The Cosmological Constant Vs. Superstrings and Loop Quantum Gravity
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The Cosmological Constant vs. Superstrings and Loop Quantum Gravity
From: Jack Sarfatti <Sarfatti@P...>
Date: Thu Jan 8, 2004 7:16 pm
Subject: Chapline on quantum gravity
On Thursday, January 8, 2004, at 01:00 PM, George Chapline wrote:
> Hi Jack,
> I happy to see you agree that dark energy is a result of quantum coherence of the vacuum state.
Yes, I had that general idea, including the explanation of low entropy for the early Universe, before I knew of your important work. The details are different of course. .
G. Volovik in Russia has also had that general idea for solving the cosmological constant problem.
> I am less happy to see you try to relate this to string theory and loop gravity; both of which are almost certainly wrong theories of quantum gravity.
Only in a superficial way. I do not need either string theory or loop theory to be correct theories of quantum gravity in detail as currently conceived. I use the "quantum of area" idea used in loop gravity, but also in other approaches. I also use the "string tension" on:
1. purely dimensional grounds since G/c^4 has dimensions (String Tension)^-1 in
Guv ~ -(G/c^4)Tuv
with Guv units as (Area)^-1
2. Hagen Kleinert's "metric elasticity" analogy for Einstein's GR where curvature is related to stringy "vortex core" like disclination defect density in a 4D Planck lattice. A perfectly tiled lattice with no topological defects is globally flat Minkowski space-time.
> One way to see this is to note that both theories claim to be consistent with the B-H entropy. David Boulware proved in 1975 that there is no Unruh effect. Boulware's result has been ignored because in the context of black holes Unruh's mistake yields Hawking radiation, which agreed with Bekenstein's entropy conjecture (derived no less from classical considerations). Unfortunately the whole Bekenstein-Hawking-Unruh business is complete nonsense.
> Cheers,
> george
Well, George, you said a mouthful there! :-) You may well be right. You know this stuff better than I do. I am a relative newcomer to this field.
StealthSkater note: for background on Dr. Chapline -- senior physicist at Lawrence LivermoreNational Laboratory -- seedoc pdf URL-doc URL-pdf . This particular article advises physicists to "throw out the window" everything they haveever been taught about black holes, for it appears they are now 'gravastars' rather thanan infinitely-dense point-like singularity."
From: Jack Sarfatti <Sarfatti@P...>
Date: Fri Jan 9, 2004 12:28 am
Subject: From Sirag
bcc
I need to look at Penrose's old paper that started the spin network craze in loop quantum gravity. I actually have it. As I recall the way Penrose did it makes the connection to spintronics qubits obvious hence to quantum computers. This connection is obscured to my mind at least in the modern developments like with Fotini Markopoulos Kalamara whose work is interesting, but requires a lot of work to understand.
StealthSkater note: for background info on Dr. Kalamara, her research was highlighted inScientific American magazine => seedoc pdf URL-doc URL-pdf.
From quantized spins as links in a string to quantized areas seems plausible to me since the line and the area are dual in 3D.
George Chapline made a bombshell remark about black hole thermodynamics and strings and loops today. I need to understand what he means in more detail. George is a deep thinker and I do not casually dismiss anything he says about physics.
On Thursday, January 8, 2004, at 08:38 PM, S-P & M-M Sirag wrote:
> "Jack,
> Thanks for the "heads up" on this John Baez reference to ADE and ALE.
> I have previously looked at Baez's "Week 62" through "Week 65" on the ADE Lie algebras, and also on John McKay's "A Rapid Introduction to ADE Theory" at .
> Baez in his answer to the e-mail "ALE Spaces: Help" doesn't really explain what an ALE space is. In Mckay's "Rapid Introduction" he says: "There have been many applications of these ideas in various contexts. Let me cite two: Peter Kronheimer has used them in his paper on asymptotically locally flat and asymptotically locally Euclidean spaces in connection with cosmological geometry."
> So ALE means "asymptotically locally Euclidean".
> McKay doesn't supply a reference to this paper. Actually there are several. I will mention two of them: P.B. Kronheimer, "A Torrelli-Type Theorem for Gravitational Instantons," J. Differential Geom. 29, 685-698 (1989)
> P.B. Kronheimer, "Instantons and the Geometry of the Nilpotent Variety," J. Differential Geom. 32, 473-490 (1990)
> So an ALE space is a type of gravitational instanton -- a vacuum solution to Einstein's GR field equations, assuming that time t is Wick rotated to it (and in this sense Euclideanized)."
Ok, so the instanton is a solution to
Ruv = 0
with +------> ++++
Has anyone studied
Ruv - (1/2)Rguv + /\guv = 0 ?
I suppose, off the top-of-my-head, this is what Susskind means when he mentions DeSitter and anti-DeSitter space?
That is for /\ = constant. In my theory /\ is a variable.
> Note: a gravitational instanton is a generalization (by Hawking) of the Yang-Mills gauge theory instanton idea.
> Such an ALE space has an "infinity" that looks like SU(2)/Gamma. This might relate to the recent claim by Jeff Weeks (et alia) in *Nature* 429,9 Oct. 2003, pp. 593-595, that the topology of the universe is dodecahedral -- i.e. it would have the topology of SU(2)/Octahedral Double group. This OD group is the McKay group corresponding to the E8 Coxeter graph (or Dynkin diagram).
> Such a gravitational instanton is very interesting mathematically: among other things it is a hyper-Kaehler manifold, which means that it has three independent complex structures and other powerful properties.
> The e-mail copied below says: "Each discrete group Gamma [a finite subgroup of SU(2)] can act on C^2 = R^4, and generate an ALE space C^2/Gamma."
> Actually, C^2/Gamma is a 4-d variety with a singularity of the type which is ADE classified by V.I. Arnold (ref: *Singularity Theory* 1981).
> The ALE space corresponding to each ADE graph is the resolved (or de-singularized) form of C^2/Gamma. This resolution occurs by lifting into the nilpotent variety which is a substructure of the corresponding ADE-type Lie algebra.
> There is a close relationship between singularity theory and catastrophe theory, which is described in Arnold's book *Catastrophe Theory* (1986). In fact the proto-ALE space C^2/Gamma is the identity fiber in the catastrophe bundle, whose base space is C^r/W, where r is the rank of the ADE-type Lie algebra, and W is the ADE-type reflection group (also called the Coxeter group or the Weyl group). So here we have a beautiful connection between the McKay group (finite subgroup of SU(2)) and the reflection group.
> McKay does not exaggerate when he says: "There have been many applications of these ideas in various contexts." In fact there are so many applications (all of interest to physics) that I have proposed that all of these applications be studied together in a program I have been calling ADEX theory. Here is a partial list of ADE classified objects [Some of these objects have a somewhat larger classification scheme; however, the simply-laced Coxeter graphs classifies the most important sub-class (which is called "simple" by V.I. Arnold, who also claims that ADE classifies all such simple objects in mathematics -- an unproven but very suggestive claim).]:
> Lie algebras (& Lie groups) Kac-Moody (infinite-dim.) algebras Coxeter (reflection) groups (also called Weyl groups)
> McKay groups (finite subgroups of SU(2))
> Regular polyhedra
> Hyperspace crystallography
>Sphere-packing lattices (root lattices)
> Error-corresting codes
> Quatizing lattices (weight lattices)
> Analog-to-digital transforms
> Conformal field theories (which live on the 2-d string world-sheet)
> Gravitational instantons (providing a link with Penrose twistors)
> Singularities of differentible maps
> Thom-Arnold catastrophes
> Heisenberg algebras
> Korweg-deVries hierarchy of non-linear equations
> Generalized braid groups (related to knots and links)
> Quivers
> Caustics
> Wave fronts
> As V.I. Arnold says on p. 92 of *Catastrophe Theory*
> "At first glance, functions, quivers, caustics, wave fronts and regular polyhedra have no connection with each other. But in fact, corresponding objects bear the same label not just by chance: for example, from the icosahedron one can construct the function x^2 + y^3 + z^5, and from it the diagram E8, and also the caustic and wave front of the same name. "To easily checked properties of one of a set of associated objects correspond properties of the others which need not be evident at all. Thus the relations between all the A, D, E-classifications can be used for the simultaneous study of all simple objects, in spite of the fact that the origin of many of these relations (for example, of the connections between functions and quivers) remains an unexplained manifestation of the mysterious unity of all things."
> BTW: John McKay in his "Rapid Introduction" mentions that: "This correspondence has appeared in the book *Roots of Consciousness* as a basis for an explanation of consciousness!"
> I should mention here that this is a reference to a 40-page paper, "Consciousness: a Hyperspace View*, which I published as an appendix to the book *Roots of Consciousness* by Jeffrey Mishlove (1993).
> I also published a short summary of this idea in the paper, "A Mathematical Strategy for a Theory of Consciousness" in *Toward a Science of Consciousness: the First Tucson Discussions and Debates, ed. by Hameroff, Kaszniak, and Scott, MIT Press (1996).
> Nuff said!
> Saul-Paul