Heuristically, gauge boson (virtual photon) transfer between charges to cause electromagnetic forces, and those gauge bosons don't discriminate against charges in neutral groups like atoms and neutrons. The Feynman diagrams show no way for the gauge bosons/virtual photons to stop interactions. Light then arises when the normal exchange of gauge bosons is upset from its equilibrium.

You can test this heuristic model in some ways. First, most gauge bosons are going to be exchanged in a random way between charges, which means the simple electric analogue is a series of randomly connected charged capacitors (positive and negative charges, with vacuum 377 ohm dielectric between the 'plates'). Statistically, if you connect an even number of charged capacitors in random along a line across the universe, the sum will be on average be zero. But if you have an odd number, you get an average of 1 capacitor unit. On average any line across the universe will be as likely to have an even as an odd number of charges, so the average charge sum will be the mean, (0 +1)/2 = 1/2 capacitor. This is weak and always attractive, because there is NO force at all in the sum = 0 sum case and attractive force (between oppositely charged capacitor plates) in the sum = 1 case.

Because it is weak and ALWAYS attractive, it's gravitation?

The other way they charges can add is in a perfect summation where every charge in the universe appears in the series + - + -, etc. This looks improbable, but is statistically a drunkard's walk, and by the nature of path-integrals gauge bosons do take every possible route, so it WILL happen. When capacitors are arranged like this, the potential adds like a statistical drunkard's walk because of the random orientation of "capacitors", the diffusion weakening the summation from the total number to just the square root of that number because of the angular variations (two steps in opposite directions cancel out, as does the voltage from two charged capacitors facing one another). This vector sum of a drunkard's walk is the average step times the square root of the number of steps, so for ~10^80 charges, you get a resultant of ~10^40.
The ratio of electromagnetism to gravity is then (~10^40)/(1/2).

Notice that this proof shows gravity is caused by the same agent as electromagnetism; by gauge bosons. It does away with needing separate quantum gravity and unobserved gravitons.

The distances between the charges are ignored. This is explained because on average half the gauge bosons will be going away from the observer, and half will be approaching the observer. The fall due to the spread over larger areas with divergence is offset by the concentration due to convergence.

The Feynman problem with virtual particles in the spacetime fabric retarding motion does indeed cause the FitzGerald-Lorentz contraction, just as they cause the radial gravitationally produced contraction of distances around any mass (equivalent to the effect of the pressure of space squeezing things and impeding accelerations). What Feynman thought may cause difficulties is really the mechanism of inertia:

Maxwell’s 1873 Treatise on Electricity and Magnetism, Articles 822-3: ‘The ... action of magnetism on polarised light [discovered by Faraday not Maxwell] leads ... to the conclusion that in a medium ... is something belonging to the mathematical class as an angular velocity ... This ... cannot be that of any portion of the medium of sensible dimensions rotating as a whole. We must therefore conceive the rotation to be that of very small portions of the medium, each rotating on its own axis [spin] ... The displacements of the medium, during the propagation of light, will produce a disturbance of the vortices ... We shall therefore assume that the variation of vortices caused by the displacement of the medium is subject to the same conditions which Helmholtz, in his great memoir on Vortex-motion [of 1858; sadly Lord Kelvin in 1867 without a fig leaf of empirical evidence falsely applied this vortex theory to atoms in his paper ‘On Vortex Atoms’, Phil. Mag., v4, creating a mathematical cult of vortex atoms just like the mathematical cult of string theory now; it created a vast amount of prejudice against ‘mere’ experimental evidence of radioactivity and chemistry that Rutherford and Bohr fought], has shewn to regulate the variation of the vortices [spin] of a perfect fluid.’

‘… the source of the gravitational field can be taken to be a perfect fluid…. A fluid is a continuum that ‘flows’... A perfect fluid is defined as one in which all antislipping forces are zero, and the only force between neighboring fluid elements is pressure.’ – Professor Bernard Schutz, General Relativity, Cambridge University Press, 1986, pp. 89-90.

‘In this chapter it is proposed to study the very interesting dynamical problem furnished by the motion of one or more solids in a frictionless liquid. The development of this subject is due mainly to Thomson and Tait [Natural Philosophy, Art. 320] and to Kirchhoff [‘Ueber die Bewegung eines Rotationskörpers in einer Flüssigkeit’, Crelle, lxxi. 237 (1869); Mechanik, c. xix]. … it appeared that the whole effect of the fluid might be represented by an addition to the inertia of the solid. The same result will be found to hold in general, provided we use the term ‘inertia’ in a somewhat extended sense.’ – Sir Horace Lamb, Hydrodynamics, Cambridge University Press, 6th ed., 1932, p. 160. (Hence, the gauge boson radiation of the gravitational field causes inertia. This is also explored in the works of Drs Rueda and Haisch: see http://arxiv.org/abs/physics/9802031 http://arxiv.org/abs/gr-qc/0209016 , http://www.calphysics.org/articles/newscientist.html and http://www.eurekalert.org/pub_releases/2005-08/ns-ijv081005.php .)