A Bohr-type model of a composite particle using gravity as the attractive force

Abstract

We formulate a Bohr-type rotating particle model for three light particles of rest mass mo each, forming a bound rotational state under the influence of their gravitational attraction, in the same way that electrostatic attraction leads to the formation of a bound proton-electron state in the classical Bohr model of the H atom. By using special relativity, the equivalence principle and the de Broglie wavelength equation, we find that when each of the three rotating particles has the same rest mass as the rest mass of a neutrino or an antineutrino (∼ 0.05 eV /c 2 ) then surprisingly the composite rotating state has the rest mass of the stable baryons, i.e. of the proton and the neutron (∼ 1 GeV /c 2 ). This rest mass is due almost exclusively to the kinetic energy of the rotating particles. The results are found to be consistent with the theory of general relativity. The model contains no unknown parameters, describes both asymptotic freedom and confinement and also provides good agreement with QCD regarding the QCD condenstation temperature. Predictions for the thermodynamic and other physical properties of these bound rotational states are compared with experimental values.

Microscopic black hole stabilization via the uncertainty principle

“…It is found that such rotational states exist and their properties are similar with those computed by treating the two-or three-rotating particle motion via the combination of HUP, special relativity, Newton's gravitational law and the equivalence principle [5,6,7]. Interestingly when the rest mass of the two or three light relativistic particles is in the range of neutrino masses (∼ 5 · 10 −2 eV /c 2 ), then the mass of the gravitationally confined microscopic Planckian or sub-Planckian rotating particle states are in the hadron ( 1 GeV ) mass range [5,6,7].…”

“…The corresponding relativistic mass γm o equals 313 M eV /c 2 which falls in the range of effective quark masses [13]. Consequently, as already shown [5,6,7], the mass of quarks can be modeled successfully by the mass of gravitationally confined neutrinos.…”

“…where γ(= (1 − v 2 /c 2 ) −1/2 ) is the Lorentz-factor, as shown already in 1905 for linear motion [10] and more recently for arbitrary particle motion [5], including circular orbits. It must be noted that the transverse mass γm o , which is equal to the relativistic mass, is not an inertial mass, since the force computed from the product of mass and acceleration it is not invariant [5,7,8].…”

“…The SR treatment of the three rotating particle model (Fig.1) has been presented already elsewhere [5,7]. In brief the special relativity equation of motion for a circular orbit [8,9] is used in conjunction with Newton's gravitational law to obtain…”

“…It must be noted that the transverse mass γm o , which is equal to the relativistic mass, is not an inertial mass, since the force computed from the product of mass and acceleration it is not invariant [5,7,8].…”