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Refutation of Waldyr Rodrigues's Archive Remarks on "Emergent Gravity"
see discussion forum at http://stardrive.org
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 the CONNECTION where the spin connections are W^a^b = C^a^b - C^b^a D = d + W/\ Metric torsion is T^a = dC^a^a + W^ac/\C^c^c Curvature is 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 On Nov 20, 2006, at 9:54 AM, Jack Sarfatti wrote: Hi Robert Given two 0-forms A and B (Goldstone phases of a vacuum ODLRO inflation field) Construct the 1-forms (emergent tetrads that also come from localizing T4 as in Kibble 1961) C = A/\dB - dA/\B dC = 2dA/\dB So what is C/\dC? Is it zero or not? 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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Refutation of Waldyr Rodrigues's Archive Remarks on "Emergent Gravity"
To Happy Jack,
Jack Sarfatti wrote: see discussion forum at http://stardrive.org PS the emergent tetrads are on the diagonal of C^a^b = A^a/\dB^a - dA^a/\B^b i.e. a = b I know ascii notation sucks, but it takes time to work what you meant to equationalize, probably I'm just bitchin on a typo. Ken .... |
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