An Exceptionally Technical Discussion of AESToE

[Lawrence B. Crowell]

On the galactic scale there are issues of dark matter and the like. For a mass embedded in a gravitating media with density \rho the gravitation acts as

<br /> {\vec F}~=~-GM\rho{\vec r},<br />

and so its motion is a particle on a spring moving in the plane. This is one reason stars move with about the same orbital frequency across a galaxy. The "stuff" which does this is labelled dark matter. Einstein lensing have pretty much indicated it exists, in particular with the recent Bullet galaxy measurements. So how a Brans-Dicke type of modified gravity fits into this is hard to cypher.

Lawrence B. Crowell

 

[MTd2]

On the galactic scale there are issues of dark matter and the like.

Did you read the papers I pointed out? It also fits that curve, as many monds do that. It's nothing so special for this gender of theories, because what bends the geometry is not only the Stress Energy Tensor, but other fields coupled to gravity.

The equivalence principle is broken, and experiments are proposed to show that. It is difficult to perform though, because the curvature must be extremely low, like outside the solar system. There is some evidence that there is a sli ghtpreferencial direction on cosmic scale.

 

[Lawrence B. Crowell]

Did you read the papers I pointed out? It also fits that curve, as many monds do that. It's nothing so special for this gender of theories, because what bends the geometry is not only the Stress Energy Tensor, but other fields coupled to gravity.

The equivalence principle is broken, and experiments are proposed to show that. It is difficult to perform though, because the curvature must be extremely low, like outside the solar system. There is some evidence that there is a sli ghtpreferencial direction on cosmic scale.

I have read the introductions to these and scanned them. To be honest I am not sure about this development. Also to be honest I find the prospect that equivalence principle is violated or that there is some preferential direction to space as troublesome. To be honest in quantum gravity I think the equivalence principle needs to be extended so that accelerated frames, for a framing on a Finsler bundle or a jet bundle, are all equivalent. The loss of equivalence between inertial and accelerated frames is something which emerges on the classical level.

This points in some ways to something I see as problematic with some of the LQG developments. Some authors have worked out systems with broken Lorentzian symmetry and the like, which appears due to some strict physical interpretation of the strutting (slice and dicing) of space and spacetime which connection coefficients are calculated in a discrete manner,

Lawrence B. Crowell

 

[CarlB]

I finally figured out how to put the generation quantum numbers plus weak hypercharge into the same idempotency (i.e. the equation BB = B) form. This is where the Koide mass formula generalization for the neutrinos came from and it might allow a mass formula for the quarks as well:
http://carlbrannen.wordpress.com/2008/03/10/quarks-leptons-and-generations/

The basic idea is to describe the preon bound state in density matrix form. The off diagonal entries of the matrix define the amplitude for various permutations to happen to the valence preons. The diagonal entries give the amplitudes for propagation without permutation and these define the weak hypercharge and weak isospin quantum numbers. The off diagonal elements can show up in three forms corresponding to the 3 generations and these give the quantum numbers for the 3 generations. As with the Koide formula, the quantum numbers for the 3 generations match the triality stuff that Garrett is doing, but now I get weak hypercharge together with the generations.

.. I am not sure what bearing this has on the preon models you are working up here. The Pascal triangle construction you are arguing for look like some polynomial system you are constructing form the MUB system. I will have to look at this more closely. I am still doing a bit to get a working knowledge of Bengtsson papers. Lawrence B. Crowell

I've (perhaps temporarily) abandoned the new preon idea. In it, weak hypercharge is supposed to come from a sum over 12 preons, but I can't seem to come up with a simple rule that naturally picks out the observed states. Actually, I can get the states, but the multiplicities are all wrong and the multiplicities indicate that I will have some real heavy lifting to make the newer preon model work.

 

[MTd2]

Also to be honest I find the prospect that equivalence principle is violated or that there is some preferential direction to space as troublesome.

Relly? :)

http://golem.ph.utexas.edu/category/2007/08/axis_of_evil_or_axis_of_opport.html

http://arxiv.org/abs/0708.4013

I was not thinking about quantum gravity, but on general phenomenological MOND models :)... and about that cosmological observations. But really, I will get note of your observations to my future research :)

 

[Lawrence B. Crowell]

Relly? :)

http://golem.ph.utexas.edu/category/2007/08/axis_of_evil_or_axis_of_opport.html

http://arxiv.org/abs/0708.4013

I was not thinking about quantum gravity, but on general phenomenological MOND models :)... and about that cosmological observations. But really, I will get note of your observations to my future research :)

A scalar-tensor, Moffat or Brans-Dicke like, theory must have some way physical mechanism for how the scalar enters into the classical field. The quantum gravity must be some conformal gravity theory, eg SU(4)~\sim~spin(4,2), and the 15 components of the scalar field must on the low energy physical vacuum assume some sort of configuration. A standard physical assumption is that \nabla^2\phi~=~0, or maybe constant. In a scalar-tensor theory some component of the scalar field remains a dynamical field, while of course breaking conformal symmetry (masses break conformal symmetry). I am not adverse to these possibilities. Yet I suspect that this sort of physics does not mean that there is some preferred direction in spacetime.

I do think that conformal gravity should exist in and E_8 or related theory of quantum gravity or supergravity. A signature of this might manifest itself in some scalar modification of gravitation. Maybe this can be found in the \mu-meter or smaller scales. Some results of nano-scaled physics have found some interesting departures from macroscopic physics, and maybe a scalar field has some role in extra-large dimensions or other hypothetical ideas about physics.

Lawrence B. Crowell

 

[Lawrence B. Crowell]

The basic idea is to describe the preon bound state in density matrix form. The off diagonal entries of the matrix define the amplitude for various permutations to happen to the valence preons. The diagonal entries give the amplitudes for propagation without permutation and these define the weak hypercharge and weak isospin quantum numbers. The off diagonal elements can show up in three forms corresponding to the 3 generations and these give the quantum numbers for the 3 generations. As with the Koide formula, the quantum numbers for the 3 generations match the triality stuff that Garrett is doing, but now I get weak hypercharge together with the generations.

An interesting prospect for the triality condition is with the icosahedral permutations, sometimes called the isocian game. This is an algebra on three symbols for each root of unity. The repeated application of any of these result in the value 1 after a particular number of steps. The rules for this are

<br /> x^2~=~1,~y^3~=~1,~z^5~=~1,<br />

As a Hamilton graph there is the unifying relationship between these symbols:

<br /> z~=~xy<br />

These elements are non-commutative symbols which generate a the group of rotations of order 60 for the rotations of an icosahedron and its dual dodecahedron.

The twelve five cycles around the icosahedraon around the vertices of the icosahedron C_i define the Mathieu group M_{12} with the elements C_iC_j^{-1}. There are in this icosahedral construction of M_{12} and its correspondence with the 120 icosian quaternions 440 3-cycles in even permutations.

Lawrence B. Crowell

 

[Kea]

...correspondence with the 120 icosian quaternions 440 3-cycles in even permutations.

Oooh, nice. There is a 120 vertex operad polytope in 3D (KP4) called the permutoassociahedron (see Batanin's papers), because it resolves the 24 vertices of the permutohedron into pentagons, representative of Mac Lane pentagons for associativity.

 

[Lawrence B. Crowell]

Oooh, nice. There is a 120 vertex operad polytope in 3D (KP4) called the permutoassociahedron (see Batanin's papers), because it resolves the 24 vertices of the permutohedron into pentagons, representative of Mac Lane pentagons for associativity.

I am familiar with the permutohedron, Voronoi of A_n. I suppose I have not heard of the permoassociahedron. This does sound similar to what I was referring to, it is an extended version of Hamilton's icosian game. I suppose I can find Batanin's paper on arxiv.

Lawrence B. Crowell

 

[Kea]

Here is a link to the slides of a talk by Batanin:

http://www.maths.mq.edu.au/~street/BatanAustMSMq.pdf

 

[Lawrence B. Crowell]

Here is a link to the slides of a talk by Batanin:

http://www.maths.mq.edu.au/~street/BatanAustMSMq.pdf

I downloaded this. It looks as if this defines a Bianchi identity of sorts. I will of course have to digest this more before I can comment further. Yet this might provide some machinery in addressing the holonomy issue for spaces with noncompact group structures.

Lawrence B. Crowell

 

[Berlin]

Hi Guys,

Been away for some weeks, very quiet between the leatherback turtles. Gave me a lot of time to re-think Garrett’s work and my own comments in the past.

I am now convinced that we should abandon triality. We don’t need it and we cannot use it, because the groups become too big (what I understand). I have come up with a different scheme.

My starting point is that we really use D2-grav and D2-EW as fully commuting groups with commuting quantum numbers. Garrett himself says so in his paper, but in a sneaky way Garrett “glues” the left and right-handedness of these groups together, that really kills its potential. In principle it should be possible to have quantum number “left” in D2-grav and “right” in D2-EW. Come up with that later.

Because I abandon triality I do not require F4 or D4. Only the product of two D2 groups and a strong group are required. I also use the “w” quantum number actively, that probably adds a U(1) or so. That is for the group theory people to fill in. A lot of new particles of Garrett’s paper turn out to be third generation leptons or quarks. Only some frame-hiiggs are new, not a bad thing!

I start with the concept of “building blocks” for the elementary particles, made up from the separate groups. These are not necessary physical states, but the product of some of them (equivalent of the adding of the E8 root numbers) produce physical particles.

Not all physical particles turn out to be E8 root numbers (12 in total). This is nothing to worry about, because this is the same for the Z-0 or the photon; they are not part of the starting symmetry either. This should be caused by some breaking mechanism.

All physical bosons have a degeneracy (can be made off two or four combinations of “building blocks”).

Main other differences with Garrett: (x.phi) particles are really quarks, some frame-higgs are really gen-3 leptons. Other gen-3 leptons turn out to be the w-L/R and B-+/- particles (or visa versa).

Issues to work on:
- What is the group structure I use?
- How do I fix the frame Q# for the gen-2 leptons and quarks? My feeling is that just a different choice of frame gauge can fix this (change the coordinate system)! I ask for your comments!
- Should all particles have w-L/R Q# different from zero and should we “frame them” with extra w-L/R quantum numbers?

Jan

 

[John G]

I am now convinced that we should abandon triality. We don’t need it and we cannot use it, because the groups become too big (what I understand). I have come up with a different scheme.

My starting point is that we really use D2-grav and D2-EW as fully commuting groups with commuting quantum numbers... Only the product of two D2 groups and a strong group are required...
Jan

You can go up to D3-grav and D3-EWS, that gets you gravity translations (and conformal transformations/dilation) plus a group with the strong/color bosons. I think though you still want the big group with triality in order to have one group from which you can get the two D3s. The big group also can give you a group for fermions and quantization (and maybe an emergent spacetime).

 

[Berlin]

Now with attachment...

Did not manage to include the attachment earlier.

Jan

 

[CarlB]

Regarding triality, there seems to be some work on replacing the 2 of complex numbers with the 3 of something else. See:
http://kea-monad.blogspot.com/2008/03/extra-extra.html

 

[Berlin]

Some re-shuffling..

I have re-shuffled assignments so that for gen-1 and 2 fermions the gravitational left-right quantum numbers are OK. It seems that for gen-2 leptons and quarks you have to find a theory where the w-3 and B13 Q# are interchanged. Therefore it seems logical to look at the left-right symmetric theories like the left-right extension of the ew or things like trinification.

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

For gen-3 leptons it seems like you have to interchange the w-3, B13 and B2 Q# (J matrix carl used with the preons). For gen-3 quarks its more difficult.

Someone an idea to proceed?

Jan

 

[Lawrence B. Crowell]

Regarding triality, there seems to be some work on replacing the 2 of complex numbers with the 3 of something else. See:
http://kea-monad.blogspot.com/2008/03/extra-extra.html

I had a thought that the triality or MUB system might have something to do with the three bases for the Dirac field on CL_{3,0} with complex vectors, bivectors and trivectors constructed from the Pauli matrices.

Lawrence B. Crowell

 

[CarlB]

Lawrence, I ended up looking at the relation between E8, Jordan algebras of 3x3 matrices of octonions, triality (which for the 3x3 Jordan algebra defined matrices amounts to a shuffling of the matrix elements), the 3x3 circulant primitive idempotent complex matrices, and the Koide mass formulas yet again. It is a little too much for me to chew, but there are a couple of papers that gave an idea of what is going on and what it has to do with string theory. The papers I ran into were these:

The exceptional Jordan algebra and the matrix string
Lee Smolin
http://arxiv.org/abs/hep-th/0104050

The Geometry of Jordan Matrix Models
Michael Rios, 2005
http://arxiv.org/abs/math-ph/0503015

I ended up looking at this from reading the Wikipedia article on Heisenberg's matrix mechanics. The Koide formula is related to what Heisenberg did in that the circulant 3x3 matrices are the density matrix version of three basis states [i.e. the three states (1,w,ww)/sqrt(3) where w is a cube root of unity] for a 3-d Hilbert space that happens to be MUB with respect to the usual diagonal (1,0,0), (0,1,0), (0,0,1) basis. And the Fourier transform is equivalent to diagonalizing a 3x3 circulant matrix as Kea pointed out:
http://kea-monad.blogspot.com/2007/10/m-theory-lesson-108.html

Anyway, the circulant matrices used in Koide's mass formula turn out to be of the form one would get if one put O_0 = O_1 = O_2 in the 3x3 matrices of octonions in either of the above papers. The triality defined on equation (7) of the Smolin paper turns out, when applied to the Koide density matrices, to be an identity. [It basically cycles the _0 to _1 to _2 and since these are equal, it leaves these matrices unchanged.]

When that triality is applied to the other density matrix basis set for 3-d Hilbert space mentioned above, that is, the diagonal primitive idempotents: (1,0,0), (0,1,0), (0,0,1), the action is to cyclically commute these three elements.

But a 3-d Hilbert space MUB contains 4 basis sets. It turns out that the action of Smolin's triality on the third and fourth basis sets also permutes the elements while preserving the basis set [that is, the action is like the action on the diagonal primitive idempotents]. The 3-d Hilbert MUBs are listed (in state vector form) near the bottom of this blog page:
http://carlbrannen.wordpress.com/2008/02/06/qutrit-mutually-unbiased-bases-mubs/

So as far as this goes, it seems to me that the natural assignment for the triality operator mentioned in Smolin's paper, in the context of the Koide mass formulas, is that it changes color charge R -> G -> B -> R. [And so I don't think this is the triality that changes generation number.]

 

[Lawrence B. Crowell]

Lawrence, I ended up looking at the relation between E8, Jordan algebras of 3x3 matrices of octonions, triality (which for the 3x3 Jordan algebra defined matrices amounts to a shuffling of the matrix elements), the 3x3 circulant primitive idempotent complex matrices, and the Koide mass formulas yet again. It is a little too much for me to chew, but there are a couple of papers that gave an idea of what is going on and what it has to do with string theory. The papers I ran into were these:

The exceptional Jordan algebra and the matrix string
Lee Smolin
http://arxiv.org/abs/hep-th/0104050

The Geometry of Jordan Matrix Models
Michael Rios, 2005
http://arxiv.org/abs/math-ph/0503015

What we can do is to form a three way basis just within the quaternions from

<br /> \sigma_i,~\sigma_i \sigma_j,~\sigma_i\sigma_j\sigma_k<br />

which forms alternative quaternionic bases, and definitions for i~=~\sqrt{-1} which give a "three-basis" structure to the spinor field. With the octonions, or E_8, there is a triplet structure which can be given by the "27" E_6 or the Jordan algebra.

I hope in the not too distant future to do a bit of a right up on this. To be honest I pursue a lot of physical thought with regards to these things. I have a site here on Physics forums on Information Preservation in Q-Gravity where I have presented some of the physical issues. This is a complementary to the more mathematical discussions here, which tend to involve irreps of groups.

More later,

Lawrence B. Crowell

 

[CarlB]

Diane Demers sends me the following articles thinking (rightly) that I would find them of interest with respect to triality:

Remarks on Circulant Matrices and Polynomial Number Systems
http://www.clifford-algebras.org/v2/v22/GARRET22.pdf

Ternary Algebras and Groups
http://arxiv.org/abs/0710.5368

The Cubic Chessboard
[about ternary relations]
http://arxiv.org/abs/math-ph/0004031

Geometric tri-product of the spin domain and Clifford algebras
http://arxiv.org/abs/math-ph/0510008

Jordan structures and non-associative geometry
http://arxiv.org/abs/0706.1406

A Program for the Geometric Classification of Particles and Relativistic Interactions
http://prof.usb.ve/ggonzalm/invstg/pblc/clsfcn.pdf

Diane's interest is in non associativity, for example:

Nonassociative Algebras
http://homepage.uibk.ac.at/~c70202/jordan/archive/bremsur/bremsur.pdf

 

[kneemo]

Anyway, the circulant matrices used in Koide's mass formula turn out to be of the form one would get if one put O_0 = O_1 = O_2 in the 3x3 matrices of octonions in either of the above papers. The triality defined on equation (7) of the Smolin paper turns out, when applied to the Koide density matrices, to be an identity. [It basically cycles the _0 to _1 to _2 and since these are equal, it leaves these matrices unchanged.]

Yup, a while back I mentioned the use of 3x3 circulant matrices over the octonions and its possible relevance. After all, if one restricts the octonions to a complex subalgebra, the Koide mass formula applies directly. As one can always diagonalize Hermitian matrices, triality transformations can be studied by acting on orthonormal sets of primitive idempotents. I did this for the diagonal primitive idempotents and found that the triality transformations actually correspond to the three embeddings of SU(2) in SU(3). In the octonionic case, the full automorphism group of the Jordan algebra is no longer U(3) but F_4, so triality emerges from a triplet of representations of SO(9) in F_4.

Triality is thus related to the three inequivalent ways of picking out one of the off-diagonal elements for matrices of the 3x3 matrix Jordan algebras. Or equivalently, triality is related to the three inequivalent ways of transforming sets of primitive idempotents while leaving one invariant.

In recent years, studies of extremal black holes in D=5 N=2 homogeneous supergravities (http://arxiv.org/abs/hep-th/0512296" ) have revealed that the entropy of BPS black hole solutions can be calculated as:

S=\alpha\sqrt{det(X)}

where X is an element of a 3x3 matrix Jordan algebra. Triality transformations are in general not determinant preserving, so can lead to an entropy change for black hole solutions. However, in the special case of 3x3 Hermitian circulants, triality transformations leave the determinant and hence the entropy invariant. This leads me to suspect that circulants play a very important role in N=2 homogeneous supergravities. Moreover, the application of the Koide formula to extremal black holes might also provide a new perspective on the lepton generations. After all, from the stringy perspective, there isn't much difference between elementary particles and black holes (http://arxiv.org/abs/hep-th/9504145" ).

 

[Lawrence B. Crowell]

I have indicated I would post some work related to this. On my part in PF

https://www.physicsforums.com/showthread.php?t=115826&page=2
https://www.physicsforums.com/showthread.php?t=115826&page=3

I have some work leading up to this. I take a more physical perspective here than what is contained in these rather highly mathematical papers. However, the last entry here is to be followed up with how this gauge theory over SU(4) leads to a knot equation, or HOMFLY. There appears to be Jone and Conway polynomials involved here, and where the three-way (triality) is involved with J^3(V).

Lawrence B. Crowell

 

[Kea]

There appears to be Jones and Conway polynomials involved here, and where the three-way (triality) is involved with J^3(V).

Agreed. Rather, a doubly categorified form of the knot invariants is involved. Thanks for the links.

 

[Lawrence B. Crowell]

Agreed. Rather, a doubly categorified form of the knot invariants is involved. Thanks for the links.

I am trying to frame this based on physical grounds. I'd have to say that I think that quantum mechanics and general relativity are relationship systems between particles. We tend to be confused about the role of theories. In particular general relativity is not about the dynamics of points per se. One can take a point x on two choices of spatial manifolds with two different spatial metrics g_{ab}(x) and g&#039;_{ab}(x) and then push these forwards by ADM geometrodynamics you get two different points as the evolute. General relativity is not about the dynamics of points, but of the relative displacement or dynamics between two particles, such as with the geodesic deviation formula. We measure the motion of bodies such as the planet Mercury, or the orbits of neutron stars. The geometric constructions exist as models by which we can understand this dynamics, the simplest being in the weak field case

<br /> \frac{d^2x^i}{ds^2}~=~-{\Gamma^i}_{tt}U^tU^t~\simeq~-\frac{GMx^i}{r^3}<br />

which is Newton's second law of motion for the force of gravity.

Quantum mechanics is another relationship system, and in fact this too is blind to geometry, but only has a representation in spacetime that does respect the causality conditions of relativity. The nonlocality effects of quantum mechanics are free of geometric constructions as entanglements can occur across any distance, and in the case of the Wheeler Delayed Choice experiment along any time direction.

How these two relationship systems are unified is of course the crux problem of quantum gravity. It is not hard to show that general relativity through the Schild construction and Quantum mechanics for spin systems have a GF(4) content, which is the Dynkin diagram for the D_4.

Lawrence B. Crowell

 

[Kea]

I am trying to frame this based on physical grounds.

Yes, I appreciate that. We are also trying to do this, and I very much agree with your remarks about relationalism. For my part, I spent a good part of the 1990s thinking about 4D analogues of topological Chern-Simons path integrals (and hence knot invariants) and other work of Witten et al, which led perhaps to too much of an obsession with the mathematics, but then I do believe our concept of QG observable hinges on some very abstract categorical definitions and that it is somewhat clearer now than a few years ago. There are many ways to skin Schroedinger's cat. Although our language is very different, our (meaning you, Carl, Matti, me, kneemo et al) physics seems to me to be quite closely related.

If you like, you can translate singly categorified to cohomological and doubly categorified to triality invariant.

 

[Lawrence B. Crowell]

Yes, I appreciate that. We are also trying to do this, and I very much agree with your remarks about relationalism. For my part, I spent a good part of the 1990s thinking about 4D analogues of topological Chern-Simons path integrals (and hence knot invariants) and other work of Witten et al, which led perhaps to too much of an obsession with the mathematics, but then I do believe our concept of QG observable hinges on some very abstract categorical definitions and that it is somewhat clearer now than a few years ago. There are many ways to skin Schroedinger's cat. Although our language is very different, our (meaning you, Carl, Matti, me, kneemo et al) physics seems to me to be quite closely related.

If you like, you can translate singly categorified to cohomological and doubly categorified to triality invariant.

The CS Lagrangian comes into play with conformal gravity. The E_6 embeds an SU(4) and an SU(2), where the SU(2) is a QCD-like gauge theory which when reduced to spacetime is multiply connected. Spin fields on the conformal spacetime have multiple connections to each other which are not determined by the geometry of the SU(4), something similar to a non-Erdos network --- which the internet is also an example of. We might think of these multiple connections as quantum wormholes. At low energy these multiple connections are lost and the "relationship" between spin fields is more akin to an Erdos net. I hope to post more details on this by the end of this weekend.

Interesting if by Matti you mean Pitkannen (sp). He has this idea that p-adic numbers or Merssene primes play a central role in QFT. These do enter into coding systems, but I think somehow he takes things to strange extremes. In writing to him 10 years ago or so he seemed a bit inflexible on some of his more outlandish conclusions. There might be a kernel of something real in his ideas, but he then appears to carry the ball off into bizarre areas of the playing field.

Lawrence B. Crowell

 

[Kea]

We might think of these multiple connections as quantum wormholes. At low energy these multiple connections are lost and the "relationship" between spin fields is more akin to an Erdos net.

Yes, I meant Pitkanen, and I also confess to finding his exposition difficult. Actually, your first paragraph reminded me a lot of his ideas on the role of CS. I have not come across Erdos nets, so I will look it up.

 

[Lawrence B. Crowell]

Yes, I meant Pitkanen, and I also confess to finding his exposition difficult. Actually, your first paragraph reminded me a lot of his ideas on the role of CS. I have not come across Erdos nets, so I will look it up.

I would have to look again at Pitkanen's ideas to see what he says about the CS lagrangian.

The Erdos net, due to Paul Erdos, applies for Ising spin systems under the nearest neighbor interaction. Yet for some phase transitions this approximation ends and the interaction strength becomes scale invariant. There every spin couples to others equally. If you go to my site on this forum

https://www.physicsforums.com/showthread.php?t=115826&page=2

https://www.physicsforums.com/showthread.php?t=115826&page=3

you will see how I related this to Landau electron liquids and a possible universality of all spin fields under scale invariant fluctuations. In the non-Erdos net every node is weighted equally with all others.

From a human communications perspective a similar phase transition has been underway. Before the 20th century communications were by post and went from town to town, where the strength of communications were weighted heavily on proximity. So prior to the 20th century the communications network was pretty much an Erdos net. This began to change with with the telephone and radio, and now has dramatically changed with the internet, where now communications can be global and one can communicate with anyone anywhere with more or less equal ease. Some nodes, eg webpages, blogs etc, are more heavily weighted than others, but weights are not determined much by geographic factors or distance.

As one who is employed in the IT and programming field (darn --- not employed doing physics!) I do consider the networked, internet and cyberconnected world which has emerged in the last couple of decades as a fascinating model for phase transitions, Ising-like systems and universal scaling principles in physics.

Lawrence B. Crowell

 

[Kea]

I do consider the networked, internet and cyberconnected world which has emerged in the last couple of decades as a fascinating model for phase transitions, Ising-like systems and universal scaling principles in physics.

Hmm. If the new world knowledge base is a model of a phase transition, then presumably it is a phase transition in an epistemological sense. Very Hegelian, which I like. And temperature is Time in some cosmic sense. Again, sounds interesting. On the other hand, I'm not convinced that any concrete models of the internet are sufficiently rich to be comparable to gravity, since I at least am guilty of a fairly classical view of the interconnectivity of the internet.

 

[Lawrence B. Crowell]

Hmm. If the new world knowledge base is a model of a phase transition, then presumably it is a phase transition in an epistemological sense. Very Hegelian, which I like. And temperature is Time in some cosmic sense. Again, sounds interesting. On the other hand, I'm not convinced that any concrete models of the internet are sufficiently rich to be comparable to gravity, since I at least am guilty of a fairly classical view of the interconnectivity of the internet.

The idea is based on analogy. Clearly quantum gravity will be more general in the algebraic symmetries of the interconnected network, while the internet is more complex according to the parsable information sent.

Time is temperature for complex or imaginary valued time. On my area referenced above I indicate how this is involved with quantum phase transitions. This is something which should be universal with all spin system. I think the universe is defined by a set of unitarily inequivalent vacua and the conformal infinity for the AdS. The first is high temperature and end is zero temperature. For spacetime physics, where spacetime has an effective negative heat capacity, this is low entropy to high. Everything in between is just an information coding system which rearranged quantum-bits, or quantum gravity-bits, so as to define a holographic map between the two endpoints on the Feynman path integral. This map in between is the universe which we perceive as in a state of evolution.

Lawrence B. Crowell