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Inertial/gravitational mass exists on a macroscopic level because of mass at the particle level. At the particle level there isn't anything but space and its curvature.
According to Einstein's General Theory of Relativity mass warps space in its vicinity. One can just as well say that the warping of space is mass.
Creatures of a three dimensional world cannot envision this warping, but it is easy to envision it for a two dimensional world. In a plane the effect of mass would be the creation of a dimple. One could say that the dimple is the mass. If there was a set of straight coordinate lines in the plane before the creation of a dimple the coordinate lines would be distorted by the creation of the dimple. Light rays traveling along those coordinate lines would deviate when passing through the dimple. The dimple would appear to have attracted those light rays.
The opposite of a dimple in the plane would be a bump (or a pimple). The bump would appear to distort the coordinate lines in the opposite way leading to the appearance that light rays are repelled by the bump.
Thus mass is not some substance like liquid mercury that is poured into a particle. Instead of mass curving space it is the curvature of space. A particle could also be characterized as a soliton. A soliton is a solution to certain nonlinear partial differential equations which preserves its character over time, even with interaction with other solitons. For more on the concept of solitons and a closely concept of solitary waves see Solitons and Solitary Waves.
Now consider Einstein's Special Theory of Relativity. According to that theory, length in a system moving with respect to an observer appears to be contracted in the direction of the motion. If the velocity relative to the speed of light is β then length is contracted by the factor (1β²)^{½}. Also, according to the Special Theory, the apparent mass of a body moving at a velocity of β with respect to the speed of light is increased by a factor of 1/(1β²)^{½}.
When length contracts the degree of curvature increases; thus mass, equated with curvature, increases. Curvature, which is the reciprocal of the radius of curvature, would be inversely proportional to a scale factor for length. Thus it is no coincidence that
where s and m are length and mass.
(To be continued.)
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