Curvature Quantization based on the Ehrenfest Paradox in the Bohr Atomic Model

Abstract

Ehrenfest Paradox has been studied in the Bohr Atomic Model as a theoretical procedure for expressing the atomic coordinate curvature in the term of electromagnetic fine structure/coupling constant α = 1/137. The strength of the curvature corresponding to the gravitational aspect depends on the principal quantum number via a new constant $\frac{16{\alpha }^2}{a_0^2}=3,0348\times {10}^{17}{m}^{-2}$, which shows that the value of the curvature is quantised. For instance n = 1, the value is 3, 0349  × 10¹⁷ m⁻². The curvature value in the Bohr atomic model can be used as a standard to compare how strong the curvatures of all systems are. This procedure can also be generalized to the strong and weak interactions in such a way that the value of the curvature can be represented by their own coupling constants. In the real situation, we can take the case of the atom near supermassive objects such as: blackhole, neutron star, white dwarf, etc. In this case, the atom is in the curved space-time, while the space-time curvature is quantized by the atom. Principally, the idea of the curvature and quantization are correlated. The excitation (the change of the state) of the atom or the atomic nuclei will generate the change of the space-time curvature ΔG_μν(α)_n that manifests a quantized curvature propagation (curvaton) through the space-time coordinate in the form of quantum stress tensor $\Delta T_{\mu \nu }^{\left(q2B\right)}=\hslash \Delta {\sigma }_n\Delta G_{\mu \nu }{\left(\alpha \right)}_n$. It can be viewed as a unit of moving curvature reduced to a gravitational wave. This theory can be considered to expand the unification between quantum mechanics and gravitation.