Rueda and Haisch, Physical Review A v49 p 678 (1994), showed that the virtual radiation of electromagnetism can cause inertial mass, and in Annalen der Physik v14 p479 they do the same for gravity in general relativity. The virtual radiation acts on fundamental particles of mass, quarks and electrons, which are always charged. It doesn’t ignore all the quarks in a neutron just because they have no net charge. A gauge boson going at light speed doesn’t discriminate between neutrons and protons, only the fundamental quarks inside them. Therefore, the background field of virtual radiation pressure besides causing inertia (and the contraction of moving objects in the direction of motion) also causes gravity (and the contraction in the direction of gravitational fields, the reduction in GR).
The coupling constant for electromagnetism is then naturally related to gravity. Between similar charges, the electric field causing the radiation pressure adds up like a series of batteries. In any line, there will be approximately equal numbers of both charges, so the sum will be zero. The only way it can add up is by a drunkard’s walk, where the statistics show the net charge will be the square root of the number of similar charges in the universe. Since there are 10^80 charges, electromagnetism will be 10^40 times stronger than gravity. Attraction is due to opposite charges screening each other and being pushed together by the radiation from the surrounding universe, while repulsion is due to the fact that nearby charges exchange gauge bosons which aren’t redshifted by cosmic expansion (and so produce a mutual recoil), while the radiation pushing them together is red-shifted by the big bang and so is weaker.
Lunsford’s CERN document server paper http://doc.cern.ch//archive/electronic/other/ext/ext-2003-090.pdf discounts the historical attempts by Kaluza, Pauli, Klein, Einstein, Mayer, Eddington and Weyl. It proceeds to the correct unification of general relativity and Maxwell’s equations, finding 4-d spacetime inadequate: ‘… We see now that we are in trouble in 4-d. The first three [dimensions] will lead to 4th order differential equations in the metric. Even if these may be differentially reduced to match up with gravitation as we know it, we cannot be satisfied with such a process, and in all likelihood there is a large excess of unphysical solutions at hand. … Only first in six dimensions can we form simple rational invariants that lead to a sensible variational principle. The volume factor now has weight 3, so the possible scalars are weight -3, and we have the possibilities [equations]. In contrast to the situation in 4-d, all of these will lead to second order equations for the g, and all are irreducible - no arbitrary factors will appear in the variation principle. We pick the first one. The others are unsuitable … It is remarkable that without ever introducing electrons, we have recovered the essential elements of electrodynamics, justifying Einstein’s famous statement …’
D.R. Lunsford shows that 6 dimensions in SO(3,3) should replace the Kaluza-Klein 5-dimensional spacetime, unifying GR and electromagnetism: ‘One striking feature of these equations ... is the absent gravitational constant - in fact the ratio of scalars in front of the energy tensor plays that role. This explains the odd role of G in general relativity and its scaling behavior. The ratio has conformal weight 1 and so G has a natural dimensionfulness that prevents it from being a proper coupling constant - so this theory explains why ordinary general relativity, even in the linear approximation and the quantum theory built on it, cannot be regularized.’