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Dear Ed,
Your Master Equation seems to generate the correct types of fields, but I am concerned that these limited fields (G,C,E,M) in 4 dimensions do not contain enough degrees of freedom to account for all known generations of "fundamental particles" - at least an SO(10) of fermions and an SU(5) of bosons. You begin with continuous fields only, and try to insert quantized "fundamental particles", but you omitted talking about Second Quantization, and this is the most accepted method for obtaining quantized particles from continuous fields. I also didn't discuss Second Quantization in my essay, because I proposed that fields and particles are both necessary complementary inverse scales.
Tajmar's explaination of a mass increase in Niobium Cooper-pairs is interesting. Superconductivity has also been implied to be the bridge between electromagnetism and gravitation by Chiao's and Podkletnov's research teams. You mention a kappa ~ 10^31, but Chiao says that a gravitational wave should have an effect of 42 orders in magnitude. I agree with Chiao because this is of order Dirac's Large Number ~ 10^41, which is one of my scale numbers (please see Equation 15 of my book for the relationship between electromagnetic and gravitational couplings). Now we can explain the Cosmological constant of Lambda ~ 10^(-123) ~ (10^41)^(-3) by the fact that we have three spatial dimensions (you said "If scale invariant is motion invariant, time has no obvious meaning"). I think that your inverse square-roots (~10^61) and inverse fourth-roots (~10^31) of Lambda should be replaced by inverse cube-roots (~10^41 - Dirac's Large Number) or by new modeling.
By the way, this variance in Niobium Cooper-pairs is fairly small. A change in the application of Statistical Mechanics may make-up this difference. Please contrast my Prespacetime Journal volume 1 issue 9 paper with Chapter 4 of my book.
You said that the "curvature of space is limited". I agree. At some energy level, we will promote matter-anti-matter pairs out of the Dirac Sea, and this may have a lattice-like "pinching off of Spacetime" effect. I propose that the core of a static black hole may be surrounded by a Buckyball (a nearly spherical lattice that has lattice bonds to resist it from being deflated by the gravitational near-singularity) consisting of the very fabric of Spacetime. The curvature of the Buckyball initiates Spacetime curvature. There is a smooth homotopy between a pair of nested Buckyballs and a lattice-like torus (donut), and this application may be appropriate for rotating Black Holes. In fact, normal Carbon fullerenes (such as the Buckyball) may have superconductor characteristics. Is the Black Hole core a Superconductor? If so, then a rotating superconducting GEM torus would produce a powerful dynamo. That would tie your ideas, my ideas, and Tajmar's, Chiao's and Podkletnov's ideas together...
I still disagree about 4 fundamental particles, but your field approach is interesting...
Have Fun!
Dr. Cosmic Ray