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Refuting Waldyr Rodrigues on "Emergent Gravity"
Note in my model Kiehn's topological torsion not to be confused with
metric torsion T^a below is C^ac/\dC^cb = 2(A^a/\dBc - dA^a/\Bc)/\dA^c/\dB^b = 2[A^a/\dBc/\dA^c/\dB^b - dA^a/\Bc/\dA^c/\dB^b] Is this zero? Note Minkowski metric raises and lowers indices here. Is dBc/\dA^c = 0 ? Is Bc/\dA^c - 0? If it's not then Kiehn's macroscopic spinors may play a role in my emergent gravity theory that Waldyr still is not able to grasp physically. But even if it is zero, it does not affect my derivation below of Einstein's GR from the Goldstone phases of the vacuum ODLRO inflation field. This is a new way of thinking completely alien to Waldyr's mind set - and to those of others besides him. Waldyr is not the only one blinded by the light outside The Cave. ;-) Meantime note that I get the world hologram result that the quantum gravity length uncertainty is deltaL = Lp^2/3L^1/3 automatically. I knew I had seen that before. That is, we have projected in 3D space only three of the 9 real Higgs-type vacuum ODLRO components with only 2 effective Goldstone phases giving stable point topological defects i.e. where all three Higgs fields vanish at the points of Kleinert's world lattice. http://mathworld.wolfram.com/CubicLattice.html The black dots are zeros of the LOCAL vacuum ODLRO parameter in 3D spacelike slice of 4D space-time where the two Goldstone phases are undefined i.e. point defects from non-trivial second homotopy group mapping from 3D space to S2 vacuum manifold as in David Thouless's book on topology in QM. Consider a closed surface of area A surrounding N point defects. Assume ONE BEKENSTEIN BIT PER ENCLOSED NODE WORTH ONE QUANTUM OF AREA Lp^2 = hG/c^3 = 10^-66 cm^2 Therefore A = NLp^2 Let n = density of point defects Therefore N = nV Therefore A = nVLp^2 Therefore n = (A/V)(1/Lp^2) = (AREA/ENCLOSED VOLUME)1/(QUANTUM OF AREA) Define 1/L = (AREA/ENCLOSED VOLUME) Therefore, in analogy with the line vortex lattice in a type II superconductor for first homotopy one Goldstone phase Point Defect World Lattice Density = 1/LLp^2 NOW WHERE HAVE WE SEEN THAT BEFORE? World Lattice Spacing = (LLp^2)^1/3 = L^1/3Lp^2/3 the oft-discussed on archive basic world hologram formula for quantum gravity metric fluctuation over scale L! Note this is like a tube of cross section Lp^2 of length L whose cube root volume maps to a cubic lattice spacing. Now when you use the measured dark energy curvature /\ = 10^-56cm^-2 World Lattice Spacing ~ 1 fermi = 10^-13 cm, i.e. a micro-nanometer or 1 Gev nucleon mass On Nov 20, 2006, at 10:04 AM, Jack Sarfatti wrote: PS the emergent tetrads are on the diagonal of C^a^b = A^a/\dB^a - dA^a/\B^b i.e. a = b Obviously the off-diagonals are essentially the CONNECTION field where the spin connections are W^a^b = C^a^b - C^b^a D = d + W/\ Metric torsion is the diagonal form T^a = dC^a^a + W^ac/\C^c^c Curvature is the off-diagonal form R^a^b = dW^a^b + W^ac/\W^c^b Therefore, contrary to what Waldyr Rodrigues wrote on the archive, I have derived Einstein's GR plus the additional structure in Kibble 1961 from vacuum ODLRO Let me be more specific Given eight Goldstone 0-forms A^a and B^b (9 real components to the Higgs field for spontaneous broken ODLRO symmetry) a,b = 0,1,2,3 C^a^b = A^a/\dB^a - dA^a/\B^b So things like dA/\dA are really dA^ac/\dA^c^b Will this kind of formal system (my model for the cosmic inflation field and emergent gravity in my archive paper) have your macroscopic spinors and be "non-equilibrium" as you mean it? Jack Sarfatti "If we knew what it was we were doing, it would not be called research, would it?" - Albert Einstein On Nov 20, 2006, at 7:34 AM, wrote: Dear sirs. I recently was told about your article http://xxx.lanl.gov/abs/quant-ph/0208068 in which you referred to my remarks in Bohmplus.pdf http://www22.pair.com/csdc/pdf/bohmplus.pdf * Let me inform you that that this article was conceived 30 years ago (1976), and is now published, in an updated version, as chapter 5 in volume 3 of a series of monographs on Non-Equilibrium Systems and Irreversible Processes, Vol 3 "Wakes, Coherent Structure, and Turbulence" R. M. Kiehn ISBN 978-1-84728-195-1 This and my other monographs can be obtained from http://www/lulu/com/kiehn in paperback form. I would appreciate if you would reference my works as they appear in these monographs, even though they appear as downloadable files on the internet. * The original article made note of the fact that there was an exact map between the Schroedinger equation in 2D + time (for an electron in an EM field) and the viscous compressible Navier-Stokes fluid, where the square of the Wave-Function was proportional to the square of the vorticity in the viscous fluid. Hydrodynamicists call this function "Enstrophy" * I was always interested in extending the ideas to a 4D system, but the solution was not found when the first draft of the monograph was published (2004) The topic was included in the second draft (early 2005) * Since that time I have realized that macroscopic Spinors are to associated with all non-equilibrium systems. Such objects (macroscopic Spinors) are eigendirection fields of anti-symmetric matrices. AS thermodynamics systems can be encoded in terms of a 1-form of action, A, the derived 2-form, F=dA always leads to an antisymmetric matrix describing the possibility of continuous topological (not necessarily geometrical) evolution. If the system satisfies A^dA = 0 , then the system is in a state of isolated equilibrium. If A^dA is not zero, then the system is not uniquely integrable, the thermodynamic system is not in equilibrium, and here is where the macroscopic Spinor pairs arise. There is a remarkable relationship between macroscopic Spinors, Surfaces of zero mean curvature, and Harmonic vector fields * The bottom line is that Spinors are NOT necessarily artifacts of microscales or relativity theory, but are artifacts of certain topological structures * In another representation, consider a set of basis vectors (or verbeins) as matrices that will map linear systems of perfect (exact) differentials into (perhaps) non-exact combinations of differentials, or a vector of 1-forms. Then it is possible to compute the Cartan connection matrix, which will be anti-symmetric if the basis set is orthonormalized. The anti-symmetry leads to the concept of Affine Torsion. However, if the system of 1-forms is integrable, then the Affine torsion can be mapped away. But, if the systems of 1-forms is not integrable, the Affine torsion can not be mapped away, and therefore Macroscopic Spinors will enter the solution set. * I am now inspired to address the Bohm-Arahanov fluid problem in 4D as a global Symplectic structure that can decay by means of dissipative processes into emergent compact domains (topological defects) with a Contact structure. Both systems are far from equilibrium for the Symplectic structure is of Pfaff topological dimension 4 and the Contact structures is of Pfaff topological dimension 3. This work will appear in Vol 5 of the monograph series. * "Topological Torsion and Macroscopic Spinors" R. M. Kiehn * I know that the Contact structure admits one conjugate pair of macroscopic Spinors, and the Symplectic structure admits two conjugate pairs of macroscopic spinors. * Regards, R.M.Kiehn http://www.cartan.pair.com |
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