  We examine the one-dimensional motion of two similarly charged particles
under the influence of only two forces, i.e. their Coulombic repulsion and
their gravitational attraction, using the relativistic equation of motion. We
find that when the rest mass of the two particles is sufficiently small (~ 0.4
eV/c2) and the initial Coulombic potential energy is sufficiently high (~ mpc2,
where mp is the proton mass), then the strong gravitational attraction
resulting from the relativistic particle velocities suffices to counterbalance
the Coulombic repulsion and to cause stable periodic motion of the two
particles. The creation of this confined oscillatory state, with a rest mass
equal to that of a proton, is shown to be consistent with quantum mechanics by
examining the particle de Broglie wavelength and the Klein-Gordon and
Schrodinger equations. It is shown that the gravitational constant can be
expressed in terms of the proton mass and charge, the vacuum dielectric
constant, the Planck constant and the speed of light. It is also shown that
gravity can cause confinement of light (~ 0.1 eV/c2) neutral particles
(neutrinos), or pairs of a neutral and a charged light particle, in circular
orbits of size 0.9 fm and period 10-24 s forming bound neutral or charged
hadron states.
