The meanings of the mysterious number 137

Abstract

The inverse of the fine-structure constant is α − 1  ≅ 137.036. Both the Nobel Prize winners, Pauli and Feynman, became fascinated with the number 137. However, physicists have not yet been able to find any relationship between this number and a physical law. Here, the integer 137 has several clear meanings, on the basis of the following two premises: (1) Form of light: Longitudinal massive particles (photons) having length λ = c / ν , where ν   is the frequency, namely, the number of photons in the same ray (continuous succession of photons) crossing a given observer in unit time; 2) electron structure: Its charge is not uniformly distributed, but it can be considered as a point particle fixed on the electron spherical surface and facing the atom nucleus during the electron orbits; the electron charge also corresponds to the photons‐electron impact point, where photons are absorbed and released. On the above bases, for the H atom, we found the following main results: n   = 1, 2, …, 137 electron different circular orbits, with n 2 being the admitted photons number along two equal circular orbits; 2 ν n / f n = n , with ν n being the photons admitted frequency on each circular orbit r n with f n   being the electron related frequency; v 0   = α c is the electron charge ground-state (g-s) orbital speed; r o =   α / 4 π R H is the g-s orbit of the electron charge, with R H being the Rydberg constant; r 1 = r o + r e = r o ( 1 + r e / r o ) =   r o / 137 α , with r 1 being the electron g-s orbit and r e   being the electron radius; r 1 / r o = 1 / 137 α = ( 1 + r e r 0 ) r e = r 0 1 137 α − 1 , different from CODATA1 value r e     = α 2 a 0 ; v 1   = c / 137   exact, electron g-s orbital speed; hence, v 1   / v 0   = 1 / 137 α ; λ 0 2 2 π r 1 = c ν 0 4 π r 1 = c 137 α ν 0 4 π r 0 =   c 137 α 4 π R H ν 0 4 π α =   137, ratio between the admitted photon length and two electron g-s orbits. As for the claimed fall of circling electrons into their nucleus due to their supposed photons emission, we found that the electrons are emitting the previously absorbed photons only during their spiral path toward lower orbits (Sec. VII).