  According to special relativity and the equivalence principle, the Newtonian
gravitational force between two particles with relativistic velocities
increases significantly with velocity and in fact becomes unbound as the latter
approaches c. One may thus construct a deterministic model of three fast
rotating light particles which uses gravitation as the attractive force,
special relativity, the weak equivalence principle and introduces angular
momentum quantization as in the Bohr model of the H atom. The model shows the
existence of stable rotational states corresponding to highly relativistic
particle velocities with radii in the fm range. When the rest masses of the
three light particles is in the mass range of neutrinos (~0.1 eV/c^2), then
surprisingly the rest masses and Compton wavelengths of these rotational states
are found to correspond to those of baryons and in fact the masses (~1 GeV/c^2)
reproduce quite well the light baryon mass spectrum. Interestingly the model
also predicts a lower limit for the lifetime of the baryons which is consistent
with their measured lifetimes and yields a good approximation for their
magnetic moments. It thus appears that this deterministic Bohr-type approach to
subatomic phenomena, i.e. a classical special relativistic treatment coupled
with the de Broglie wavelength expression to seek conformity with quantum
mechanics, may be a useful zeroth-order model to explore some quantum gravity
problems.
