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August 25, 2019

CATEGORY: Blog [back]
TOPIC: Talks, talks and more talks from the Azores [refresh]

FQXi Administrator Zeeya Merali wrote on Jul. 14, 2009 @ 20:02 GMT
Now that the Azores conference is officially over, I will try and quickly catch you up on (some of) the more serious sessions and the 46 odd talks that were given. I also recommend visiting Backreaction for Sabine Hossenfelder’s take on the meeting in general and the future of sex in particular (the latter being a topic brought up when delegates pondered scenarios for the next 100 and 1000 years, as I posted earlier.)

Wednesday kicked off with a talk by Paul Davies with the tongue-twisting title, “Teleology without teleology,” about the search for a law of increasing complexity in the universe.

Alan Guth and Frank Wilczek (or a virtual version of Frank Wilczek via video link, photo courtesy of Max Tegmark) both updated talks I have blogged about previously, so I’ll just direct you to those posts for a detailed description of Guth’s thoughts on finding a measure in the multiverse, and Wilczek’s thoughts on the foundational questions that still remain to be answered.

Both Guth and Wilczek’s talks fed into later debates. Guth had made an interesting point in motivating his belief in the existence of a multiverse, asking how many nouns in the dictionary lend themselves to the thought that there is only one of them? “Two: ‘God’ and ‘universe’,” he said. “Scientifically it makes more sense to lump ‘universe’ in with planets, galaxies...and assume there is more than one of them, than lump them in with God.”

However, in the discussion afterwards there was a passionate split over whether it makes any sense to talk about the multiverse when there was no (current) way of testing whether such a thing exists. Meanwhile, some of the ideas brought up in Wilzcek’s talk were revisited when delegates were asked to come up with scenarios for the future of the universe/multiverse.

Friday had a mixed bag of 27 talks (stunningly the schedule only overran by 15 minutes) covering time, cosmology and quantum gravity.

John Wheeler once wrote: “No question about quantum gravity is more difficult than the question, ‘What is the question?” and that was apparent during the day. Claus Kiefer advocated “quantum geometrodynamics” as a way to tackle the problem. Rodolfo Gambini is investigating how you can even define a clock in the realms where quantum gravity rages—a question that Andy Albrecht also works on.

Ettore Minguzzi reprised his discussion of why we can’t take global time for granted from the FQXi Nature of Time contest. Laura Mersini-Houghton (photo courtesy of Max Tegmark) stated that the arrow of time can be explained in the multiverse view: assuming that there is time symmetry in the multiverse, the act of a new universe budding off from the background breaks this symmetry and creates an arrow within the baby universe. How compelling people found that depended a lot on whether they are fans of the multiverse picture or not.

Fred Adams took a path into some of those alternative universes with different physical laws and made us all feel a little bit less special by showing that stars can still develop in universes with parameters that differ from ours. This suggests that the parameters in our universe may not need to be as finely-tuned as we thought for life to occur, with possible repercussions for the anthropic principle.

Anthony Aguirre wins the prize for the best Douglas Adams shout-out, by discussing the arrow of time with the aid of slides (to come) of a piano decomposing into a gas, which by freak chance reassembles itself into a bowl of petunias (“but not a whole whale as that would be too complex.”) Unfortunately, I was so pleased about the reference to Hitchhiker’s, I forgot to note what the graphic was meant to demonstrate, so I’ll let Anthony come in and explain that his himself, when he has time.

Olaf Dreyer set up an interesting philosophical fight between two views of special relativity: Einstein’s (in which matter conforms to the background) and Lorentz or Bell’s view (in which matter defines geometry). He then pondered if by extending the Lorentz view into general relativity it would be possible to find a way that geometry could emerge from a phase transition (something that isn’t possible when looking at Einstein’s GR).

Steve Savitt found himself as the only philosopher in a room full of physicists. He argued that simultaneity is still consistent with a notion in which the past, present and future are ontologically different. The problem, he said, was in the use of inappropriate language to describe time as “flowing” or “moving” (which he says it doesn’t do) rather than “passing” or “lapsing” (which it does do).

Back on the cosmology track again, Glenn Starkman weighed up modified gravity theories against dark matter and dark energy.

Garrett Lisi attempted to unify the standard model and gravity in one slide. Xiao-Gang Wen described his string-net liquid model with the same goal in mind.

Sabine Hossenfelder promised to talk about something truly “repulsive” and she did: antigravitation. But she didn’t levitate any frogs. Instead, she talked about a second copy of the standard model, identical to the one we know, except with a negative gravitational interaction.

Finally, lone experimentalist Dmitri Budker talked about tests of whether the constants of nature are really as constant as advertised.

The final session on Sunday covered quantum mechanics. Bob Coecke, Dan Browne (not the one responsible for this, thank goodness), Howard Barnum and Caslav Brukner tried to recast quantum mechanics in terms of information theory (discussed in detail in Bob Swarup’s article, “The End of the Quantum Road?”

Coecke did so in terms of “quantum spiders.” I googled “quantum spider” and came across the line: “Just ran into one of those quantum spiders in my apartment-- one of the ones that emerges spontaneously from the vacuum. And if I had a vacuum (cleaner, that is) it'd be vanishing back into it . . .” That’s not quite what Coecke had in mind, nor was he talking about Spiderman’s nemesis. Rather he was introducing a new graphical technique to describe the interaction between classical and quantum data in quantum informatic protocols to aid in quantum computation. You can see if they really do look like spiders in his paper here.

While Browne investigated whether Bell’s inequalities can be written in terms of information theory, Joy Christian made the controversial statement that Bell had based his theorem on mistaken assumptions and that quantum entanglement is an illusion. If correct, Christian could take the spookiness out of quantum mechanics; but most in the audience stood by Bell.

But speaking of spookiness, the most important thing I learned from the Azores trip? In a land where there is one cow for every human resident, you really don’t want to mess with the cows. (Photo courtesy of Max Tegmark.)

You can find out more about the conference here.

this post has been edited by the forum administrator

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John Merryman wrote on Jul. 15, 2009 @ 02:05 GMT
To raise a question about the term "universe;" Does it refer to "unitary," as I always assumed, or "unit," which is what those taking about multiverses must mean. Obviously if there are other dimensions which we are not yet aware, but can connect with, the relationship is still unitary. On the other hand, if one is to take Inflation theory to be true and our universe expanded to many, many times its visible size in a fraction of a moment, there better not have been any other unit-verses in the area, or we would seriously know about it. Or, more likely, wouldn't, because the shock wave would have washed over this puny little 13.7 billion year old unit-verse. So if they are outside the expanding universe, it doesn't seem at all likely we would ever be able to detect them. If they exist as some other dimension, would they really qualify as the Big Bang type universe the cosmologists describe, not windows into other dimensions of this one?

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Lawrence B. Crowell wrote on Jul. 15, 2009 @ 18:21 GMT
Unitarity is a particular structure operators have. A unitary matrix is one where the transpose M_{ij} --> M_{ji} and complex conjugation (i = sqrt{-1} --> -i) of the operator gives the inverse of that operator. This is usually written as

U^\dagger = U^{-1} dagger is a cross shape

So the matrix is nonsingular and so forth. Also if that operator U = exp(iH) then it is not hard to show that if H^\dagger = H, which means it is Hermitian and pertains in quantum mechanics to an observable. Unitary operators are transformation operators and evolution operators.

With gravitation quantum states in one region of spacetime are not necessarily unitarily equivalent to those in another. So a vacuum state in one region will appear as a vacuum plus a thermal distribution of partles elsewhere. This is the basis for the Hawking quantum irradiance of black holes and the Unruh effect.

Lawrence B. Crowell

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John Merryman wrote on Jul. 16, 2009 @ 09:29 GMT
Lawrence,

I'm sure scientists know what they are talking about, but they are not very careful about how it appears to a broad audience. Multiple universes can start to sound like discussing how many angels can dance on the head of a pin.

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Lawrence B. Crowell wrote on Jul. 16, 2009 @ 11:50 GMT
Other cosmologies come about, or the idea of them coma about, due to the fact that strings can wrap on branes or extra dimensons beyond spacetime can fold up in a vast number of ways. There is a lot of math-technology behind this, Calabi-Yau theory, K^3 theory, orbifolds and so forth. Each of these configurations is a possible universe, or some configuration a universe could take. Whether these other universes actually exists or not is somewhat academic. The configuration a cosmology takes is determined as such, and this further involves how a Higg field or inflaton reaches a minimum in a potential landscape.

All of that is a work in progress, so to speak. I have certain problems with some of these more extreme speculations, where I suspect that physicsists have gone far beyond the bounds of empirical science.

Yet I thought I would clarify what unitarity means. It is a well known element of mathematics and physics.

Lawrence B. Crowell

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John Merryman wrote on Jul. 17, 2009 @ 00:43 GMT
Lawrence,

Thanks for the clarification. I'm just pointing out that natural tendency to speculate about all possibilities can lead to unintended consequences. It's a necessary process of growth, intellectual and otherwise. There is just an equally natural tendency to consolidate.

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Jason Wolfe/wulphstein@gmail.com wrote on Jul. 18, 2009 @ 19:59 GMT
Lawrence,

Thank you. You've been giving me lots of great ideas for a website on UFO technology. Actually, I decided to go with the idea of the tesselation of space-time with E8xE8 polytopes which reproduces the solid state effect; space-time is very similar to a conduction band; space has no physical reality other than that of a project/shadow/hologram, where the physical constants are enforced by the tesselated "hyperspheres". Particles in space-time are like phonons in a crystal. I decided to define "hyperspace" as the next higher energy "conduction band" with a velocity (energy) range from 100c to 1000c. Getting into hyperspace requires the generation of a "hyper-field" which will require tachyon/exotic particles. The idea is to get the hyper-field to completely wrap around the space-craft. When it's energy is raised along the conduction band axis (done slowly and delicately), the hyper-field will be raised into hyperspace. The space-craft within the hyperfield is in a precarious state where the laws of physics are still standar model. If the field should breach, then the laws of physics of hyperspace will fill the space contained in the hyperfield, and everything inside will disintigrate. In the same way that most quarks are unstable in our space-time, our hadrons and leptons are not stable in hyperspace; so no hyperfield breaches can be tolerated.

I believe that hyperspace is a really high energy environment where its hyperphotons are incredibly more energetic than cosmic rays. I want to assume that the planck constant is the same, so E=hf still holds. The hyper speed of light c'=1000c; so E=hc'/lambda, so wavelengths are much smaller.

Gotta go, my girlfriend is dragging me away to see Harry Potter.

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Ray Munroe wrote on Jul. 18, 2009 @ 21:58 GMT
Dear Jason,

The E8xE8 is a 16-dimensional hyperspace, not spacetime, which goes back to Lawrence's comments that alternate Universes are imaginable in a many-branes environment. I can find an E8xE8 in a Supersymmetric "E12"x"E12", but finding support for "E12" and a new variant of Supersymmetry may be difficult...

The idea of conduction bands is an interesting new twist to my idea (and a variant of Lisi's idea) that hyperspace is a crystalline lattice. But it is not a single "conduction band". I think we have three "conduction-branes": the Weak-brane, the Gravity-brane, and a third brane that I have discussed with you privately.

I hope all is going well for you.

Ray Munroe

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Jason Wolfe wrote on Jul. 19, 2009 @ 04:52 GMT
Welcome back Ray,

I want to thank you for helping me get the details correct. As a hobby, I think a website about UFO technology is helpful if it can be based in theoretical physics. Even if the aliens could sit down and try to explain hyperdimensional physics to me, I don't have enough understanding of the mathematics to be able to differentiate between E8xE8 and E12xE12. Either one is possible. When you speak of conduction branes, it sounds like you mean them as boson/force conduction branes. That would mean that our physical universe has four intersecting conduction branes (four forces). I was approaching the conduction band idea as a region of space where the physics constants (h, c, G, cosmological const) are stable and allow 3D space. Obviously, to get a hyperspace for travel, you need a larger speed of light, c'=100c (minimum). I was under the impression that the speed of light, c, can also be described as an energy/time relationship where the more energy density in a region R, the slower the clock runs in that region. I hypothesized that event horizons arounds a black hole are evidence of an upper limit on energy, like the upper energy bounds in a conduction band. From there, I guessed that the next higher conduction band would have a lower and upper energy (minimum and maximum velocity).

I think that alternate universes with different laws of phyics is very likely; although leptons and hadrons from our space-time would be unstable in those universes. I predict that hyperspace wormholes as a "highway system" makes more sense. And if you exit the hyperspace wormhole without using an exit gate, you might get lost in another dimension, incinerated by a high energy cloud or experience instabilities in the hyperspace physics constants.

My gmail account is down right now so it may take some time before I can respond to you by email.

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Jason Wolfe wrote on Jul. 19, 2009 @ 05:03 GMT
Ray,

I just thought of something. If each of the four forces has its own conduction band with a lower and upper energy range of El to Eh, then c is proportional to Eh - El. That means that gravity, and the conduction band/brane that holds its superstrings, must have a higher velocity. I predict that the velocity of gravity is higher than the velocity of light (electromagnetism). What do you think?

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Anonymous wrote on Jul. 19, 2009 @ 16:46 GMT
Hi Jason,

You gave me the idea of conduction-branes yesterday. Admittedly, I have not had to time to fully develop such an idea. Yes, we have at least four forces, but I'm not sure that leads to at least four branes. For instance, look at page 18 of Lisi’s paper. He rotates his eight basis charges to obtain a Cartan (w,x,y,z) subspace. I think that our two strongest forces, Color and Electromagnetism, yield our four dimensional Spacetime via a rotation similar to Lisi’s, such as:

$(g^3,g^8,\gamma,Z)->(x,y,z,t)$
.

Spacetime becomes inflated, but the remaining branes are under-inflated, compact, and thus require high activation energies. I don’t know if the speed of light is faster or slower in these branes. I don’t know if these branes can take us to the other side of our Universe, or just one nanometer away.

I gave the E8xE8 some more thought. If they are two random E8’s then our product would be 16 dimensional. If the E8’s are related (say via Supersymmetry) then their product might fall in the same 8 dimensional parameter space. Have you been reading Baez?

Good luck in your search for a hyperdrive. I still think my tachyons might help…

Ray Munroe

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Lawrence B. Crowell wrote on Jul. 19, 2009 @ 18:04 GMT
I am not sure where ideas about E_{12} are coming from. There are the A_n, B_n, C_n, and D_n are the simple Lie groups, and the G_2, F_4, E_6, E_7, E_8 are the exceptional groups. That is in extent of it. There are sporadic groups, the Mathieu group, Janko up to the Conway groups and the Fisher-Griess group, called the monster group.

If you want to pop up beyond E_8, then the basic group might be the Mathieu group M_{24}, which is equivalent to the Leech lattice. In an expansion of Jacobi theta functions this is "composed" of three E_8's. There is a decomposition of this which is S^3xSL(2, 7), which is a copy of the Fano plane on a three sphere. This has analogues to the Bloch sphere, where along three independent directions there are independent copies of E_8. So this connects up with some well known physics. To understand this it requires some theory of boundary lagrangians, or Chern-Simons Lagrangian. But by extending the analogue we may think of the system as similar to a 1/2-spin system. There is a +/- spin direction along a chosen axis, which are possible chiral eigenstates of E_8. So under this broken symmetry the three E_8s are reduced to a Z_2 system of E_8's and the remaining E_8 is a tesselation of an AdS spacetime.

The sphere packing of the Leech lattice defines the Mathieu group. The boundary or Chern-Simons Lagrangian mentioned above in the fermionic sector is a Skyrme field theory, which constructs knots of fields. In this case under the symmetry breaking from S^3 to Z_2 this knotted field structure are what we call strings. This connects in part to the structure of the graviton in the 26-dimensional string. There are 24 physical states and two tachyon states which are "removed." The states

a^i_{-1}a^j_{-1}|0> = |Ω^{ij}>

which contains a symmetric spin-2 field in the SO(24) theory, and the anti-symmetry part is a rank-two tensor connected to the graviton by supersymmetry. The E_8 decomposes into an SO(8), plus a lot of other stuff. The SO(24) is a singature of the three copies of E_8 at higher energy.

Lawrence B. Crowell

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Ray Munroe wrote on Jul. 20, 2009 @ 00:40 GMT
Hi Lawrence,

I call it "E12" for simplicity, but technically, it is a semi-simple E8xH4 Lie Algebra product. The H4 inflates to become Spacetime and the E8 becomes a Hyperspace lattice. The fundamental brane structure of "E12" is also different from E8.

I cannot make a simple E8 or a Supersymmetric E8xE8 into a Theory of Everything, and I've had many friendly conversations with Garrett Lisi about that. I wish him luck in trying to figure out a TOE in such a compact format. M24 might be the true TOE in a 26 dimensional world, but I was trying to find something closer to 11 dimensional String Theory. "E12" is weird because it appears to be 12 dimensional, but I think we have a dimensional collapse (probably related to symmetry breaking and the geometrical nature of the Gossett lattice) that allows all bosons and fermions to be defined in 11 dimensions or less.

I thought I was ready to publish my latest findings on E12 a few weeks ago, and shared some of my research with Jason. I have since decided to rewrite it. I am clearly defining my postulates and giving many examples. Because "E12" is somewhat radical and new, I need to be as mathematically rigorous about it as I can be.

Sincerely,

Ray Munroe

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Lawrence B. Crowell wrote on Jul. 20, 2009 @ 01:41 GMT
You are actually talking close to what I am thinking. H_4 is the 120-cell group. Further the Weyl group W[E_8} = diag[H_4, H_4] plus permutations of 8, where the second H_4 corresponds to the dual 600-cell. The H_4 is the tesselation of the AdS spacetime, and the other H_4 is the dual lattice. Since these two exist in an E_8, why not make the system more balanced or symmetrical and let there be three copies of E_8 which exist in the Leech lattice Λ_{24} according to Jacobi θ- functions. There is a lot of machinery here, which I am willing to discuss, but via alternative means.

The physics is then the H_4 at lower energy from the decomposition of the Grosset polytope for E_8, which defines the tessellated AdS spacetime, where the symmetric part of

Ω^{ab} = α^a_{-1}α^b_{-1}|0>

defines gravitons the closed strings act upon. The α^a_{-1}α^b_{-1}are the string operators. So the flat background, or locally flat for scales much larger than the string length. In this setting the remaining E_8x_8 for the R-L modes on the closed string are a type of gauge action on the AdS. Then the graviton, and expansions to higher order in α’ in the Hilbert-Palatini action R + α’ + α’^2R^2 … are weak gauge-like action on the AdS with scale parameters > 10L_string, for L_string = sqrt(8π}sqrt{Għ/c^3} or momenta much lower than the Hagedorn temperature.

I worked out last spring how H_4 tessellates the hyperbolic anti-de Sitter spacetime (AdS), so this looks realistic. I have been working on a little problem involving how strings which define Susskind’s stretched horizon on black holes are dual to strings as seen by a comoving observer that falls with the closed string into the BH. I am trying by other grounds to lay down some physical basis with black hole duality how spacetime is configured by parts of the root space representation of E_8.

Lawrence B. Crowell

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Lawrence B. Crowell wrote on Jul. 20, 2009 @ 01:44 GMT
I messed up the H-P action which should read as

R + α’R^2 + α’^2R^4 …

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Ray Munroe wrote on Jul. 20, 2009 @ 12:47 GMT
Hi Lawrence,

I prefer a supersymmetric (E8xH4)x(E8xH4) (which might be 12 dimensional, and not 24 dimensional) over an E8xE8xE8 for two reasons: 1) the structure of Spacetime falls out more easily, and 2) I think the union of an octonion (E8) and a quaternion (H4) may explain the nature of quantum gravity via Clifford algebra.

It sounds like we both have similar research that we would like to keep private a little longer. If you want to discuss this privately, you may e-mail me at mm_buyer@comcast.net.

I have a doctorate in hep-ph from Florida State University 1996, but I have been out of the physics world for 10 years and my math is a little rusty.

Sincerely,

Ray Munroe

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Ray Munroe wrote on Jul. 20, 2009 @ 15:53 GMT
Hi Lawrence,

I am reserved in accepting M24 = E8xE8xE8 as the 26 dimensional TOE, because I am still holding out for the possiblity that the TOE may be a Supersymmetric E26xE26, where E26 is defined by

$E_{26}->E_{12}XE_{14}->(E_8XH_4)X(E_8XH_4XI_2(7))$
.

Of course, there are many similarities between this and

$M_{24}XI_2(7)$
.

Sincerely,

Ray Munroe

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Jason Wolfe wrote on Jul. 20, 2009 @ 16:51 GMT
In the construction of these various lattices, are there any assumptions that the physical constants (c, h, G, cosmological constant) are still constant? I was planning to let those take on other values. The fact that strong/weak forces are short range and electromagnetism/gravity are long range creates a wrinkle for individual velocities for each force. However, I still think that gravitons are tachyons (which is why we can't measure them). If they were not , then why does the gravitation of a black hole still operate even when light gets trapped inside of the event horizon?

I'll bet that Higgs particles are tachyons as well, but right now, it's just a hunch.

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Lawrence B. Crowell wrote on Jul. 20, 2009 @ 17:02 GMT
I will comment more privately about this later today. The H_4 icosian, a 120-cell quiver of quaternions, and its dual 600-cell define the matrix [H_4, H_4] in the Weyl group of E_8. The dodecahedrachoron defined by H_4 will tessellate a hyperbolic spacetime. The attached file illustrates how H_3 tessellation or honeycomb will fill a three dimensional hyperbolic space, such as AdS_3 ~ QCD.

The idea of E_{12} =: E_8xH_4, with E_{12}^2 would be a lower energy physics than the M_{24} with three E_8's according to Jacobi theta functions. It is not exactly E_8xE_8xE_8. The heterotic string E_8xE_8 is a theory on a flat background spacetime metric, where the graviton is a perturbation on that background. Globally the background space is AdS, where locally on a scale >> L_string spacetime is flat.

The 26 dimensional bosonic string can be found from the F_4 group, or the 24-cell (octahedrachorion). This is the minimal tessellation of flat R^4. The 24-cell has F_4, D_4 and B_4 representations, and the quotient F_4/B_4 defines the sequence

F_4/B_4:1  spin(9)  F_{2\52}  OP^2  1

Where OP^2 is the projective octonionic plane, which I think is the I_2(7) above, and its 168 elements define the number of octonionic multiplication tables. The 52 elements define the 26-dimensional bosonic string.

Anyway, it appears that what you refer to as E_{12}xE_{12} is a lower energy breakdown of a full M_{24} theory on the Leech lattice Λ_{24}

Lawrence B. Crowell

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Lawrence B. Crowell wrote on Jul. 20, 2009 @ 17:28 GMT
erratum: The sequence did not show up right. The boxes are arrows and F_{2\52} should read as F_{4\52}

F_4/B_4:1 --> spin(9) --> F_{4\52} --> OP^2 --> 1

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Ray Munroe wrote on Jul. 20, 2009 @ 17:50 GMT
Dear Jason,

The Higgs field is a special tachyonic field that redefined the zero energy-squared point of our entire Universe. The expectation is that the Higgs field has the most negative vev of all of the types of tachyons that can couple to the Electroweak sector.

Are these fundamental constants different on different branes? First, realize that these branes are necessary to define some of these constants. For example, some of my mathematics is motivated by the philosophy that Dirac's Large Number (related to h and G) is defined by the "size" of the gravity-brane. But this is not a mathematical proof, simply a personal expectation. Certainly, we could have alternate Universes with different properties hidden within the various branes.

Dear Lawrence,

I am excited to find someone working on something even remotely related to "E12". I have felt isolated and shunned by the mainstream physics world.

Sincerely,

Ray Munroe

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Lawrence B. Crowell wrote on Jul. 20, 2009 @ 19:36 GMT
Join the club. I look at it this way. String theory came out of the old bootsrap approach to hadron physics. It ran into trouble then, but it predicted a spin = 2 field. Due to Scherk and Susskind it got reformulated as string physics near the Planck scale. We might then ponder whether something similar is happening here. Chan-Paton factors for endpoints of open strings on p-branes are particle-like as it is. String theory involves boundary or cocyle actions (Chern-Simons), which is similar to Skyrme theory of fermions. That has been found in some condensed matter systems as knots of field flux. So it is entirely plausible that strings are similarly flux knots or tubes that emerge from similar physics. The analogue of the ions in condensed matter physics is the tessellation of the space, whether it be the total space Λ_{24} or the reduced spacetime tessellated by H_4 in a chosen frame bundle.

A tachyon as a HIggs field? The tachyon is for α’M^2 = -1 or -4, for open and closed strings. This is the first excited state α^i_{-1}|0, p>. The negative sign in the mass is a signature of this field. The application of additional α^i_{-1} gives positive definite fields. The Higgs field is a standard scalar field with a φ^4 potential that is positive definite. So I would not call the tachyon the Higgs field, or at least I don’t see it as such. It might be argued that the action of the Higgs field introduces a mass term which cancels out the negative mass of the tachyon. The interaction of the Higgs with the tachyon might introduce a term α^i_{-1}H α^i_{-1}, which would determine an expectation based on α^i_{-1}α^i_{-1} being a positive M^2 term times the value of H on the vev. So it might be that the Higgs destroys the tachyon field. The usual argument is that in the early universe tachyons can’t have zero velocity in any frame and thus run off to infinity.

I started a little exercise a while ago where I put an Alcubierre waro drive in an AdS spacetime. If you think about it the limit where the warp bubble becomes very small recovers a tachyon-like particle. Further, the negative condition on energy for the solution is in line with that of the tachyon field in string theory. Visser wrote a paper arXiv:0904.0141v1 [gr-qc] on how the warp bubble is destroyed by an Unruh type of effect in a spacetime. I thought by extension the tachyon would be unstable in spacetime and in AdS. To compare to Higgs field we might think of the three E_8’s in Λ_{24} as decomposing into E_8xE_8xH_4xH_4, where the H_4 are quivers of quaternions which tessellate the AdS spacetime. The onset of the AdS spacetime then renders the tachyon unstable.

Lawrence B. Crowell

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Lawrence B. Crowell wrote on Jul. 20, 2009 @ 19:44 GMT
Oops, goofed again. The authors of the paper I mention above are:

Stefano Finazzi,1, ∗ Stefano Liberati,1, † and Carlos Barcel´o2,

LC

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Ray Munroe wrote on Jul. 20, 2009 @ 22:49 GMT
Dear Jason,

Lawrence is correct. We need to be careful not to confuse the Higgs with tachyons. Although both start out with a negative energy-squared, the Higgs is a true scalar spin-0 particle, whereas my tachyons appear to be "scalar fermions" (an obvious oxymoron). They appear to be "scalars" because their Left Isospin projection is zero, and their Right Isospin projection is zero (I know this isn't even defined in Standard Weak theory, but it is in my SU(7) Boson GUT theory), but it maintains a spin of 1/2 (like a fermion should) in higher gravity-related dimensions that we cannot observe. Lawrence probably thinks I'm crazy...

Dear Lawrence,

I am still rewriting my paper on "E12" theory. It is currently 30 pages long. I would like to share it with you. I think our separate research ideas may help inspire new ideas.

Sincerely,

Ray Munroe

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Lawrence B. Crowell wrote on Jul. 21, 2009 @ 02:22 GMT
I made a statement that is a bit confusing. The Regge trajectory is J ≤ α’M^2 + b, for b = 1 or 4 for open or closed string. The tachyon ground state for the 26-dim bosonic string is α’M^2 = -b, which gives an imaginary mass-energy, not negative. There has been some work on tachyon condensates, where the instability of the tachyon runs away. The scalar field interacts...

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Steve Dufourny wrote on Jul. 21, 2009 @ 08:48 GMT
Hello ,

Quaternion ,Octonions....complex hypercomplex....a big joke in the reality .

The strings too a big joke .

Gosset ...interesting ....E8 E x E y ....but so far of the truth .....a theory of nothing ,That's all .It's like if the tittle was important ....falses informations imply incredible notoriety .It's like a play .It's like want find a water drop in a fire .

Waw viva el sciences .

The lost of times and the business decrease the velocity of evolution like the stupidity .

The theory of all ,it's too late ,the quantum spheres....spheres ....Universal sphere....but we can improve it .

Spherization Theory is foundametal ,Eureka from Belgium .

HIHIHI my Vanity .Vanity of vanity all is vanity .

Steve the spheric man

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Ray Munroe wrote on Jul. 21, 2009 @ 12:27 GMT
Dear Lawrence,

We are saying the same about tacyhons. I called them negative mass-energy-squared and you called them imaginary mass-energy. I like lattices (such as the Gosset lattice) because of sphere packing.

Dear Sphere-keeper Steve,

Do not give up on us. You know that I have been playing with the Kissing Number problem in multiple dimensions. Spheres are relevant, but it may not be as simple as you would like it to be. Control your vanity - your ideas are not popular until the scientific culture tells you so. Do you expect the Paparazzi to show up at your doorstep tomorrow morning?

Have Fun!

Ray Munroe

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Lawrence B. Crowell wrote on Jul. 21, 2009 @ 15:09 GMT
The kissing numbers for sphere packing in various dimensions I list below. I hope the tabs show up when sent in this editor, lest it becomes a jumble of numbers. If we consider this according to FCC cells the number is 1/2 these values and reflects the structure of the spherical coding group. The special dimensions are 1, 2, 3, 4, 8, and 24, where particularly elegant structures emerge. What I did not list is the center density of the sphere packing, which are 1, 1/2, 1/(2sqrt{3}), 1/(4sqrt{2}), 1/16, 1 for the special dimensions. The E_8 defines a Grosset polytope that tessellates an 8 dimensional space, where by duality conditions there are self-dual 4-chains which have H_4 tesselations --- the 120 and 600 cells

Dimension Lower bound Upper bound

1 2

2 6

3 12

4 24

5 40 44

6 72 78

7 126 134

8 240

9 306 364

10 500 554

11 582 870

12 840 1,357

13 1,130 2,069

14 1,582 3,183

15 2,564 4,866

16 4,320 7,355

17 5,346 11,072

18 7,398 16,572

19 10,688 24,812

20 17,400 36,764

21 27,720 54,584

22 49,896 82,340

23 93,150 124,416

24 196,560

This is a crystallographic structure described by the packing of spheres, similar to crystalline solids. Yet beyond that what becomes important is less the sphericity of the vertices, but the algebraic structure of the polytopes involved.

Lawrence B. Crowell

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Jason Wolfe/wulphstein@gmail.com wrote on Jul. 21, 2009 @ 16:11 GMT
Lawrence,

From what I remember of solid state physics, the repeating rows, columns and planes of packed spheres gave rise to Fourier series mathematics, which generated all of the really interesting behavior. But I attributed that to quantum mechanics. If the same general approach is to work for tesselated AdS space, where repetition gives rise to a Fourier Series/Transform (or its hyperdimensional equivalent) then the underlying assumption is that quantum mechanics is an absolute unto even the tesselations of AdS space-time. In other words, it suggests that QM is fundamental in physics.

I believe that there are classifications of tachyons, entire groups with different fundamental properties. Because these particles cannot be represented by a mass with a positive, real number, they are largely blocked from existing in the physical (measureable) universe. I am confident that time travel is impossible/restricted. However, getting around the speed of light limitation by abandoning positive real mass (becoming tachyonic) allows one to slip out of the space-time continuum and move unhindered by "the Laws of Physics". I predict that the US military is going to catch wind of this and want experts in the field. The 1984 movie, The Philadelphia Experiment, was about this very topic. But I don't think the government really knows how to do it; but they wish they did.

Have any of you heard of Doubly Special Relativity? A friend of mine send me an video to watch (haven't yet). It suggests that the speed of light is dependent upon wavelength - which might give us a way to probe down to the planck length. I'll pass on the warning: this video is anti-string theory.

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Ray Munroe wrote on Jul. 21, 2009 @ 16:24 GMT
Dear Lawrence,

You have obviously been thinking some of the same multidimensional geometries that I have. I have been playing with simplices (ultimately the FCC close-packing lattice is just a tetrahedral 3-simplex crystal) moreso than the special dimensions. The progression of the center density of the sphere packing for n-simplices follows the inverse square root of the progression of Special Orthogonal orders: (1,3,6,10,15,...).

What do you think of this site http://www.research.att.com/~njas/lattices/kiss.html ? This table of Kissing Numbers is different from yours. Is their table incomplete?

We don't have to expose all of our ideas on the internet. You may contact me directly.

Sincerely,

Ray Munroe

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Ray Munroe wrote on Jul. 21, 2009 @ 16:38 GMT
Dear Jason,

You mentioned the Fourier Series in Solid State Physics. The Fourier transformation allows us to transform from the Direct Lattice (Spatial information) into the Reciprocal Lattice (Momentum information).

In my theory, the Fourier transform allows us to transform from the Direct Lattice (Fermion information) into the Reciprocal Lattice (Boson information).

The comparisons seem very similar to me.

Have Fun!

Ray Munroe

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Lawrence B. Crowell wrote on Jul. 21, 2009 @ 19:11 GMT
The numbers have changed a bit over time. It is interesting that a hard number exists for n = 16, the Barnes-Wall lattice. My numbers are close to those in Conway and Sloane's "Sphere Packings, Lattices and Groups." This subject is an ongoing domain of mathematics research.

It is worth noting that the icosian as a quiver of quaternions has at each vertex a group G, which in the E_8xH_4 theory is an entire E_8. The 120-cell, called the hyperdodecahedron or dodecachoron, which is a polychora with 120 octahedron boundaries, 720 pentagons, 1200 edgelinks and 600 vertices, and Schlafli index {5, 3, 3}. The dual is the 600 cell with 120 vertices (dual to the dodecahedra in the 600 cell) which carry in information of the dodecahedra of the 120. The Schlafli index index for the 600 cell is {3, 3, 5}. So assign to each vertex a quaternionic valued group E_8, the quaterionic octonions. The edgelinks between them are chiral fields that transform according to maps between the two vertices they connect, of which there are 720. This is a pentagonal associator between these quivers by I_3(5). Now think of these two lattices as linked by light rays. These two exist in an extended 5 dimensional space, and the extra dimension is a time direction, in fact the second time direction the AdS spacetime exist within. So each vertex in the 120-cell emits a pulse of light and where these light pulses merge defines a second lattice, which is the 600-cell. As with Fourier transform optics the 120 and 600 cell lattices are Fourier transforms of each other.

I doubt that tachyons are going to be a practical aspect of physics. The problem is that any attempt to construct some coherent over complete set of tachyonic states will result in self-iinteractions of the field which destroys the negative M^2 of the field.

As for the Philadelphia experiment, there is a lot of funny stuff going on. I think snopes,com is in order. What I know about it is it was an experiment to use microwaves to destructively interfere enemy radar waves in order to avoid detection. That is pretty basis electrical engineering stuff. I think claims that during WWII there was some attempt to teleport objects or ships around are a bit exaggerated.

Yes, I am aware of double relativity. The theory written by Smolin & Magueirjo hep-th/0112090 is clever in a way. However, their result only makes sense if it is about the renormalization of the Planck scale. The speed of light is just an intertwiner between spatial coordinate and temporal coordinates. It really is just a conversion factor. Smolin is a loop variable guy, and is pretty anti-string theory. To be honest I think loop variables might operate as constraints in string theory

Most of what I have written here is pretty generic really, but I should take this off the FQXI blog here.

Lawrence B. Crowell

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Lawrence B. Crowell wrote on Jul. 21, 2009 @ 19:57 GMT
There is an intersting FQXI article "The Black Hole and the Babel Fish

Uniting string theory and condensed matter—with a black hole as a universal translator." by Kate Becker which connects up with this.

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Ray Munroe wrote on Jul. 21, 2009 @ 20:25 GMT
Dear Lawrence,

I am familiar with most of your mathematics and expressions, but what is a "quiver of quaternions"? It sounds cool, but is it supposed to mean 8 quaternions?

It may be decades before we can separate out the experimental distinctions between String Theory, Loop Quantum Gravity, and Causal Dynamical Tringulation, etc...

I am building a model out of reasonable assumptions, and think (?) that it might be compatible with any other reasonable theory. For instance, I mentioned that I am using simplices, and simplices fit naturally with CDT. However, I refuse to exclude the posibility that a properly confined String Theory may also look like CDT on the local scale.

You may contact me directly at mm_buyer@comcast.net. I'm "Ray B. Munroe, Jr." but if you research me on HEP Spires you need to drop the "Jr.". I'm a maverick physicist and I'm not associated with a University (I gave up teaching 10 years ago to go into the family business), but I'm not crazy. Unfortunately, I won't really have anything new until I'm finished rewriting this paper.

Sincerely,

Ray Munroe

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Jason Wolfe/wulphstein@gmail.com wrote on Jul. 21, 2009 @ 21:33 GMT
Ray,

Am I understanding this correctly when I say that Fourier Series/Transforms work because they are elaborate manifestations of the Heisenberg Uncertainty Principle? F.SeriesF.Transform reflect delta x delta p > h-bar.

I'm trying to figure out if (1) QM is most fundamental and (2) h-bar is the same value, 6.6x10-34 J-s in all space-times.

BTW, my gmail account is working.

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Lawrence B. Crowell wrote on Jul. 21, 2009 @ 23:05 GMT
A quiver is similar to the term in archery, it is a holder of a set of vector, which are in this case contained in some Lie group. For E_8xH_4, the H_4 is a discrete system and each of the 120 vertices (in the 600-cell rep) holds an E_8.

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Ray Munroe wrote on Jul. 22, 2009 @ 00:16 GMT
Dear Jason,

Given a lattice with regular spacing, there is a natural QM wave solution

$e^{ikx}$

from de Broglie's basic wave mechanics postulate (no need for Heisenberg's Uncertainty Principle, but Planck's constant often arises in QM problems). With a Fourier Transform, we integrate (sum) over all possible standing waves.

Dear Sphere-keeper Steve,

It is ironic that spherical packing can lead to a regular lattice (such as Face-Centered Cubic close-packing), that in turn has wave (string) solutions. We come full circle back to particle-wave (sphere-string) duality. By the way, Louis de Broglie was a Frenchman (I know you are Belgian, not French) who came up with a very simple and fundamental idea that won the Nobel Prize very quickly.

I am sorry if I was too hard on you earlier. I am sorry if I have too little faith. I published my book a year and a half ago. About a year ago, I thought I was on the edge of breaking into mainstream physics. It never happened...

Have Fun!

Ray Munroe

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Jason Wolfe/wulphstein@gmail.com wrote on Jul. 22, 2009 @ 07:04 GMT
Ray,

All of these E8xE8 (and variants) are a little over my head. But they give us some very useful Solid State properties. Correct me if I'm wrong, but doesn't E8xE8 represent the tesselation of a sixteen dimensional space with two sets of 8 dimensional spheres where one set of spheres is placed within the interstitial space of the other? In any event, this should give you all sorts of valence and conduction bands. I think you might be right when you said that superstrings will see these energy gaps as d-branes. It really wouldn't surprise me to see string theory bridge the gap (energy gap) between the conduction/valence bands of a tesselated crystal, and particle physics. Wouldn't we expect General Relativity to be related to how the energy gaps spread out in space? When huge quantities of mass/energy accumulate at one location (a black hole), then shouldn't we expect all of that mass to deform the conduction band/energy gap resulting in a curvature of space-time? Also, would the particles of one conduction band be considered tachyonic with respect to other conduction bands where those particles wouldn't be stable? I would be surprised if we couldn't figure out a way to couple forces between two different conduction bands (different space-times). I'm also hoping there is a way to keep a tachyon or some kind of foreign particles stable within our space-time (conduction band) by locally altering the energy gap of our space-time; for example, keeping charmed and strange quarks stable inside of a special chamber at the LHC, by using exotic materials to change the some of the constants (c, G, cosmological constant) inside of the chamber.

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Steve Dufourny wrote on Jul. 22, 2009 @ 08:38 GMT
Dear Ray

You beleive what of me....attention the team of E8 and strings

Don't touch dear friends ,They can be furious .

Ray I see what when a people has an idea you are the fisrt to contact him ,first the theory of nothing after Tegmark ,after barbour after me after Lawrence and after what God

Let's be serious some people are incompetents and some are competents ,the non competents rest with not competent and others with others .It's like that

The whole dear Ray

You know Ray ,it's not me who search the notoriety ,but you and after the E 52 AND THE hiddens variables .and others members

Personnally the notoriety begins for me because I work seriously .

Really it's incredible ,don't understand it's not my primary language .

I suspect what the paparazzis are at the conference ahahaha I am laughing

I read here always the same and really nothing interesting .A lost of times.

Some people think they use complexity and in fact it's a little part of the problem ,and so simple always the same is said .Ahhhahaha

Ray the whole math physic chemistry biology ecology philosophy .....

It's sad to see this busines and stupidity in sciences .

But fortunally it exists real sientists who works to find the truth .

The LHC a&hahah don't use the imaginaries and don't use these ideas ,FERMILAB,ilc ,......thus it's time to change .

toc toc toc sorry the paparazzis are here ,hello how are you ah it's cool I waited .and now the business but there is a problem I dislike that the monney and I fuck the monney You understand Ray .

Friendly

Steve

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Steve Dufourny wrote on Jul. 22, 2009 @ 08:57 GMT
You want details of my theory ,no problemo .

Until soon .And with real tools .

The" kissing number ,Have you forgot my Fractals of spheres correlated with cosmological numbers with rotations ,volumes and mass ...your Kissing spheres (Lawrence and you)are a past and so far of the truth because your spheres are the same and the lattices too and moreover the time evolution and the contraction is not there thus still a big joke ,a lost of time .

Have fun

Steve

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Steve Dufourny wrote on Jul. 22, 2009 @ 09:00 GMT
The difference is what I don't need of a platform to be respected .

and don't use this facility of wriing in English ,or please learn french and you shall understand better of me .

Thanks

Steve

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Steve Dufourny wrote on Jul. 22, 2009 @ 11:24 GMT
The harmonic analyze of Fourier series are relevant indeed for differential equations ,Ray ,it's foundamental ,it's a interesting theory of vibrations if I can say

Sn(x)= a0 + a1 cos wx + a2 cos 2wx.......+ an cos nwx.....+b1 sin wx + b2 sin 2wx ..............+ bn sin nwx .

where w=2 pi/T and we can change the coefficients Of Fourier and insert the integrality ,derivation ,inegration ....

The properties of Fourier permit a approached distribution F(x) with trigonometric add with a quadratic error .

For all fonctions limitedand continue in o < x < T .THUS A CONVERGENCE and the egality of Parseval .

Furthermore if F(x) is in the Dirichlet conditions ,we can extrapolate CORRECTLY .and if it's periodic thus is continue and the derivations too .

The symetry always .

If we continue we can insert the Bessel Formules indeed .

What is iteresting is Sn(x)=a0/2=a1 cos 2pi x/T =a2 cos 2 2pi x/T .....+an/2 cos n 2pi x/T + b1 sin 2pi x/T = b2 cos 2 2pi x/T......+b n-1 sin (n-1) 2 pi x/T .We can thus solve the problem of Trigonometric interpolation .

If we insert the Krylov method or the Lopchitz method .

I invite tou to use it .

1....1-0.134....0.5....Som 1 som 2 diffe 1-2 with of course the cos terms and sin terms .Synthesis ........

You use badly your series because many parameters are forgotten .Regular series ,incredible and the time evolution and the link quantum cosmolo ...and that and that .

I invite you to insert the Legendre equations ,maclaurin and Taylor series too and the series of expon.

We can too comparate the curves with a method X= x ,y =x/a+bx,Y=x/y ,X=1/x and Y +1/y.

Interpolations ,extrapolations ,empirical equations .

The problem is always the same in fact ,imaginaies or reals ,it's the same with all chaos or harmony ,business or universality ,humility or vanity ,equilibrium or.....

Steve

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Steve Dufourny wrote on Jul. 22, 2009 @ 11:28 GMT
Yes indeed you touched me .

Sorry too I wrote too a little too hard sorry

You are still my friend ?

Steve

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Steve Dufourny wrote on Jul. 22, 2009 @ 11:40 GMT
I am going to say one thing ,dear Ray

I am here because I find you are an rare intelligence ,I like discuss with big mind like you and Paul .

I am here to discover inetresting poeple and not for the pub ,I know my discovery and many friends say me ,Steve you are going to have many grants ,but you know all the monney will be for the sciences senter and my friends ,I dislike really monney ,it's the most incredible stupid invention of the humanity ,it implies chaos simply .

You know Ray ,I am isolated and I win 650 euros /months at this time due to my psychiatric problems before ,I amm always at home with my guitare ,XING and books .I refuse so many opportunities ,and it's normal my economic situation ,my qi is a problem ,my emotional quotient is a big problem too ,that's why I rest isolted and it's well like that for my health .

I have difficulties to adapt me on the system ,I had created an enterprize when I was 23 years old but some people didn't help me and hop chaos .

It was an horticultural enterprize .You know Ray I learn very quickly ,and I don't finish my universities ,In fact I create many projects and many systems on the net but my situatio is always the same ,at home with my mother who is not very well and my 650 euros .You imagine the difficulty to live correctly in a pure system of consumation .

Take care Ray ,sorry still and thanks .

Steve

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Ray Munroe wrote on Jul. 22, 2009 @ 13:46 GMT
Dear Steve,

I sent you an apology e-mail. I did not intend to offend you. Are we still friends?

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Steve Dufourny wrote on Jul. 22, 2009 @ 15:26 GMT
Dear Ray ,

Yes of course ,thanks it's nice .

I apologise too ,I am too arrogant .I am not offended ,

I was a little sad what you beleived that of me .

It's so important for me this humanitarian project .

My fight is all my life ,my spherization Theory and its applications too ,but help people is my reason of living .

I am moderator of Africa Unite on Xing ,and the Transqure Project too ,where we put systems on synergies for optimum results on ground .

Do you know Deborah Boyd dear Ray ,and the prosperity coalition .

Dr Naima Benali and Transqure ,Kleber Biboum and Xspace Africa ,Cadir ONG and Prosper Annyen Bosaw in RDC .And many others friends ,consultants ,NGO...

We are in contact too with the african commission .

In fact we create some spheres and the International Humanistic Sciences Center will be the central sphere of adapted productions for our fellow man ,our priorities are Darfour,RDC Sierra Leone,Madagascar and others .We must produce foods ,improve water ,improve numeric ,Schools ,hospitals ,.....it's there it's interesting when the synergies of complementarity are a reality between systems .I try to centralize ONG ,intersting systems ,activists ....

You know Ray ,the skills are important in sciences and it's an aim of the sciences center ,centralize interesting people .It exists so many intresting people .In fact we are all complementary ,all unics .Anybody is better than his fellow man .It's important to say that .

On the other side ,it exists some bad people due to a bad education ,thus it's simple for me I take some distances .

In all case ,Your facility of playing with equations is very intersting ,I don't like imaginaries in reality ,attention I like the idea for some applications but I don't use it in my model ,the limits are important in my model .

In all case you are welcome when the center will be created in a humanitarion optic of course .

If some people want to help us ,they are welcome ,the united for a better world for the forgotten .

You know Ray ,I have many inventions in ecology ,in vegetal multiplication ,I have interesting results .For exemple for the hunger problem ,the aim is to produce mini plants in alveols ,0.8 cm X 0.8cm X 1 cm it's my last results ,the mix for the substrat is optimum or near .I test always with compost ,argil,matters mix ....and produce fruits ,vegetables...too and after a strategy of diffusion .It's there that the complementarity of NGO is important .

Regards

Steve

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Lawrence B. Crowell wrote on Jul. 22, 2009 @ 17:39 GMT
As Ray points out a lattice of ions in a solid induces a periodic wave on the ions and phonons with a fundamental k vector with magnitude 1/L, L = lattice spacing.

E_8 has a system of roots which in eight dimensions defines the Gosset polytope. Polytopes are categorized by the Schlafli number. A polyhdronn is {p, q} if it has p-gons for faces and each vertex is surrounded by q faces. Hence the tetrahedron is {3, 3} and a cube is {4, 3}. A three symbol for four dimensional polytope (polychoron) is {p, q, r} if it has p polygonal faces, {p, r} 3-cells, {q, r} polyhedral vertices and r polygonal edges. The 24-cell is {3,4,3}, where the {3,4} is the octrahdra, in tetrahedral cells {3, 3} (three cells around each edgelink) and the vertex figure is a cube {4, 3}. The 120-cell has {5,3,3}, composed of dodecahedra {5,3} with three around each edgelink.

This symbol for complex polytopes is written according to the edgelinks in the Dynkin diagram for the corresponding group. For this reason the E_8 has the symbol {3^{4,2,1}}. The Gosset polytope can construct a honeycomb. The E_8 Dynkin diagram

*--*--#--*--*--*--*

where # stands for a vertical *--*. This diagram is extended by an additional element *, denoted by an encircled dot, on the right. The Schlafli symbol is {3^{5,2,1}}. This is a tessellation of R^8 by a discrete set {x_i ε Z^8U (Z + 1/2)^8, Σ_ix_i = 0 modulo 2}. This discrete set has a basis which is given by the Cartan matrix, who's entries define vectors to this points.

Lawrence B. Crowell

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Lawrence B. Crowell wrote on Jul. 22, 2009 @ 17:49 GMT
It sounds as if we are all having a bit of a rough go here. My situation is that I went into industry and I am now holding on to my situation with white knuckles. I will say that I am also increasingly dismayed by some developments in our modern age --- primarily things are just becoming butt ugly. Yet, I keep on going on. That's all one can expect.

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Steve Dufourny wrote on Jul. 22, 2009 @ 18:05 GMT
Sorry to all for my arrogance ,I say sometimes stupid things ,it's like that ,I am the first who is vanitous hihih

Lawrence ,it's there interesting what you say about the gosset polytope ,there it's interesting ,I am arrogant but It's not for nothing lol .

Let's continue dear friends ,let's create with imaginaries or reals ,aftyer all ,all is free .

Take care all

Steve

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Ray Munroe wrote on Jul. 22, 2009 @ 18:41 GMT
Dear Lawrence,

In this morning's e-mail, I gave you a Dynkin symbol for "E12". Does it make sense?

Keep holding on with those white knuckles... I quit teaching physics full-time 10 years ago to go into the family business. I continued to teach astronomy part-time (because I enjoyed it) up until 2003 at the local community college. Three years ago, I was selected to be the CEO-in-waiting. The current CEO won't retire and leave me in complete charge, but that's OK too because it gives me some time to play with my physics (whereas being the CEO would probably consume all of my time for a while). This difficult economy has hit us (Florida is one of the states in which it started), but we will survive...

Dear Steve,

It would be a wonderful world if we all used our talents and spare time to help those less fortunate. Your talent is growing plants. My talent is playing around with imaginary numbers and dimensions that others don't (or don't want to) understand. I applaud your talent and your efforts to build your Center and feed Africa. I hope that someday I can visit you at the Center or on a mission trip to Africa.

Ray Munroe

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Lawrence B. Crowell wrote on Jul. 22, 2009 @ 22:45 GMT
I am thinking about the dynkin number you gave for what you define as E12. I have not had time to digest this as yet. Unfortunately I have to think and work on this inbetween work and other things. I will try to get back to you this evening on it.

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songjoong sdfsd df wrote on Dec. 27, 2017 @ 07:05 GMT