The model of the elementary particles presented in the first post makes it tempting to philosophize over the nature of mass and gravitation. Is there a logical concept of these matters that smoothly fits in? I have made an attempt to find one...
Obviously, a clue must be that the mass of at particle is proportional to its total energy. Assuming that electromagnetic waves travel in a background medium1, one should expect that the waves displace some of it. In fact, it is this displacement that defines the wave. In the enclosed waves making the elementary particles, the net displacement of medium is radially outwards because of the 180° twist for each half wavelength. This will hold true for simple circular waves as well as for folded ones. The more energy contained in an enclosed wave, the more medium it displaces. The mass is a measure of the total medium displacement, and is therefore a function of the total energy of the wave. Generally, outside the enclosed wave the medium will be compressed, and inside the wave it will be diluted2. This assumes an elastic medium. If the background medium is perfectly elastic, the gravitational field will never reach zero.
Because the electromagnetic wave compresses the medium in two dimensions (and not in three), the degree of the compression is inversely proportional to the square (and not to the cube) of the distance from the wave-particle. Gravitation is therefore an inverse-square law.
This interpretation can explain the gravitational attraction observed between two objects with mass: When the compression of medium created by one particle partly coincides with the dilution created by another, their total displacement of medium is reduced. Their total mass and energy are reduced accordingly. As the objects approach each other, medium displacement (mass) is reduced even more, and energy is lost in radiation.
Because the area of diluted medium inside a particle usually is very small compared to the squared distance to a neighboring particle, their common reduction in mass is negligible compared to their total mass. A notable exception is of course the case in the atomic nucleus.
1 This medium was thought to be a “luminiferous aether" in the late 19th century, but this idea was rejected by the famous Michelson–Morley experiment in 1887, and also by following experiments. Today, the medium that carries electromagnetic waves is generally thought to be spacetime itself.
2 Charged particles will also produce an area of dilution outside the particle, enabling electrostatics. This will be discussed in a later post.