Hi Ed,
I think the magnetic monopole makes Electric and Magnetic fields S-dual, but I haven't studied these ideas in a while. The Gingras Spin Ice article involving magnetic monopole quasiparticles is attached.
Have Fun!
Dr. Cosmic RayAttachment #1: 1_Gingras_Spin_Ice.pdf
And a couple of interesting points about the Gingras Spin Ice paper attached to the prior post:
1) He uses tetrahedra - which are the basis of the Face-centered cubic (FCC) close-packing lattice that I used in my essay, and
2) He also refers to the "reciprocal space" of the real-space lattice in the crystals as I did in my essay.
Have Fun!
Dr. Cosmic Ray
Magnetic monopoles are similar of S-duality. S duality exchanges IIB and I strings where the fields on them are dual. A type of magnetic monopole of this form would be a case of S duality. So if there is a U(1) field on a IIB with an electric charge a magnetic monopole on a type I string would be S dual.
Cheers LC
Dear Ray,
Having already read the ice paper a while ago, I would nonetheless like to support Edwin concerning magnetic monopoles. I should feel a bit like David in front of several Goliaths like you.
I share a lot of your arguments, and I admire your elegant representation. However, I am not sure whether "the interrelationship between Scales and SUSY may provide a mathematical umbrella capable of explaining the unnaturalness of "Infinity"" a "unification of Bosons and Fermions". Do we need an explanation for the unnaturalness of a point? Where may I find an explanation of how you understand the notion Scale? Perhaps did you mean a common theory and not a physical merger between Bosons and Fermions.
Maybe, you will agree in that cosine transform switches a discrete function into a continuous one and vice versa. Engineers like me are convinced that in reality there are neither ideal continuous nor ideal discrete signals.
If A and B do not agree it is certainly opportune to have a balanced opinion: all are half correct. However logic also allows an answer in Gotthold Ephraim Lessing's style too: Maybe both A and B are wrong.
If I am correct in my essay then some mathematical generalizations are at least questionable. I invite you to take issue.
Regards,
Eckard
Dear Eckard,
You said "Do we need an explanation for the unnaturalness of a point?"
I think that a point is physically unnatural, but OK as a model. A physical infinity cannot exist within a finite Observable Universe (13.7 billion light years is finite). Thus, I disagree with the idea of a Black Hole "singularity", and expect the Black Hole core to be similar to a Buckyball of Spacetime (the "Spacetime lattice" equivalent of a Carbon-60 Buckyball) as Lawrence Crowell and I presented in a recent article.
You also said " Where may I find an explanation of how you understand the notion Scale?"
I didn't really define scales thoroughly - Laurent Nottale has done that over the last two decades, and he has a book coming out this year (I've read part of it, but - as I recall - it is 600 pages long). Nottale defines scales in terms of complexity and energy content. By Scales, I mean that some numbers are large, some are small, and some are inverses. Consider the differences of conjugate (essentially inverse) scales of position and momentum (or energy and time as Lawrence Crowell developed in his paper).
You also said "Perhaps did you mean a common theory and not a physical merger between Bosons and Fermions."
IMHO, a TOE must include both Bosons and Fermions, and both Spacetime and Hyperspace, but all of these concepts might not fall into the same Lie algebra (unless it is something like SO(32)~E8xE8?) because bosons and fermions need to be inverse/reciprocal/conjugate-like variables with respect to each other.
You also said "Maybe, you will agree in that cosine transform switches a discrete function into a continuous one and vice versa."
Equation 4 in my essay is the general form of a cosine transform (using e^(ix) = cos(x) i sin(x)) in multiple dimensions, and Equation 2 is distantly related (the matrix inversion is related to a Fourier transform) to these transforms.
You also said "Engineers like me are convinced that in reality there are neither ideal continuous nor ideal discrete signals."
I agree. That was the first sentence of my Abstract, and the last sentence of my Conclusion. It all goes back to Wave-Particle Duality.
Have Fun!
Dr. Cosmic Ray
Hi, Dr. Ray:
It is my position that reality has both the continuous and the discrete.
The big questions are basically what fundamentals get quantized and how these fundamentals get quantized. I think my essay points to the answers.
Because we obviously have hierarchical discrete/quantized phenomena, it is plausible that overall the cause is also a hierarchical process. Perhaps this is why you have your scales.
You might also consider a full-tensor (3-D) factor in the relativistic mass equation, instead of just the Lorentz half-tensor (2-D) factor -- after all mc2 (final E) is not m0c2 (initial E0).
Castel
Dear Raphael,
Please call me Ray.
You said "It is my position that reality has both the continuous and the discrete."
I whole-heartedly agree! And this conclusion is due to Wave-Particle Duality.
You said "The big questions are basically what fundamentals get quantized and how these fundamentals get quantized. I think my essay points to the answers."
I propose that the sub-quantum (Dirac sea) scale behaves like a close-packing lattice, and the near-lattice and discrete properties of my essay's Table 1 (and Lisi's E8 Gosset lattice TOE) are caused by this close-packing property.
You said "Because we obviously have hierarchical discrete/quantized phenomena, it is plausible that overall the cause is also a hierarchical process. Perhaps this is why you have your scales."
Yes - there is a hierarchy. Why are both the Weak and TOE energy scales stable when radiative corrections should drive the Weak scale up to the TOE scale? This hierarchy implies the importance of SUSY and Scales.
You said "You might also consider a full-tensor (3-D) factor in the relativistic mass equation, instead of just the Lorentz half-tensor (2-D) factor -- after all mc2 (final E) is not m0c2 (initial E0)."
In the absence of fields, we can decompose the general 3-D Lorentz transform into an equivalent 2-D transform with components that are parallel and perpendicular to the motion.
My E=mc^2, etc. equation on page 1 is the same as your E=mc^2, etc. equation at the bottom of page 5 of your essay, but you further break the equation down into the low-energy classical approximation. I didn't because that approximation wasn't necessaary for my argument.
I quickly skimmed your essay, but need to reread it more carefully before I'm in a position to comment on it.
Have Fun!
Dr. Cosmic Ray
Dear Ray,
Thank you for confirming that we agree in almost all questions. However, I am not sure. How may I interpret your refusal to rebut my main argument? I found overwhelming indications for a suspicion of mine: Ideal symmetries tend to be artifacts. You are quite right the matrix inversion is related to a Fourier transform. The question is, does our possibility to describe nature allow and possibly even require matrices that do not exhibit Hermitian symmetry?
If it is possible, reasonable, and as I am arguing natural to restrict scales to merely positive values by appropriately shifting them, then only half-matrices are required. Please feel challenged to object here. Edward Klingman so far confessed being unable to object. I pointed to consequences.
Regards,
Eckard
Dear Ray,
I was actually impressed by your view's bit of focus on the wave-particle duality. Basically, my bit of focus is on the fundamental idea of motion.
The electromagnetic theory describes transverse wave motion. So, to me, light, the phenomena in nature, is of the fundamental essence of motion - and the electric and magnetic are of the same fundamental essence.
My idea regarding particles is that the waves/motions get wrapped or folded into the particulate essence - perhaps in somewhat the same manner as that of the loops of space of Astekhar, Smolin and Rovelli, only that I see loops of motion instead of space.
I have been thinking about the idea of a hierarchical cosmos wherein the cosmic subsystems have alternating periods of densification and attenuation that establish the upper and lower limits for the quantization of the particulate cosmos. My idea is that gravity gathers and densifies the cosmic subsystems, and eventually, with their increased mass-energy, each cosmic subsystem is taken by its own increased orbital momenta towards an orbital apex that initiates a period of attenuation with the cosmic subsystem getting fragmented. This renders a picture of an expanding and spiralling cosmos but with cosmic mass-density accordingly maintained and the particles multiplied.
The above is a difficult picture. But, is this possible in your view?
It would be a beauty if you can describe a picture of how your scales look like - especially if you go 'vectorial' just a little bit in your explanations.
(What I've described above is still a rather simplistic picture. What I really envision is a process that involves relative motions from all directions for each cosmic subsystem in the hierarchical cosmos. This suggests to me the reason for the occurrence of gravity and why the observable phenomena are 'waves' of radiant motion or 'particles' of concentric motion wrapped around their centers. This is somewhat like the cyclical chicken-or-egg reasoning; and I am therefore a bit abashed to present the idea in full.)
Anyway, I just wanted to express my opinion - hoping that I might get some positive ideas from you.
In any case, many thanks to you.
Rafael
Dear Eckard,
I like Hermitian matrices, but I don't limit myself exclusively to Hermitian matrices in my search for a TOE. I'm still searching and don't have an answer...
Hopefully I can read your essay next week. I enjoy your applications and insights.
Have Fun!
Dr. Cosmic Ray
Dear Rafael,
I was hesitant to present all of the details of my ideas, because some are a bit maverick, and probably too detailed for this type of essay. I competed in the second FQXi essay contest, was in the top five after the public and community votes, but didn't finish in the top 18 - I attributed this to the fact that that essay was very mathematical.
In my "The Interrelationship of Spin and Scales" paper, I suggested that the Multiverse (or super-Cosmic) scale is the largest scale from which we can feel effects. If a larger scale exists, we may never know. The Multiverse scale is related to the Graviton (and the origin of gravity), and is a continuous (boson-like) space. Complexity of this scale may be infinite, although this also implies an infinite Multiverse.
Below the Multiverse scale is a Cosmic Scale. This Cosmic Scale is related to the Gravitino, and is a discrete(?) (fermion-like) space. This discrete structure may exhibit itself as cosmic strings and their effects. Perhaps the discrete Holographic Principle occurs at this scale. The mass distribution of our Universe is not isotropic and homogeneous, but is coursely grained. Complexity of this scale may be based on the number of possible string vacua of ~10^500.
You said "I have been thinking about the idea of a hierarchical cosmos wherein the cosmic subsystems have alternating periods of densification and attenuation that establish the upper and lower limits for the quantization of the particulate cosmos. My idea is that gravity gathers and densifies the cosmic subsystems, and eventually, with their increased mass-energy, each cosmic subsystem is taken by its own increased orbital momenta towards an orbital apex that initiates a period of attenuation with the cosmic subsystem getting fragmented. This renders a picture of an expanding and spiralling cosmos but with cosmic mass-density accordingly maintained and the particles multiplied."
I think that our ideas are complementary, and perhaps even identical.
Below the Cosmic Scale is the very familiar Classical Scale. The Classical Scale is related to Vector Bosons, and is a continuous (boson-like) space. Complexity of this scale is based on Dirac's Large Number of ~10^41.
Below the Classical Scale is the Quantum Scale. The Quantum Scale is related to normal matter Fermions, and is a discrete (fermion-like) space. Complexity of this scale may be of order 496 ~ SO(32) ~ E8xE8*.
Below the Quantum Scale is the sub-Quantum or Dirac Sea Scale. This Dirac Sea Scale is related to Scalar Bosons, the so-called Higgs Mechanism and the origin of mass, and is a continuous (boson-like) space. Complexity of this scale may be of order 32.
You said "My idea regarding particles is that the waves/motions get wrapped or folded into the particulate essence - perhaps in somewhat the same manner as that of the loops of space of Astekhar, Smolin and Rovelli, only that I see loops of motion instead of space."
Of course position and momentum space are reciprocal lattices, and conjugate variables. We may have quantization of position such as Kissing Spheres or Causal Dyanamical Triangulation that provides lattices and their reciprocal scaled lattices (that appear continuous because of the large number of states). OR we may have quantization of momentum such as String Loops or String Winding modes that provides lattices and their reciprocal scaled lattices (that appear continuous because of the large number of states).
I agree that it is a Chicken-Egg type of question, that both continuous waves and discrete particles are fundamental, and the existance of either probably necessitates the existance of the other.
Along the lines of this wave-particle duality, I think that fields require mediating bosons and vice versa. The Electric Field required the Photon with fine-structure constant of 1/137, whereas the magnetic field requires the magnetic monopole with coupling of 137/4 (with an apparant S-Duality). My Quantum Statistical Grand Unified Theory does not predict a force of strength 137/4, nor have we observed the magnetic monopole. Thus the question should be 1) Does the magnetic monopole exist at a scale we haven't yet observed? or 2) Did the magnetic monopole degrees-of-freedom get absorbed into another physical effect (such as my interpretation of Edwin Klingman's ideas whereby the gravitational magnetic monopole degrees of freedom may explain the CKM and/or PMNS matrices).
I know that my ideas are maverick, but I also think that we are a long way from a TOE without some radical thinking.
Have Fun!
Dr. Cosmic Ray
Thus far, from you posts, I see the following:
- the Super-Cosmic scale (Multiverse scale), with the [Vector] Gravitons, and this scale is associated with a Graviton space or field (continuous)
- the Cosmic scale (Universe scale), with the [Vector] Gravitinos, a Gravitino space (discrete)
- the Classical scale, with the Vector Bosons, a Vector Boson space (continuous)
- the Quantum scale, with the matter Fermions, a Fermion space (discrete)
- the sub-Quantum scale (Dirac scale), with the Scalar Bosons, a Scalar Boson space (continuous)
you indicated "the Higgs Mechanism and the origin of mass" in the Dirac scale
You described scale 'boundaries' - the Cosmic scale (I presume the scale of the observable universe, the Universe scale) and the Multiverse (super-Cosmic) scale. You also say that "the Multiverse...is the largest scale from which we can feel effects." And you mention the implication of "an infinite Multiverse". You say "The mass distribution of our Universe is not isotropic and homogeneous, but is coursely grained." And you also mentioned elsewhere that a black hole singularity (infinitely dense) cannot exist in a finite universe.
By 'finite' I am of course assuming you mean the 'scale', not the 'amount' of the components that meet the measures of the scale... By "coursely grained", I will presume that you mean "coarsely grained" as to discrete texture and not "coursely grained" as to mean grained by coursed flow or routed with direction. (Although this is also a beauty.)
I will not question the categorization of the scales to continuous and discrete. I'll wait until I can have a clearer image of the possible lattices and how they stretch or curve.
According to your suggestion of possible effects of the Multiverse scale on the Cosmic scale, which I assume would mainly be a gravitational condensation effect because of the Graviton space or field, I now ask:
What sort of process would produce such effects? Gravitational-mass-induced mass-energy condensation? Incident gravitational-vacuum-induced radiative expansion? Could it be both? And if both, could it be alternating? simultaneous? Gravitational momentum? Perhaps, something else?
I am thinking of the scales for the range of kinematic densities exemplified by the voids at the vacuum end, by everything in the middle, and by the black holes at the superdense end. I am interested in where you place the supervoids and the superdense in your scales (or what supervoids and what superdense you put in what scales) and what processes govern their states. So, I can't help but ask:
What particular types of constructs are coarse in what scales? How are the voids made vacuous in your scales? How are the black holes made dense in your scales?
You have of course given complexity numbers - but how do the processes look like in terms of incident equilibrium states between condensation and radiation in the appropriate scales?
I am interested in how the processes look like so that I can properly fit them in my idea of motion transformations. I'd like to see the processes within volumetric space. It appears to me that whatever your answers, they could fit in my ideas of "motion constructs" and "motion transformations".
Ray, I've been rather alone regarding my idea of the "transformations of motion"; everyone else seems to be talking "spacetime transformations". My googling and yahooing found hardly anything consoling...
I sincerely would like to learn of your opinions regarding the above - even just the little that you can allow yourself to dislose.
I know I am being a bit devious here, since I am hoping somebody else could work out the mathematical (numbers) and logical (words) answers to my own questions. (hehe!) I carry a lot of question marks for my queries, but few exclamation marks for my own eurekas. I hope you won't mind so much.
Rafael
Dear Rafael,
You started out summarizing some of my prior posts. I would like to clarify a couple of points. You mentioned [vector] gravitons and [vector] gravitinos. Gravitons are spin-2 tensor bosons, and gravitinos are spin 3/2 fermions. If these quantum charges can be represented by "crystalline" lattices, then the "vectors" (reciprocal space) that connect one "gravitino-like" vertex to another "gravitino-like" vertex may represent the tensor gravitons.
You said:
"And you also mentioned elsewhere that a black hole singularity (infinitely dense) cannot exist in a finite universe. By 'finite' I am of course assuming you mean the 'scale', not the 'amount' of the components that meet the measures of the scale..."
I am proposing that the largest physical number that can exist in our Observable Universe is Dirac's Large Number of 10^41 and geometrical powers thereof, which is "close" to infinity without actually being infinity.
Then you asked the following:
"What sort of process would produce such effects? Gravitational-mass-induced mass-energy condensation? Incident gravitational-vacuum-induced radiative expansion? Could it be both? And if both, could it be alternating? simultaneous? Gravitational momentum? Perhaps, something else?"
In my book, and in the "Interelationship of Spin and Scales" paper, I proposed an SU(5) of "Hyper-SUSY" that could potentially explain these spins and hierarchies. I think that your quantized momentum approach is a more "common sense" approach to String Theory - particularly closed loops and winding modes.
I also like Lawrence Crowell's and Philip Gibbs' approaches involving quantum entangled strings.
You also asked:
"I am thinking of the scales for the range of kinematic densities exemplified by the voids at the vacuum end, by everything in the middle, and by the black holes at the superdense end. I am interested in where you place the supervoids and the superdense in your scales (or what supervoids and what superdense you put in what scales) and what processes govern their states. So, I can't help but ask:
What particular types of constructs are coarse in what scales? How are the voids made vacuous in your scales? How are the black holes made dense in your scales?"
This is the so-called "Cosmic Scale", and I think that these structures and mass-density-variations such as Black Holes and Super Voids could have been caused by Cosmic Strings and turbulent vortices in the early life of our Observable Universe.
You also said:
"You have of course given complexity numbers - but how do the processes look like in terms of incident equilibrium states between condensation and radiation in the appropriate scales?
I am interested in how the processes look like so that I can properly fit them in my idea of motion transformations. I'd like to see the processes within volumetric space. It appears to me that whatever your answers, they could fit in my ideas of "motion constructs" and "motion transformations"."
I think that the upper scale limit is the speed of light, the lower scale limit is the Planck scale, and that Spacetime warps at these scale boundaries to form lattice-like structures. Perhaps the outer boundary of our Observable Universe is a graphene-like lattice as Subir Sacdev proposes, and perhaps the core of the Black Hole is a Buckyball-like lattice. These lattice-like structures cause the Spacetime curvature to collapse such that we cannot see these scales. Simultaineously, these lattice-like structures may be useful in describing the Holographic Principle - whereby quantum gravity at the Multiverse scale is converted into Spacetime curvature at the Cosmic scale (Observable Universe).
You said:
"Ray, I've been rather alone regarding my idea of the "transformations of motion"; everyone else seems to be talking "spacetime transformations". My googling and yahooing found hardly anything consoling...
I sincerely would like to learn of your opinions regarding the above - even just the little that you can allow yourself to dislose.
I know I am being a bit devious here, since I am hoping somebody else could work out the mathematical (numbers) and logical (words) answers to my own questions. (hehe!) I carry a lot of question marks for my queries, but few exclamation marks for my own eurekas. I hope you won't mind so much."
I need to thoroughly read your paper to address all of your questions and concerns. I'm backlogged on papers - I also need to read Jason Wolfe's, Eckard Blumschein's, and Edwin Klingman's (again - like yours, I skimmed his paper) papers as well...
Rafael, I have been blogging on FQXi for nearly 3 years because I feel mostly isolated in my Physics ideas. I left acedemia (full-time in 1999 and part-time in 2003) so that I could manage my family's business. My ideas were pretty radical before I left acedemia, and they seem to have gotten more radical recently. Lawrence Crowell and I have collaborated some. I have made other friends on this blog site as well - some that I agree with, and others that I don't fully agree with. We all want to contribute something, and I don't mind bouncing ideas off of each other to see which ones stick.
Have Fun!
Dr. Cosmic Ray
Ray,
I am taking our discussion to my own FQXi forum link. I think this will inspire me a bit more and make our discussion more interesting. I hope you will grant me the courtesy of following our discussion at my turf. HeHe!
Rafael
I posted this response here and on Rafael Castel's blog site (topic # 835):
Dear Rafael,
You asked:
"Considering the idea of the Multiverse - what do we have in the spaces between the myriad of universes of the multiverse? Do we have quantum Gravitons there?"
I think that the Multiverse is an infinite Cantor set - hollow but not empty - with self-similar scales. The phase transition that caused Inflation could have caused other scales of inflation. The speed of light scale limit limits us to seeing objects within 13.7 billion light years of our location, but what if more exists and we cannot see it because it expanded faster than the speed of light (with a scale of greater complexergy)? I think that quantum gravitions can exist at the Multiverse scale because of its greater complexergy, but cannot exist (abundantly - yes there may be some ridiculusly small fraction like 10^(-123)) at our Classical scale because of our lesser complexergy. The "space" between our Observable Universe and the Multiverse is separated by the speed of light scale limit, and may collapse into an effective "boundary" that provides the Holographic Principle.
You also asked:
"Do we have a Multiverse composed of relatively similar universes? In other words, do we have homogeniety at the level of universes?"
Yes - our Multiverse is comprised of self-similar scales. I'm not sure I would call this homogeneity, but similar patterns would appear at every scale.
You also asked:
"Or would you say there are clusters of universes, clusters of clusters of universes, superclusters of universes, clusters of superclusters of universes, and so on?"
Certainly Super Clusters of Galaxies exist within our Observable Universe. Perhaps "clusters" and "voids" are part of the pattern that we should expect at every scale.
You also asked:
"And finally, at what level do you see any possible decoupling of components according to the scale limits?"
I think we have maximal simplicity at the sub-Quantum scale, and maximal complexity at the super-Cosmic scale. All of these extremes are relevant to a TOE.
You said:
"Ray, I must let you know - I find the articulation of a Multiverse rather superfluous, since I am inclined to believe in an infinite hierarchical cosmos and in spite of the idea of perhaps the 'decoupling' at the very large scale."
Rafael - I agree with Nottale that at least 4 scales must exist. I think that most of us would admit to a Classical and Quantum scale. Additionally, a sub-quantum scale explains the Planck scale limit. And a super-classical scale explains the speed of light limit. I have proposed one more scale to complete the analogy with Particle Physics expectations of fundamental particles with spins of (0, 1/2, 1, 3/2, 2). Regardless of whether we have 4 or 5 scales, we must have at least one scale beyond the speed of light. I prefer to call the largest scale the "Multiverse", but I realize that term carries its own baggage. I don't like the idea of the common "multiverse" whereby these hierarchal numbers are part of a random number generator, but rather prefer the idea of a "Multiverse" whereby complergy content of the various scales necessitates these hierarchal numbers.
I hope I answered your questions thoroughly. We are using slighly different terminolgy and language, but I think that we are on self-similar pages.
Have Fun!
Dr. Cosmic Ray
Ray
Excellent read (between all those numbers!) and I found myself more convinced than I'd expected with your notions.
I've already raised this with Edwin, but have you considered the toroid form of tokamaks as a complete unit scalable both up and down, my current paper identifying them as not only the galactic black hole and quasar configuration, but also as a candidate for recycling the universe in the Big Blazar! How's that for a crazy notion.
The point of it is it has intrinsic spin, and dual axis / helical spin, producing... anyway I'm sure you understand them much better than me.
I feel a good score coming in your diretion. I particularly agree with the equivalent of your conclusion, most current physics is at least half wrong!
I'd be interested in any views on my own paper, if you can think without numbers!?
Best wishes
Peter
Dear Peter,
Thank You!
If you read my 2009 FQXi essay, you would know that I was holding back on those numbers!
The torus is important. The rank of a Lie Algebra is related to the minimum toroidal dimensionality of representation of that group. When I say that E8 is 8-dimensional, I mean that it can be reduced to an 8-D torus. E8 is also cool because it can be represented by the 8-D Gosset lattice.
In my (and Lawrence Crowell's) "The Nature of Dimensions" paper, we proposed that the Black Hole "singularity" may be similar to a Carbon-60 Buckyball lattice (only made out of "discrete spacetime" rather than Carbon). You can convolute two nested buckyballs into a torus - which once again confirms a potential toroidal application.
Besides, I briefly worked on the TEXT Tokamak at U. Texas (Austin), and like toroidal geometry.
I apologize that I haven't been more active in this review process. I was out of town on business last week, and haven't caught up yet. Your paper is on my "to read" list.
Have Fun!
Dr. Cosmic Ray
Hi Peter,
A little more detail to my earlier response:
There is a smooth homotopy between a pair of nested buckyballs and a torus. Please see:
http://mathworld.wolfram.com/TruncatedIcosahedron.html
On Jan. 22, 2011 @ 16:15 GMT , I wrote the following to Steve Dufourny:
"Does the core of a Black Hole approach a singularity (I reason that a phisical infinity cannot exist within a finite observable universe), or does a lattice structure prevent its full and complete collapse? IMHO, the strongest lattice with the most proper symmetries is the Carbon-60 Buckyball (once again, realize that I am talking about a lattice built up from the very fabric of Spacetime). It is true that a sphere has the perfect symmetry, but a sphere is not a lattice - there are no lattice bonds to prevent gravity from crushing and deflating a perfect sphere.
The Buckyball might explain the non-collapse of the Black Hole core, but succesive radial layers of lattices would build one Buckyball inside of another Buckyball (with flipped symmetries). After about a thousand vertices, these layered Buckyballs will begin to resemble another lattice - the very strong Diamond lattice."
Perhaps a static Black Hole does build layers of nested and flipped buckyball lattices into a distorted (distorted at the center) diamond lattice as I suggested earlier. But perhaps spinning Black Holes crush and rotate successive layered pairs of buckyballs into tori, and layers of tori. These layers of tori may behave like spin-2 Gravitons and/or WIMP-Gravitons and/or GEM-Gravitons (or would that be Gravi-Electro-Magnetons?)
Also, I discussed tori on the last page of this attached article:
Ray Munroe, "Symplectic tiling, hypercolour and hyperflavor E12", Chaos, Solitons and Fractals 41 (2009) 2135-2138.
Have Fun!
Dr. Cosmic RayAttachment #1: CHAOS6407.pdf
Ray,
You've probably noted my comment to Lawrence and to others that they should check out Joy Christian's new work here.
It is highly mathematical, but then, so are you. I was surprised upon reflection to realize that I don't really know where you stand on issues of 'non-locality' and 'non-reality'. Anyway, I would love to hear what you have to say about Joy's work. [Some of my earlier remarks said 'she', but Joy is a man.]
I particularly hope that you manage to study this work before drawing any conclusions about my essay. My essay is based on a theory of local realism that goes against the grain of the 50 year old 'non-local', 'non-real' entanglement interpretations that have flowed from so-called 'violations' of Bell's inequality, which, if Christian is correct, were all based on Bell's faulty calculation of 2 instead of the correctly calculated 2*sqrt(2). This is major.
As a consequence of Bell's result, 'local realism' fell into disfavor. On another thread Florin remarked that something "has the smell of local realism", even though I pointed out many current quotes from Phys Rev Lett that clearly stated that these issues had not been proved beyond a doubt [for reasons that may no longer be relevant.] As a further consequence, any theory, such as mine, that *is* based on local realism starts off with three strikes against it. For this reason, I am overjoyed [pardon the pun] that Christian has shown Bell's calculations to be in error, thereby rescuing local realism from near death.
I have placed some further comments summarizing Christian's results on my page, and don't wish to clutter up your page with such.
I look forward to any comments you might have.
Edwin Eugene Klingman
Dear Ed,
Yes - I saw your conversations about Joy Christian's paper. I fell behind last week with my business trip to Orlando, and I've been playing catch-up. I have downloaded JC's 23 page paper and plan to read it.
Where do I stand with Hidden Variables?
Garrett Lisi's E8 TOE *might* imply hidden variables, because all particle properties are (supposed to be - Lisi goofed it a little) a result of their position within the 8-D Gosset lattice "charge space".
To correct Lisi's goof, Lawrence Crowell and I have proposed an SO(32)~E8xE8* TOE that could correctly imply hidden fermionic variables within the direct E8 lattice (that could be a "local" hyperspace), and hidden bosonic variables within the reciprocal E8* lattice (the reciprocal scale to a quantum or sub-quantum hyperspace may be a cosmic or super-cosmic multiverse).
However, this SO(32) model seems too small to include all of the Dimensions or Scales or Holography that I expect. And if Holography occurs at a super-Cosmic Scale, then Gravitation cannot be a local hidden variable unless infinitely fast tachyons redefine the concept of "local".
Do tachyons redefine our concept of locality? I'm pretty sure that my 5-fold "pentality" symmetries (similar to my essay's Appendix Figure) predict tachyons.
Does my answer sound too wishy-washy?
Have Fun!
Dr. Cosmic Ray
