is very dependent on wavelength. Blue light has a shorter wavelength than red light, and is thus more likely to interact and scatter with gases in the Earth's atmosphere. Likewise a Blue Ray player uses blue laser light as opposed to a DVD player that uses red laser light, and thus Blue Ray can hold more data on a comparably sized disc. The blue scatters out of the Sun's spectrum first, making the sky blue and the direct solar radiation less blue. At sunset, the sky is also absorbing most of the mid-wavelengths like yellow, and this makes the sunset red because red is the primary color remaining.

Most world-class telescopes are on mountains, so they have less Rayleigh scatter