Dear Peter Cameron,
Thank you for re-reading my essay. I very much appreciate it. I have also reread your essay and it is no surprise that you feel as you do. We believe too many different things for them to make sense. First let me repeat my main thesis that physicists project math structure onto reality, then come to believe that physical reality has that structure. Cristie Stoica discusses isomorphism. Mathematicians know that one structure is isomorphic to another [see his 'number Scrabble' versus 'tic-tac-toe'] and can easily switch between them. But physicists "freeze" one structure as physical reality, and get stuck there.
You ask me to define 'local gravity'. I feel local gravity at this moment. It pulls me toward the center of the Earth with a strength and preferred direction that differs from the gravity I find in the asteroid belt, or between galaxies. Light is deflected in gravity, and, even according to Einstein, "propagates" in gravity.
We have very different concepts of the 'wave function'. Like Bell, I believe it is real and possesses energy. In my reply to Christian Corda above, I reference The Nature of Quantum Gravity, based on the gravito-magnetism of ultra-dense matter, such as the electron. This picture is of the deBroglie-Bohm-like induced waves [ del x C ~ rho v ] and is compatible with Born's probability interpretation, so I think of it as physically realistic at the particle level. It is a wave function that is compatible with deBroglie, Born, Bohm (to some extent) and explains Bohr's 'orbits' and two-slit behaviors. It also makes sense statistically, i.e., for quantum mechanics. I do not believe this is the way in which you conceive of 'wave functions'.
Similarly, you identify a 'medium' as curvature. I do not. Einstein's 'curvature' is equivalent to energy density in Cartesian space. You note Hestenes and others demonstrated equivalence of GR in 'curved space' and gauge theory gravity in flat Minkowski space. Weinberg and Feynman separately showed the same thing. So 'curvature' is not really part of my thinking - it effectively leaves out the mass and focuses on empty space surrounding mass. It is the inverse of distributed energy density and is of limited utility. Even so, the gravito-magnetic field "curves" around ultra-dense matter in motion, but I view this as curvature of the field, not of space.
One result of the above is that I find no use for the 'vacuum wave function'. QFT is to me a "bookkeeping scheme", that ignores the physics of particles while keeping track of the results of this physics in terms of 'excitations' in the vacuum. It is generally isomorphic to the phonon excitations of condensed matter physics. Calculations of vacuum energy are off by 123 orders of magnitude, called "the worst error in physics". Again, Feynman diagrams replace continuous reality with the lattice of 'events', and provide a bookkeeping scheme based largely on conservation of energy. Sometime 'ghosts' are needed to preserve energy, but they are projected into the formalism without a second thought.
To switch topics a little, in The Nature of Quantum Gravity I discuss Ohanian and Ruffini's statement:
"That the linear equations imply the full nonlinear equations is a quite remarkable feature of Einstein's theory of gravitation."
Most physicists believe that Einstein's "weak field equations" [contained in eqns(1) of my essay], by virtue of this linearity, actually apply to linear gravity, as if removing non-linear terms from a description actually has an effect on the physical field. It does not. The non-linear terms are recovered by iteration. Gravity is always non-linear. It might be of interest to you that a treatment of Einstein's 'weak-field' equations based on Geometric Algebra makes no use at all of the concept of field strength, hence 'weak-field' is not a relevant concept for GA, only for Einstein tensors.
To summarize, I identify non-linear gravito-magnetic field as the continuum reality on which our universe is based. When Big Bang and LHC energies exist, the field behaves like a perfect fluid. Particles 'condense' according to the laws of equations(1) and then interact. The gravito-magnetic circulation and ultra-dense matter is equivalent to deBroglie's wave particle postulate that underlies quantum mechanics. It is what Bell was searching for. The 'quantum vacuum' is a figment, an isomorphism of the bookkeeping scheme that ignores gravity and keeps track only the results of such interactions. It is sufficient to solve statistical physics problems but cannot even calculate the masses of the particles. Pauli's 'qubit', Heisenberg's iso-spin, and SU(3) etc. symmetries are projections of math mistaken as realities of physics. For more on this aspect of quantum projection, see my response to Cristi Stoica above at Feb. 20, 2018 @ 00:56 GMT.
In short, it is no wonder you have trouble making sense of my essay. I respect you for trying to do so.
My very best regards,
Edwin Eugene Klingman