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According to special relativity and the equivalence principle, the Newtoniangravitational force between two particles with relativistic velocitiesincreases significantly with velocity and in fact becomes unbound as the latterapproaches c. One may thus construct a deterministic model of three fastrotating light particles which uses gravitation as the attractive force,special relativity, the weak equivalence principle and introduces angularmomentum quantization as in the Bohr model of the H atom. The model shows theexistence of stable rotational states corresponding to highly relativisticparticle velocities with radii in the fm range. When the rest masses of thethree light particles is in the mass range of neutrinos (~0.1 eV/c^2), thensurprisingly the rest masses and Compton wavelengths of these rotational statesare 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 modelalso predicts a lower limit for the lifetime of the baryons which is consistentwith their measured lifetimes and yields a good approximation for theirmagnetic moments. It thus appears that this deterministic Bohr-type approach tosubatomic phenomena, i.e. a classical special relativistic treatment coupledwith the de Broglie wavelength expression to seek conformity with quantummechanics, may be a useful zeroth-order model to explore some quantum gravityproblems.

A model of possible gravitational confinement of fast light particles