Alright, I read these papers. I was disappointed.

1) His main idea seems to be – 3d ang. momentum to SU(2) spin nets is the same as spacetime angular *and* linear momentum to SO(3,2) spin nets. This isn’t true generally, so he spends most of his effort patching up the problems by contracting SO(3,2) to Poincare. This is a mistake – the idea itself is good, but the realization is not (see below).

2) His transition from 2-spinors to 4-spinors is hand-waving nonsense. As we know, this amounts to going from the restricted Lorentz group to the full one including spacetime parity. The physical net gain is antimatter, which he never mentions.

3) His identification of s_m4 with y_m is itself not correct, so he gets the Clifford algebra wrong. For the purpose of his application this is harmless, but for the purpose of the correct approach it’s fatal.

What’s the correct approach? You need to do it for SO(3,3) – then one has real translations without the need for approximation, like this…

The Lie algebra has terms that look like (indices go 1-4)

[ Jm5, Jn6 ] = i gmn J56 = i gmn M (mass!)

[ Jmn, Jp5 ] = -i (gmp Jn5 – gnp Jm5)

[ Jmn, Jp6 ] = -i (gmp Jn6 – gnp Jm6)

etc.

Calling Pm = Jm5 + iJm6 and Qm = Jm5 – iJm6 we see that both Pm and Qm represent translations abstractly, but they go off shell into complex spacetime, so one needs *two* of them in succession to get a *real* displacement. Since they are translations, they still commute. Thus one can build up finite translations in spacetime *without contraction*. This should allow one to build a 4-d checkerboard model on the lines of Gersh’s and Feynman’s 2-d model. One should also be able to construct a spin network model of the 6d spacetime. I’ve been meaning to do this but occupied with other things. Note that the Weyl theory on SO(3,3) – SO(3,3) neutrinos – leads to the Dirac theory on spacetime, with the two neutrino helicities correpsonding to positive and negative mass terms. A paper on this subject should appear soon.

-drl

I have to walk very slowly in these circumstances, being the layman, I am just learning to walk on these topics.

Speculation?

1. Background Independence And The Holomorphic Anomaly

Finding the right framework for an intrinsic, background independent formulation of string theory is one of the main problems in the subject, and so far has remained out of reach. Moreover, some highly simplified special cases or analogs of the problem, which look like they might be studied for practice, have also resisted understanding.

I assume a high energy consideration from the early universe.

G -> H -> … -> SU(3) x SU(2) x U(1) -> SU(3) x U(1)

Here, each arrow represents a symmetry breaking phase transition where matter changes form and the groups – G, H, SU(3), etc. – represent the different types of matter, specifically the symmetries that the matter exhibits and they are associated with the different fundamental forces of nature

Some might have assumed a false vacuum as existing instead of “nothing”, and from it, a true vacuum to emerge. This would encapsulate, and like bubble eversions, explain what would have been held to the brane, and what is allowed to roam in the bulk? I know this might seemed far fetched as I am trying comprehend the nature of of the abstract world given to defining feymans integral paths as loops, defined in that abstract geoemtrical thinking. This because of it’s background dependancy, had to be modifed in order to to speak from the compactified dimensions, and find themselves revealled in spacetime. You see?

I apologize to those of you who may find this easy.

You don’t have to indulge in any speculation. If a theory has a Lagrangian and variational principle where everything in sight is varied, leading to equations involving all the elements, then that theory is background independent practically by definition. So for example the Einstein-Hilbert action is

S = integral R sqrt(det(g)) dx..dt

R is a function of g_mn and its first and second derivatives, and this appears again in the volume element sqrt(det(g)) – so the equations that come out of delta S = 0 are background independent. The Maxwell action

S = integral Fmn Fab g_ma g_nb sqrt(det(g)) dx..dt

leads to Maxwell’s equations in vacuo and these are not, because the g_mn are not varied. You might ask what happens if I vary the g_mn in the latter as well as the A_n (F = curl A) – answer: because no derivatives of g_mn appear in the action the Euler equations are simply

F_am F_mb + 1/4 F_mn F_mn g_ab = T_ab = 0

F_mn,n = 0

that is, the energy tensor for the EM field also vanishes, and so there is in fact no field.

The best you can do with both, in the existing scheme, is to paste together an ad-hoc Lagrangian

L = R + k W

where k is an additive (dimensional) constant – one then can get

R_ab – 1/2 R_mn R_mn g_ab = -k T_ab

that is, the Einstein-Maxwell equations (Maxwell in curved space with the field energy as a source of curvature). So, Einstein-Maxwell is background free, but *not* unified, because the Lagrangian is not irreducible. To sum up, background-freeness is not a mystical property, it’s simply the statement that all the essential elements can change from place to place.

-drl

The Problem of Dynamics in Quantum Gravity

The problem of dynamics in quantum gravity is still a big challenge. We don’t know how to make spacetime a truly dynamical entity with local degrees of freedom while taking quantum theory into account. Neither string theory, nor loop quantum gravity, nor the spin foam and causal dynamical triangulation approaches have yet found a background-free quantum theory with local degrees of freedom propagating causally. We sketch some avenues for making progress in this direction.

As I was trying to comprehend how gravity was to be inclusive in string theory, it soon became apparent that it was background dependant. Truly as John Baez implies this is not desired, by others as well.

But if we assume background dependancy, then from what I understood, it became the background and the quantum mechanical discription of the spacetime fabric. Please anyone correct this perception if it is wrong.

Thus from this perspective, a emergent geometry would have been allowed to surface, where all other geometrical approaches, could not have been allowed?

Again this is not what is desired of string theory and the background independance is most preferred. I have many links on quantum grvaity that would innuadate your selection DRL.

I would rather a concensus on whether any geoemtry shall emerge(what shall emerge in the Third Superstring Revolution) and how it shall do that. If we do not consider this context, then we are left to consider, the value of glast determinations and the link Peter offerred.

Inside Gamma Sphere:

The device’s 110 gamma-ray detectors point to the center of the spherical array, where a beam of nuclei from a particle accelerator smashes into a thin target. The collisions create unstable nuclei that decay by emitting gamma rays, an extremely high-energy form of light. Gammasphere catches and measures as many of the gamma rays as possible, so that scientists can study what happens to nuclei under extreme physical conditions.

http://www.symmetrymag.org/cms/?pid=1000017

Is this a bad thing? No it reaffirms the direction of glast on the cosmological scale and secures QF visionist on the roads to percieving how quantum grvaity makes sense leaving GR alone(Smolin’s position ?).

But as I said, without th econsistancy of a geoemtry to emerge, there is no hope for a perspective to form around quantum geometry as a discritor of quantum gravity?

It’s damned unbelieveable, what?

Strings depend essentially on KK theory, a failed attempt to extend Riemannian geometry to encompass the A field as part of an ersatz cylindrical metric in 5-d. The simplest contradictory logical loopbacks seem to be beyond the Greenes of the world. They remind me of our neocons.

Now there really *is* an effort to make quantum geometry, see for example

http://www.physics.gatech.edu/people/faculty/dfinkelstein.html

You won’t find any hippocoprolitic stringism there.

-drl

Furthermore, what sort of disingenuousness is it to say “field theory is ugly”, when string theory would have to reproduce that same ugliness to be taken seriously? (It won’t, but this is rhetoric.) Whatever next step turns out to be the right one, it will have things that look like gauge fields, energy tensors, etc. etc. and people will say “Ah! Now we know why field theory was that way – how beautiful!”

Great observation! As Hestenes, in his New Foundations for Classical Mechanics, observes: “[Newton] deserves the title of “founder” (of classical mechanics) because he integrated the insights of his predecessors into a comprehensive theory.”

However, while your statement hits the nail right on the head, it also assumes that a successor will be successful, as was Newton, in moving modern physics forward “by integrating the insights of his predecessors into a comprehensive theory.” This may not happen. As Hestenes points out, Newton did more than integrate these insights into a more encompassing theory, he launched “a well-defined program of research into the structure of the physical world.”

The two great revolutions in physics of the 20th century, QM and GR, are the great insights to be integrated, but it may take a theory that does more than integrate them to move us forward, it may require a new “program of research into the physical world.” Of course, that’s a tall order, but it’s the “new physics” everyone talks about these days, but in the true sense of the word; that is, in the sense of a new program of research, rather than new phenomenology.

That such a program would be characterized by the simplicity of geometry and the beauty of fundamental,powerful ideas, unencumbered by the excesses we see today, is certain in my mind. The mathematical indulgences and wild speculations so popular in normal science today remind me of the days when doctors proudly wore blood smeared smocks as testimony of their professional virtuosity. The irony is palpable.

According to Hesetenes, the central hypothesis of Newton’s program “is that variations in the motion of a particle are completely determined by its interaction with other particles,” and that [Newton's program of research] has been interpreted as a dictum: to focus on forces. He says, “The aim is to classify the kinds of forces and so develop a classification of particles according to the kinds of interactions in which they participate.”

Perhaps, however, such a focus cannot deliver the goods. I think that Newton understood that force was a property of motion, and that motion was the proper study of physics, not forces, and that a new program of research, focusing on motion, that is, the reciprocal relation of space and time, may be more fruitful now than to continue the present course, as successful as it has been. We have explained the diverse properties of objects in our experience in terms of a few kinds of interactions among a few kinds of particles, but it appears that we have reached the limit of our methodology. Thus the challenge has reverted to the epistemological side of the reciprocal relation between methodology and science as described by Einstein. The old man, it turns out, was right on once again.

“The gravitational treatment of point particles thus brings in one further difficulty, in addition to the usual ones in the quantum theory.” This is rather curious coda since the above problems are really as relevant classically, and of course they are very different from the perturbative nonrenormalizability issues that have dominated all subsequent studies. After this pioneering foray, Dirac’s original publications in the field waned, apart from one later paper [17] on conformally invariant extensions of GR.

Now for me when a picture enters my mind, it is unassociative for a bit, but neuronically connected, and relevant. So to Mona Lisa’s smile and the trampoline.

DRL,

Figure 10.1 When standing on the Mona Lisa trampoline, the image becomes most distorted under your weight

The Heart of Reimannian Geometry

This example cuts to the heart of Reimann’s mathematical framework for describing warped shapes. Reimann, building on earlier insights of mathematicians Carl Friedrich Gauss, Nikolai Loachevsky, Janos Bolyai, and others showed that a careful analysis of the distances between all locationson or in an object provides a means of qauntifying the extent of its curvature…..

The Elegant Universe, by Brian Greene, page 232 & 233

One has to still endure the geometry that is progressive, and has developed along side of the physics. One does not disavow what the world of gauss(the roads leading too hyperdimensional space) is doing in light of Maxwell’s gains. That any toy model is found correlated in relation to QFT, was a monumental effort by Kaku, in his loop calculations?

You see. So between Smolin who adopts the GR attitude of leave Gr as it is, a Einsteinain way, and strings to adopt, the quantum mechanical discription of the background, neither can reject the ideals of the quantization of gravity, and a geoemtrical perspective.

What geometry shall emerge?

“But now, almost a century after Einstein’s tour-de-force, string theory gives us a quantum-mechanical discription of gravity that, by necessity, modifies general relativity when distances involved become as short as the Planck length. Since Reinmannian geometry is the mathetical core of general relativity, this means that it too must be modified in order to reflect faithfully the new short distance physics of string theory. Whereas general relativity asserts that the curved properties of the universe are described by Reinmannian geometry, string theory asserts this is true only if we examine the fabric of the universe on large enough scales. On scales as small as planck length a new kind of geometry must emerge, one that aligns with the new physics of string theory. This new geometry is called, quantum geometry.”

The Elegant Universe, by Brian Greene, pg 231 and Pg 232

Enjoy:)

I read these papers years ago in school, and filed them in the “very interesting” drawer.

Also interesting here is the dropping of the name Wyler and his work on the fine structure constant.

Again, nice papers, very nice.

-drl