On Tuesday, October 21, 2003, at 11:56 PM, S-P & M-M Sirag wrote:

> "Jack,
>
> A brief summary of a big topic, Reality, Mind and the Physical world:"

Yes, that was my essential question.

"The Question is: What is The Question?" (JA Wheeler) [A much improved version of the talk I gave in Paris at Vigier IV is now at http://qedcorp.com/APS/StarGate.mov Quick Time movie made in Keynote with all the animation that enhances comprehension of the ideas http//qedcorp.com/APS/WheelerAustin.ppt interactive version Power Point Version on-line now is close to 99% of what I will present this Friday in Austin, Texas to Society for Literature and Science

Tim Ferris is giving a talk on same subject BTW at that same meeting.

Remember this multi-dimensional presentation in conceptual hyperspace is to a literate audience of academics from the Two Cultures hence I have jazzed it up with reference to great Art, Drama, and lots of humor. It's a show, it's edutainment, but the physics is real not watered down to New Age psychobabble as is too common today.]

> "My approach to a theory of reality, which includes consciousness, is
> to postulate that reality is the vast entity (cf. Phillip K. Dick's VALIS)
> that underlies the entire set of A-D-E Coxeter graphs (and even goes
> beyond these graphs as V.I. Arnold has led the way)."

I think this is close to the Level IV Super Platonism in Max Tegmark's "Parallel Universes" in May 2003 Scientific American? All mathematics is implemented physically is his idea. You agree? You further think that V.I. Arnold's math may be the Mother of All Math - The Mathematical Theory of Everything. Then we have Wigner's "The Unreasonable Effectiveness of Mathematics in Physics."

On the VALIS theme, its historical roots are well-presented in Erik Davis's "Tech Gnosis."

> "This means that each of the
> many types of mathematical object that is A-D-E classified is a
> separate window into this vast reality. [Note: Mathematicians are wondering
> what mathematical entity underlies the A-D-E graphs. I say it is not a
> mathematical entity, but reality itself--physical, mental, and perhaps
> more than these (much debated) categories entail. The mathematics is the
> set of mathematical categories classified by the A-D-E graphs, each providing
> a different "map" of the territory of reality. The overall name for my
> approach is ADEX-theory -- the study and application of all the A-D-E
> graphs, with the X indicating the (mostly unknown) reality underlying
> the set of A-D-E classifications; and X also indicates the aspect of going
> beyond the A-D-E graphs via the three E type graphs as doorways into
> the enormous extension of the graphs (which has been only partly explored
> by V.I. Arnold and his students)."

OK. Good. This is the clearest you have been on this. I would like you to include this in the third book of the Space-Time and Beyond Series

"Star Gate Universe."
>
> "On eigenvalues: I believe that the deepest principle of quantum
> mechanics is that only eigenvalues (of measurement operators) can be observed."

Yes, that is true for orthodox micro-quantum theory like one sees in all the text books.

No question that Von Neumann measurement theory, that you summarize here ,works in its proper domain of validity, which is essentially scattering experiments using probe beams that are statistical ensembles of "single particle states" hitting targets that are also simple. The targets can also be many-particle systems in which the scattering is described in terms of target quasi-particles and collective modes as poles of single-particle and pair Green's equilibrium temperature-dependent Green's functions like in Bohm-Pines-Nozieres et-al work in the 50's on.

However, P.W. Anderson's "More is different" principle came in 1967 and was never absorbed into the thinking of the quantum measurement Pundits. For example, I see no evidence that Stapp and Penrose have any inkling of it? I could be wrong.

Note my paper "Goldstone Theorem and the Jahn-Teller Effect" 1966 with Marshall Stoneham at Theoretical Physics Division of UKARE, Didcot, Berks, Oxfordshire published in 1967 Proceedings of the Physical Society of London and cited in AIP Resource Letter on Symmetry in Physics, anticipates PW Anderson's "More is different". I was at Anderson's first talk on the subject at UCSD in 1967 where Wheeler would often also come to give long seminars that I attended. This was partly because I was in Keith Bruckner's group and they often had meetings of the DOD ARPA JASONs there. I also met Frohlich at UCSD. Frohlich told me "What is wrong in physics is the idea of the point particle." He agreed with Vigier on that one. Below I show how a spatially extended electron micro-geon in strong short range gravity induced by partially cohered zero point fluctuations (mainly vacuum polarization not electromagnetic) is stable and looks like a point particle as the resolution of the Heisenberg micro-quantum microscope is increased by increasing the energy in the center of mass of the probe-target frame. The basic explanation here is in Kip Thorne's picture P3 p. 31 in the Prologue of "Black Holes and Time Warps" where Kip writes:

"the circumference of the thick black circle is far less than 2pi times its radius"

This space warp increases as the momentum transfer p in the scattering increases since the Schwarzschild radial coordinate outside the event horizon

r ~h/p (Heisenberg microscope equation)

where the effective micro-gravity coupling on the scale of 1 fermi and less is G* ~ 10^40 G(Newton)

I say:

1. Orthodox "eigenvalue" quantum measurement theory, i.e. results of measurement are real eigenvalues of Hermitian generators of Unitary groups breaks down completely for emergent complex systems with MACRO-QUANTUM ODLRO in the ground state for real particles, and the vacuum for virtual particles because of what P.W. Anderson calls "generalized phase rigidity".

2. Of course, orthodox "eigenvalue" quantum measurement theory, equivalent to Stapp's "the statistical predictions of orthodox quantum theory, does apply to the elementary excitations (quasi-particles like dressed electrons in metals, and collective excitations like plasma oscillations) above the ground state (or vacuum in which case the elementary excitations are I suppose fundamentally the transverse string vibrations of the 2D world sheet you mentioned, but at lower energy they are the lepto-quarks and gauge force bosons etc. as first pointed out by Nambu in the 60's using the relativistic ODLRO super conducting vacuum where the Dirac energy gap 2mc^2 is essentially a non-analytic (z -
> 0) non-perturbative "BCS gap" of form we^-1/z. But the "eigenvalue" measurement folklore breaks down completely for the LOCAL MACROQUANTUM COHERENT CONDENSATE ODLRO GROUND STATE (VACUUM) ORDER PARAMETER (a complex number at low energy):

PSI(x) = (HIGGS FIELD(x))e^i(GOLDSTONE PHASE(x))

It's the "rigidity" in the GOLDSTONE PHASE local field (x is an event in 4D space-time that can be generalized to hyperspace with fermionic dimensions and even PSI itself may become a hypercomplex number when x is also a hypercomplex number as in non-commutative spacetime geometry) that prevents the "collapse" into "eigenvalues" of this huge non-classical local wave with the substantiality of a classical electromagnetic field as PW Anderson emphasizes in his series of More is different writings in "A Career in Theoretical Physics" (World Scientific).

For example, suppose I Fourier transform PSI(x) to get PSI~(p), in no sense can you PHYSICALLY do a kind of Stern-Gerlach filter measurement to get a power spectrum |PSI(p)|^2 as a measurement for p. There is no "diffraction grating" big enough to do the job! See Bohm's classic text "Quantum Theory" on the use of diffraction gratings to measure p etc.

The Born probability interpretation needed for the "eigenvalue" measurement folklore simply breaks down completely for MACRO-QUANTUM things. That is one of the implications for the "More is different" principle that is for emergent order of complex systems what the equivalence principle is for Einstein's gravity and what Heisenberg's uncertainty principle is for micro-quantum theory.

3. From the work of Antony Valentini we qualitatively understand why "signal nonlocality" e.g. the "presponse" of the MACRO-QUANTUM conscious mind is observed by Dick Bierman et-al

4. P.W. Anderson's phase rigidity is, for the unstable vacuum of the micro-quantum Dirac electron field in globally flat space-time is precisely Andrei Sakharov's "metric elasticity" for the "background independent" emergence of c-number Einstein gravity + unified exotic vacuum "dark energy/matter" out of the zero point vacuum fluctuations in a way consistent with t'Hooft-Susskind "world hologram" + Hagen Kleinert "world crystal lattice" + Bohm's realist interpretation.

5. All of the key phenomena of the new precision cosmology of dark energy and dark matter as well as of high energy physics i.e.

1. stability of the electron (Abraham-Poincare stress problem for self-energy that Feynman failed to solve)

2. zero point fluctuation induced rest mass of electron ~ 0.5 Mev ~ (e^2/c)/*zpf^1/2

2. point-like appearance of lepto-quarks in deep-inelastic SLAC scattering i.e. space-warp micro-geon effect

(close relation of quasi micro-black holes to your vibrating strings of M theory)

3. Universe Regge slope (string tension) of hadronic resonances - basic data of string theory

J ~ G*M^2/hc

(consistent with my "f-gravity" rotating black hole work with Abdus Salam at ICTP 1973-74) published in "Collective Phenomena" edited by Frohlich & Cummings)

G* = c^3Lp*^2/h

/*zpf = 1/Lp*^2

Lp* = Lp^2/3(c/H)^1/3 (world hologram) H is the Hubble cosmology parameter

Lp^2 - hG(Newton)/c^3

4. Blackett effect (actually astrophysics)

e ~ G*^1/2m
>
> "With respect to the A-D-E graph (read as classifications of Lie algebras)
> each graph node corresponds to a set of basic mirrors (which generate a
> full set of mirrors) in what I call reflection space, but could also be
> called eigenvalue space. This is because, attached to each mirror are
> two vectors called positive and negative roots. These roots carry a set of
> eigenvalues (one eigenvalue for each dimension of the reflection space,
> which is the number of nodes in the graph."

There is no doubt this applies to micro-quantum measurement theory in its proper domain of validity, which is part of "The Question" here. It may also have a more universal significance in MACRO-QUANTUM theory as the unfolding (topology change) of Rene Thom catastrophes on the complex hypersurfaces of PSI(x,L) as a wavelet transform at scale L. When PSI(x,L) is the human conscious mind field the topology changes of the PSI(x,L) landscape (as in complexity theory, e.g. Murray Gell-Mann's "The Quark and the Jaguar") signal emergence and fading away of conscious qualia.

When PSI(x,L) is the physical vacuum MACRO-QUANTUM PARTIAL COHERENCE of ALL the zero point fluctuations of the lepto-quark/gauge boson quantum fields, or ALL the transverse vibrations on the 2D string world sheet at the deeper level, then the topology changes are in the structure of the physical vacuum itself.

This immediately takes us to the "ICE 9" Doomsday WMD problem that Sir Martin Rees describes in Chapter 9 of his "Our Final Hour" book. Our book "Destiny Matrix", Saul-Paul, has reference to this "ICE 9" WMD issue and our book came out in November 2002 several months before Martin's! Also you and Elizabeth Rauscher may remember I wrote reports about this issue in 1973-74 from Abdus Salam's ICTP in Trieste. I lectured on it at the Nuclear Institute in Lubljana, Yugoslavia. Fred Alan Wolf was with me. One of the people who heard me talk in Lubljana was at the Vigier Conference in Paris Sept 2003. He told me he was there. I think it was Domitan Popescu? http://www.mindspring.com/~cerebroscopic/Program.html Lev Okun published and also told me that Andrei Sakharov was very worried about this problem in the same period the 1970's that Rees makes public. Okun's writing is in my Austin APS talk at http://qedcorp.com/APS/

Though the conventional nuclear, bio-chem WMD in Iraq may be Neo-Conned "Deception" rather than "Destruction", the WMD in the sky, whether asteroids colliding with earth or dark energy/matter "bottled" for small-scale technology use, is real in the not too distant future not imagined IMHO.

>
> " These roots are lattice points in the root lattice, and root
> eigenvalues are bosonic eigenvalues carried by the force-type
> particles.Dual to the root lattice is the weight lattice which carries fermionic
> eigenvalues."

OK at micro-quantum level of application of ADEX - nice insight.
>
> "Each root(as a set of eigenvalues) corresponds to a single
> eigenvector, which is a basis element of the Lie algebra corresponding to
> the Coxeter (Dynkin) graph. This is according to the Lie algebra
> eigenvector equation:
>
> AV = [A,V] = AV - VA = eV
>
> where A runs through a set of basis elements of the Cartan subalgebra of
> dimension equal to the rank r of the Lie algebra, i.e. the number
> nodes in the graph. Thus there will be r eigenvalues corresponding to a
> particular eigenstate V.
>
> The adjoint representation of the Lie algebra provides the root
> eigenvalues. Whereas other representations provide various weight
> eigenvalues. For example in E7, there is a 7-d Cartan subalgebra (and
> reflection space), a 133-d adjoint representation (corresponding to the
> dimensionality of the Lie algebra itself). So there are 126 non-zero roots,
> and 7 zero roots (corresponding to the 7 elements of the Cartan
> subalgebra that commute with each other). These 126 non-zero roots form the
> vertices of a 7- polytope (which defines the sphere packing of 126 6-d spheres
> around a central sphere in the 7-d reflection space. This is a lattice
> packing, and the lattice also generates the Hamming-7 error-correcting
> code. [Note: the IT (eigenvector) from BIT (binary error-correcting code),
> or BIT from IT, is evident in this mathematical structure.]
>
> The 126 roots carry bosonic eignevalues, so the IT in this case is
> bosonic. The fermionic eigenvalues are carried in a 56 vertex polytope
> (corresponding to the 56-d representation of the E7 Lie algebra.
>
> The ultimate IT from BIT must be in the E8 lattice, which is self-dual
> and thus does not distinguish between bosonic and fermionic
> eigenvalues.
> This lattice generates the Hamming-8 code (which is merely the
> Hamming-7 code with an extra parity check digit). And the E7 lattice structure
> is a sub-structure within the E8 lattice."

Yes, I agree this smells like something very fundamental as in

"The Word made Flesh" (Genesis Old Testament)

"IT FROM BIT" (Wheeler)

"We are such dreams that stuff is made from." (Variation on Shakespeare's "Tempest" Prospero)

"Explicating the Super-Implicate Order" (Bohm-Hiley)

>
> "The finite group generated by the mirrors is the Coxeter reflection group,
> and is (in Lie theory) called the Weyl group. This reflection group
> sends vertices of root polytopes into each other, and weight polytopes into
> each other. In this way the fundamental particle rules are obeyed.
> On collapse of the wave function (or rather projection of the state
> vector):I speculate that there is an infinitesimal "blip" of awareness
> associated with every reflection--i.e., with every change of eigenstate. A
> nervous system is a means of concatenating an enormous quantity of such
> "blips" of awareness into the rich experience we call individual consciousness."

Here I differ with you. What you suggest I think is too vague and cannot be mathematized.

This is where "More is different" comes in essentially.

Micro-quantum theory is

IT FROM BIT without BIT FROM IT is nonlocal micro-quantum theory with signal locality as shown in Bohm & Hiley p. 30 corresponding to Antony Valentini's "sub-quantal heat death" with Von Neumann measurement theory of projection to micro-quantum eigenstates - that all works well where it should for simple enough systems below the consciousness threshold IMHO.

"More is different" -
> BIT FROM IT

No action without reaction.

BIT = MIND

IT = MATTER

Generation of inner conscious qualia is "back-action" BIT FROM IT

Just as mind moves matter in IT FROM BIT

So matter induces consciousness in mind in BIT FROM IT.

Just as geometry moves matter along the timelike geodesic (neglect hyperspace Kaluza-Klein for now to keep it simple),

So matter warps geometry to induce gravity.

No action without reaction.

> "Now, because of the other A-D-E classifications, such as catastrophe
> structures (via V.I. Arnold's singularity theory approch), other
> aspects of the mind-body relationship come into the picture. The action of the
> reflection group on the reflection space generates the orbit space
> which is the base space of a catastrophe bundle. The mirrors of the reflection
> space get mapped onto the separatrix in the base space. The identity fiber is
> C^2/g (where g is a finite subgroup of SU(2). This is a singularity
> containing 4-d space, which when lifted up into the Lie algebra (in
> just the right way) becomes "desingularized". This is a hyper-Kahler manifold,
> and is a particular type of gravitational instanton whose "infinity" is the
> orbit space SU(2)/g. (This discription is due to Peter Kronheimer,
> 1989,1990)."

OK this is getting closer to what I am talking about above in a more informal "Wheeler" way.

>
> "The identity fiber C^2/g can also be "unfolded" by choosing a
> series of points on some path in the base space. Moving the along this path
> entails picking a new fiber at each point of the path -- and moving along the
> path corresponds to a time advancing. Whenever the path crossed the
> separatrix a topological change occurs in the fiber."

Yes, cool. Does this explain Brian Greene's "topology change" in current Sci Am "11 Dimensions"?
>
> "There is much more to say on this topic of catastrophe
> structure--base on the work of Rene Thom, V.I. Arnold and others. I will only point
> out the Thom himself regards the catastrophe bundle as a mathematical model of
> the interaction of "soul and body" in a single geometrical structure.
> And Arnold regards the great multiplicity of the A-D-E classifications
> as a 'manification of the mysterious unity of all things.'"

Yes, that is essentially the correct way to go IMHO.
>
> "In addition to the mathematical categories described above,there are at
> least a dozen other mathematical categories classified by the A-D-E
> graphs that can usefully be brought into the picture. I will mention only a
> half dozen.
>
> Conformal field theories (which live on the 2-d string world sheet)
> Heisenberg subalgebras of the A-D-E Lie algebras.
> Korweg de Vries hierarchies of non-liner equations
> Quantizing lattices (for analog-to-gigital transforms)
> Generalized braid groups (related to knots and links)
> Wave fronts.
>
> Nuff said ;-)
>
> Saul-Paul
>
>>
>> Correct me if I am wrong Saul-Paul but what is your picture of the
>> connection of this group structure to consciousness. Do you have in
>> mind orthodox quantum measurement theory with the results of
>> measurement being "eigenvalues" along lines of Wigner & Stapp i.e.
>> "collapse." I have argued against that view for consciousness. However,
>> the A-D-E structure also applies to catastrophies and in my picture
>> there is a MACRO Q-BIT landscape in ordinary space. Think of a giant
>> Bohmian real quantum potential Q in ordinary space made from PSI(x) the
>> coherent order parameter that is literally the physical mind field.
>> This PSI may have a fractal structure. Actually what we have is not
>> PSI(x) but a wavelet transform PSI(x,L) at scale L and so we have a
>> family of complex functions PSI at different scales L and there are
>> topology changes of this what sheaf of landscapes with coupling at
>> different scales - gets very complex and that's I think how V.I.
>> Arnold's theory of singularities come in. Indeed the dynamics of the
>> mental landscape, say in the real representation of Q(x,L) ~Q(x,L)^-1
>> Grad^2Q(x,L) (or maybe the wave propagation generalization) can
>> actually be pictured in computer simulations allowing us to literally
>> read thoughts! There is a great simplification in that the
>> MACRO-QUANTUM mental field of the living mind in my theory is a local
>> complex field in ordinary 3D space and a lot of its features can be
>> pictured in terms of the dynamics of the real MACRO-QUANTUM potential
>> Q. Of course both the amplitude and phase of PSI will also have
>> physical importance. Since MACRO-QUANTUM PSI is literally a fusion of
>> IT and qubit in the condensate one has to ask if there is any analog
>> to a localized ball rolling on it as there is in micro-quantum theory.
>> The answer I think is no. But there is a distributed say electric dipole
>> moment IT distribution D(x,L) in two-way relation to the BIT PSI(x,L).
>> D(x,L) at some scale L will be directly related to nerve impulse
>> firing patterns for example. On smaller scales to MRI and so on.
> From: Thomas D Angelidis
> Date: Wed Oct 22, 2003 9:03:10 AM US/Pacific
> To: Jack Sarfatti , S-P & M-M Sirag
>
> Subject: Re: Conformal Group & Exotic Vacuum Dark Energy/Matter Link?
>
> On Tuesday, October 21, 2003, at 09:28 pm, Jack Sarfatti wrote:
>
>
>>> On Monday, October 20, 2003, at 04:27 PM, S-P & M-M Sirag wrote:
>>> ..............
>>> There is, of course, one force missing in the above unification --
>>> gravity.
>
>>
>> There you need Diff(4) from breaking the 4-parameter translation
>> subgroup of the 10 parameter Poincare group. Gravity as curved
>> spacetime is a broken symmetry of global translational invariance.
>> The Poincare group, in turn, is from breaking I suppose a 5-parameter
>> subgroup of the 15 parameter conformal group of the light cone used
>> in Penrose's "twistors." One parameter is dilation. I forget - what
>> are the other 4? What is the physical interpretation of the 5
>> additional generators of the Conformal group Lie algebra? 4-momentum
>> from translation sub-group and space-time rotations from 6-parameter
>> Lorentz sub-group. What are the others? Shipov in his torsion theory
>> seems to want to break the symmetry of the 6 Lorentz group parameters
>> to get the torsion twists generalization of space-time rotations!
>> That makes sense actually. What about those 5 conformal generators?
>>
>> Starting from 15 parameter conformal group of the light cone,
>>
>> C(15) = ?(5) T(4)O(1,3)
>>
>> Is ?(5) = D(1)?(4)?
>>
>> D(1) a one parameter dilation whose breaking of symmetry introduces
>> the rest mass m into E^2 = (mc2)^2 + (pc)^2 mass shell
>>
>> What are the 4 missing generator "charges" to add to 4-momentum and
>> space-time rotations?
>>
>> What about the dilatation and the 4 other things? What are they
>> physically? They should already be there in global special relativity
>> without gravity hidden as rest masses of quantum fields in some way?
>>
>> The 4 other "charge" generators of the conformal group, must,
>> therefore, be the 4-gradient of the Higgs Field! That sort of makes
>> physical sense. Will there be a compensating gauge field?
>>
>> to be continued
>>
> Professor Angelides wrote:
> "Jack and Saul-Paul, the 4 missing elements of the special conformal
> group are known as inversions (actually, they are products of
> inversions and translations)."

Aha! Thanks. I need to do some homework on that. I am glad to see the Lie algebra of the missing stuff is not too different from that of the Pu Lie algebra. I was worried about that. I am glad to see that essentially we have another copy of the translation group since I need two such copies to modulate both the Goldstone phase and Higgs amplitude of my QED vacuum polarization partial coherence ODLRO parameter PSI(x,L). I get Einstein's gravity from locally gauging one of those translation sub-groups in the usual way Kibble did it at Imperial College in the 60's and I think we should get the unified w = -1 exotic vacuum dark energy/matter field by locally gauging this second copy of the translation group with the extra "inversion". Is this related to Brian Greene's "mirror symmetry" with "two geometries and one physics" in the current Sci Am?
>
> "Geometrically, this is done by the successive application of an
> inversion f^1 through a unit circle centered at the origin O, an
> inversion f^2 through a unit circle
> at some point, say, p, and a translation f^3 by the vector Op. That
> is, f^3 o f^2 o f^1 (o stands for composition).
>
> The conformal inversion maps infinity, which is not a point of
> Minkowski spacetime, into a finite point and conversely. The action of
> the conformal group is
> defined on the so-called conformally compactified Minkowski spacetime."

Right which is important in Penrose's Twistor theory that I vaguely remember from attending his seminars at Birkbeck in 1971. BTW Thomas I will have access to a 2Bdr apartment in Kensington section of London soon, so I will be seeing you and Simon. Will take Saul-Paul.
>
> "What are they physically ? In the physics literature, these elements
> have been referred to as "acceleration transformations". Whether these
> can be linked to
> gravity, I am not so sure..."

Any URLs on this. This is something I must understand much better since it is the modulation of the Higgs in my model that gives the lepto-quark rest masses like

m(electron) ~ (e^2/c^2)/zpf*^1'2

where /zpf* = 1/Lp*2

in the quantized circulation "vortex core" of the micro-geon "ring singularity" (A Ya Burinski, Vigier IV Paris Sept 2003) where Higgs Field -
> 0 like in a Type II superconducting lattice.
>
> "One last point of logic: Since all these "small" groups are subgroups
> of Diff(4), then whenever Diff(4) holds, so does each of its subgroups
> a fortiori.
>
> I hope this helps."

What I mean here is that in Einstein's curved space-time the translation subgroup of the global Poincare group no longer holds. Of course, you can say that once the translation sub-group is locally gauged then the local conservation of Pu is restored including the curvature as a dynamical degree of freedom as in the Bianchi identities -
> Tuv(x)^;v = 0

Now all that comes from Kibble's locally gauging only the translation sub-group of the 10 parameter Poincare group.

I think Utiyama in 60's locally gauged the full 10 parameter Poincare group to get the torsion fields from the 6 parameter Lorentz group years before G. Shipov got there.

My question now is what is the physics of locally gauging the dilaton + the 4 translations with these "inversions"?

If my theory is right what we get physically are dark energy/matter exotic vacuum fields.

That is gravity + torsion + exotic vacuum dark energy/matter + dilation field We know that Universe is 96% exotic vacuum at large FRW scale.

We did not really know that last year for sure.
>
> A"ll good wishes
>
> Thomas.
>
> PS Jack, your references to the so-called quantum nonlocality and
> signal locality (a rather silly idea) etc need to be corrected (but I
> am not going to start
> quoting chapter and verse; you know what I mean...). "

On that we really need to Pow Wow at length with The Pundits including Hiley, Valentini, Stapp, Bierman (the experimentalist) and Duke it all out. :-)

A good place to do this is Simon's Private London Club on Portman Square which has wireless for our laptops. I will get to London ASAP probably early next year for an extended stay of a week or two or three depending on how long I can get the Kensington apartment at that time.

I suppose you mean "quantum nonlocality" is the "silly idea" since you argue for "signal locality". The big issue is "signal nonlocality" for which there is evidence IMHO. How good that evidence is, is also part of "The Question."

Sirag wrote:
> Jack & Thomas,
>
> On the role of the conformal group SU(4) or SU(2,2):

Yes, for Penrose twistor spinor of conformal space-time.

>
> The extended E7 Coxeter graph is
>
> 1-2-3-4-3-2-1
> |
> 2
>
> From this it follows via the McKay correspondence between the E7 (Kac-Moody)
> Lie algebra and OD (the octahedral double group as a subgroup of SU(2)) that
> the complex group algebra C[OD] is equivalent to the direct sum of total
> matrix algebras:
>
> C[OD] = M1 + M2 + M3 + M4 + M3 + M2 + M1 + M2
>
> Since the squares of the numbers on the Coxeter graph (which I call balance
> numbers) sum to 48 (in accord with the 48 elements of OD), we see that the
> matrix algebras span the full 48-d vector space of C[OD].
>
> In my "Consciousness: a Hyperspace View" paper (published in 1993 as a 40
> page appendix in Jeffrey Mishlove's book *Roots of Consciousness*) I wrote:
>
> In the scheme of this paper E7 is the high-energy symmetry group, but
> because of the McKay correspondence between E7 and OD, the unitary group P
> in C[OD] is a 48-d principal bundle projecting down to a 10-d base space S,
> each point of which is a copy of the 38-d fiber G. We write these spaces out
> as the following Lie groups:
>
> S = U(2) x T^6;
> G = U(1) x SU(2) x SU(3) x SU(3) x SU(4) x SU(2)
>
> where U(2) is a 4-d spacetime called *conformally compactified
> Minkowski
> space*; T^6 is a 6-d torus = U(1) x U(1) x U(1) x U(1) x U(1) x U(1).
> We consider S as the 10-d spacetime of superstring theory and G as the
> symmetry group of the following six forces, which we identify in sequence
> as: electromagnetism, weak, strong (color), hyperweak, gravity and perhaps
> the feeble force.
> We can write: P = S x G. Since U(2) = U(1) x SU(2), we can rearrange S
> as S = SU(2) x T7. We regard SU(2), i.e., spherical 3space S^3, as the space
> of cosmology -- the space in which we as macroscopic bodies appear to live.
> Every point of a macroscopic body is a point of S^3. Thus, if we view
> S as a fiber bundle, every point of a macroscopic body is actually a 7-d spce
> which is a copy of T^7. Note that the 7=torus T^7 incorporates the factor
> U(1) from the U(2) spacetime, and thus includes time. Now T^7 corresponds
> (via McKay's theorem) to the 7-d reflections space of E& as follows:
>
> T^7 = R^7/Lr
>
> where R^7 is the *real* part of the E7 complex reflection space C^7, and Lr
> is the E7 root lattice. This means that all the points of the lattice
> are identified as a single point, the identity element of T^7, and every
> other point of T^7 is a copy of Lr.
>
> [end of quote from my 1993 paper]
>
> Note that SU(4) is the 15-d conformal group, and if you need a fancier
> version of this group it is sitting in C[OD] as M4 -- which is the set of
> all 4 by 4 complex matrices. The set of all invertible elements in M4 is
> GL(4,C), and the set of all unitary elements is U(4) = U(1) x SU(4).
>
> This is the paper that John McKay referred to in his short paper "A
> rapid introduction to ADE theory," which can be found at:
>
> http://math.ucr.edu/home/baez/ADE.html
>
> [Note:
> It may be that the cosmological space of this paper S^3 = SU(2) should
> be replaced by SU(2)/g where g is a finite subgroup of SU(2). McKay's
> correspondence consists of a profound A-D-E classification of these
> subgroups, which I have called McKay groups.
>
> Cf. October 9 *Nature* paper by Luminet et alia.
>
> Morover, in 1989 Peter Kronheimer (a graduate student of Michael Atiyah)
> proved the A-D-E classification of C^2/g as gravitational instantons
> (closely related to twistor structures). The "infinity" of any such
> instanton is SU(2)/g.
>
> In addition, it is very interesting that C^2/g is the identity fiber of
> an A-D-E classified (via V.I. Arnold) Thom type catastrophe bundle.
>
> BTW: There is a different conformal invariance involved in string
> theory. The 2-d world sheet is conformally invariant (and 2-d Lorentz
> invariant) so that a 2-d conformal field theory lives on this space -- and
> is a basic entity in superstring theory. And it just so happens that 2-d
> conformal field theories are A-D-E classified.
>
> For this and many other reasons, I believe that the study of all
> classifications of the A-D-E graphs (which I call ADEX theory) is the key to
> the deep study of reality.
>
> All for now.
>
> Saul-Paul

I have not yet absorbed your last message Saul-Paul. Leaving for Austin, Texas soon.