The discrete nature of time might be compared to a numerical ordering. I carry this further to consider a discrete structure in general.

Cheers LC

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  • Post #20

On Dec. 7, 2010 in 782#post_29212 you wrote:"Signatures of this structure lie around us in the universe, such as the images I attach. So fractal geometry is important, and in fact what I outline above is what my essay will entail.

Cheers LC

attachments: cosmic_filaments.JPG, cmb_popup.jpg "

"AdS circlelimit.JPG" is also a nice but naked figure without an explaining legend. I have humbly to admit to be a layman who not even heard of tessellated AdS. Let me try a wild guess: In't there a Tom Essel, and could dS stand for de Sitter? A? Hm, maybe Arahonov? Anyway, a certain part of your readers would certainly appreciate at least a list of abbreviations.

Eckard

The discussion was on fractal structure. I have a bit of a crazy idea on convolving Sloan Digital Sky Survey (SDSS) data with CMB data. After Planck has done its survey I might do this. It will be interesting to see if the Hausdorff dimensions of the two structures are equal or related in some way.

The discrete group structure and cosets defines a Schottky set. The partitions of the manifold, or regions partitioned by Jordan curves, have a self similar structure, or a Moebius group realization, which makes it a Cantor type of set. The Cantor set, or "comb partition" of the interval, is an elementary form of a fractal geometry. Mandelbrot in fact found a self similar form of noise in transmission lines which had a Cantor set structure within any time interval.

If this structure is present in quantum gravity and the quantum wave function of a cosmology, then it should persist through the inflationary epoch and have signatures on the large scale. This discrete fractal structure might be the source for non-Gaussian structures in the CMB.

Cheers LC

Dear Eckard,

AdS stands for anti de Sitter space, and it is very important for the AdS/CFT correspondence. See:

http://en.wikipedia.org/wiki/Anti_de_Sitter_space

So you were close when you said "and could dS stand for de Sitter?".

Have Fun!

Dr. Cosmic Ray

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  • Post #23

Dear Ray,

It happens that even the wildest guess comes close. So I will try and add one more horrible speculation: Abelian and non-abelian? I read that Abel died in a duel when he was a young man, and Christian Felix Klein was at best a baby at that time. Perhaps, Abel's symmetry was a simple one. Non-abelian sounds to a layman like me a bit like non-Euclidean, non-Newtonian, transfinite, ueberabzaehlbar, hyperreal, superluminal, postmodern, and other once excitingly modern notions.

Lawrence Crowell wrote: "Of course supersymmetry remains a hypothetical, though some signatures of it have been detected. We will have to wait for the LHC to yield such results before anything is conclusive." Here I guess: I am too old for that.

Right now my essay has been posted. I found three plausible deviations from very basic current tenets, and I tried my best to explain them as simple as possible. Nonetheless I hope for having selected the most compelling arguments.

Regards,

Eckard

After the LHC starts up at full steam in 2012 data on SUSY should start coming in. I think it likely SUSY will be found by 2015. The Higgs particle is more difficult to separate from the noise and it might take a bit longer. I think that by the end of this decade we will have MSSM data and will be working on more sublte issues of AdS~CFT and so called soft black holes with heavy ion data.

Cheers LC

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  • Post #25

Eckard,

Tesselation is a term from geometry. It approximately means the close packing of infnitely repeated shapes that completely fill the plane. Tesselation is also called tiling of the plane. Anti deSitter space is a space of constant negative curvature, i.e., hyperbolic. So when Lawrence tiles the plane in AdS, with the Escher print, one sees the Escher shapes grow infinitely small at the rim of the disc, but never disappear. It's what hyperbolic space does.

Tom

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  • Post #26

Dear Eckard,

You said "It happens that even the wildest guess comes close. So I will try and add one more horrible speculation: Abelian and non-abelian? I read that Abel died in a duel when he was a young man, and Christian Felix Klein was at best a baby at that time. Perhaps, Abel's symmetry was a simple one. Non-abelian sounds to a layman like me a bit like non-Euclidean, non-Newtonian, transfinite, ueberabzaehlbar, hyperreal, superluminal, postmodern, and other once excitingly modern notions."

Consider the Standard Model: SU(3)xU(1)xSU(2). SU(2) and SU(3) are considered non-Abelian because their mediating bosons can interact with one another. For instance, couplings between the W and Z exist. We even speculate on the possibility of glue-balls because three gluons could theoretically couple to one another in such a manner as to yield a net color of white. On the other hand, the U(1) of Weak hypercharge represents Electromagnetism, which is Abelian and its mediating boson, the photon, does not interact with itself at tree level (although we do have radiative corrections of order the fine-structure constant squared and smaller caused by ghost loop electrons).

Gravity is a paradox. On one hand, gravity is an inverse-radius-squared force with "infinite" range - as is Electromagnetism, and so we might expect gravity to have an Abelian nature. On the other hand, the theoretical graviton quanta interacts with mass, mass interacts with curvature, and curvature interacts with gravity, which seems non-Abelian. Perhaps the characteristics that we call "Gravity" are two different forces. I think that Edwin Klingman would be pleased with that idea...

I travelled this week and got behind on this blog site. Hopefully, I can read your essay next week.

Have Fun!

Dr. Cosmic Ray

It was Galois who died in a duel.

With quantum gravity in a QFT setting has a quadratic momentum dependence on the graviton vertex V[k] ~ k^2. This is due to the form the action takes in an expansion of the metric density {\tilde g}_{μν} = g^{1/2}g_{μν } with

{\tilde g}_{μν} = η_{μν } + κ^2{φ^α}_μ φ_{αν}.

The action L ~ κ^{-2}φi^{α μ;α}{φ_{αμ}}^{;α} gives a three point vertex function which is quadratic in the momentum.

A general Feynman diagram will also have internal lines I[k] ~ 1/k^2 and loops with L[k] ~ ∫^kd^4 p. So the internal portion of a Feynman diagram will have internal lines, vertices and loops. The Euler characteristic for a graph 1 = V[k] - I[k] + L[k] is used in conjunction with the degree of divergence of these parts of the graph D_V = 2 D_I = -2 D_L = 4 with a total divergence D = 4L[k] - 2I[k] + 2V[k], so that D = 2(L[k] + 1). Consequently the divergence has an unbounded growth with the order of each Feynman diagram.

As pointed out above the gravitational constant has units of [G] = Area, which differs from the fine structure constant α = e^2/ħc and other gauge couplings which are unitless. The dimensional content of the gravitational constant is related to the problem of quadratic vertices. The interest in holography and AdS/CFT correspondence is with how gravity in an AdS space with negative Gaussian curvature may be replaced by quantum field on the boundary. So the divergence in a naïve QFT theory of gravity may be substituted with a stringy theory on the boundary of a space where these divergences do not exist.

Cheers LC

Lawrence,

That's a lot of math to reach the strong conclusion that "there is only one electron, one proton (well really one up quark and one down quark), one photon and so forth in the entire universe, and what we see as multiple copies of them are a sort of illusion induced by a large scale decoherence and the subjective appearance of decoherent classes of histories."

Why hold back? Why not say something radical?

Have you figured out where consciousness [with or without free will] comes from in this scenario?

Also, I missed how W's and Z's fit into this scheme and the three generations. Are these included in the "and so forth"?

Edwin Eugene Klingman

The conjecture that there only exist one type of quark, or electron and the like is not substantiated as yet. The world may only have 496 bits, or eigenstates, which of course radically simplifies everything. These eigenstates are fundamental from a group theoretic perspective. The particles in these states form superpositions through a set of other states induced by spacetime. For instance a state for a quark |u> may exist in a huge number of momentum states, so |u> - -> |u>|k> = |u(k)>, such that the momentum states are a property of the emergent spacetime. So for a large number of momentum states the up quark becomes

sum_k c(k) |u(k)>

The occurrence of a vast number of particles is then due to this superposition. The path integral for these field is in line with Feynman's original idea of the path integral, where a particle traverses a path throughout the world, both forwards and backwards in time.

I am not concerned about consciousness. It is not that I regard consciousness as unimportant, but at this time I question whether we can adequately address the problem. I question the extent to which fundamental physics is able to address the question as well. So for the time I regard consciousness as an unknown which at this time I don't try to answer.

Cheers LC

Lawrence,

I really try to understand you, but I continually fail. I can't even understand your summation in your essay, as to whether you come down on the side of a discrete or continuous universe. I point out in my essay that since digital and analog filtering are equivalent, the answer cannot be mathematical, but must be answered physically.

I think that when God made your and my mind, he decided to see what orthogonal minds would look like. I think he succeeded. They both work, and they both work well, and they probably even share the same universe, but there's no overlap.

You seem to come down on both sides of the fence, and state that it will simply give philosophers a lot to do. In my essay I propose several experiments that I believe can distinguish between continuous fields and real particles. Is this just an exercise for you, or am I missing something important?

Edwin Eugene Klingman

I don't come down on either side. The dynamics is governed by mathematics which is continuous, but the measurements correspond to qubits which are discrete. In a funny sense you must have continuous dynamics, but with that are discrete group actions which define nilpotent points and Noetherian charges. However, the dynamical equations involve Noetherian currents, which are not defined in a discrete setting, say for a group SL(N,R) replaced by or which embeds SL(N,Z). Ultimately the universe is composed as an interplay between the two.

It might be argued that since we measure things which are discrete that the discrete sector is "more real." Of course reality here is funny with respect to quantum physics as it is. The continuous stuff corresponds to fields or waves, while the discrete stuff corresponds to what we measure. What we consider as "reality" is not something we can reduce to classical physics, or reality as defined by classical logic. Since the GHZ state gives the violations of Bell inequalities with a single measurement it is not clear to me that the discrete aspects of nature have some higher reality than the continuous part.

Cheers LC

Lawrence,

As you are aware, I believe that if particle properties do exist, and if the 'twins' are treated differently, then the properties may change differently en route. If this is the case then violation of Bell's inequality doesn't have any meaning as to non-locality or non-reality. But I'm not trying to argue that here with you, simply to state my case.

On the other hand, I would like to ask your opinion on the following. Noetherian 'theory' has for a century or so identified conservation with symmetry. I believe that is backward. I believe that conservation implies symmetry, not symmetry implies conservation. Do you believe that every symmetry implies a conservation law?

Edwin Eugene Klingman

Logically in theoretical analysis we have symmetries imply conservation laws. This is just how the theorem is provem. From an empirical perspective the observation of a conservation law supports the existence of a symmetry. In that case you do not have a proof, as is the case with all science.

I am not sure what you are trying to say about Bell inequalities.

Cheers LC

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  • Post #34

Hi Ed,

You asked "Do you believe that every symmetry implies a conservation law?"

Which came first - the chicken or the egg?

I believe that every new symmetry implies new fundamental particles and a new conservation law.

Have Fun!

Dr. Cosmic Ray

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  • Post #35

In all honesty, do you think time travel is possible dear Lawrence?

I don't need points of vue but a simple answer.

Cheers Steve

    I do not think classical closed time loops are possible. So I don't think time travel per se is possible. In quantum gravity I think correlation between pre and post selected states have an ambiguity in time ordering. This is a subtle issue with what an event in spacetime means with holography. However, this does not translate into any ability to time travel.

    Cheers LC

    A symmetry in QFT or strings implies a root-weight structure which are eigenvalues for particle states. The particle states are constants of the motion for the Hamiltonian of the system. The Hamiltonian is then the Cartan center of the algebraic generator of the symmetry. The Cartan center in adjoint rep consists of matrices which commute with the rest of the algebra.

    Cheers LC