Quantum Gravity of IED Particles

The internally electrodynamic (IED) model\footnote{See e.g. a) {\it arxiv:0812.3951}, b) {\it J Phys Conf Ser}{\bf 128}. 012019, 2008.}, developed based on overall experimental observations since 2000, briefly states that {\it a simple material particle like electron is composed of an oscillatory charge of a characteristic frequency $\Omega$ and zero rest mass, generally also traveling at velocity $v$, and the resulting Doppler-effected electromagnetic waves $({\bf E},{\bf B})$'s}. Based on first principles solutions for the IED processes a range of basic particle equations/properties have become predictable. One prediction is: two IED particles of masses $M_,M_{2}$ ($=\hbar \Omega_i/c$, $i=1,2$) and charges $q_1,q_2$ separated at $r$ apart in a dielectric vacuum act always on one another an attractive force $F=\sqrt{F_{12}F_{21}}=\frac{C M_1M_2}{4\pi\epsilon_0 r^2}$, where ${\bf F}_{i j}=q_{j} {\bf v}_{pj} \times {\bf B}_{i} $ is the Lorentz or depolarization radiation force on $q_j$ due to the radiation depolarization field ${\bf E}_{pi}=-\chi_{0^*} {\bf E}_{i}$ of $q_{i}$, electric field ${\bf E}_{i}$, and magnetic field ${\bf B}_{i}$, with ${\bf E}_{pi} $ driving $q_j$ into motion at velocity ${\bf v}_{pj}= \int \frac{q_jd {\bf E}_{pi}}{M_j})$, $i,j=1,2$; $C = \frac{ \pi \chi_{0^*}e^4}{ \epsilon_0^2 h^2\rho_{_l}}$ with $q_1,q_{2}=\pm e$ and $e, \epsilon_0, h$ fundamental constants of the usual meaning. $F$ resembles directly Newton's gravitational force. The fields $E_i,B_i$ are by nature quantized at the scale of Planck constant $h$; consequently $E_{pi}$ and therefore $F$ are each quantized at the scale $h$. The present work gives a formal quantum electrodynamic re-derivation of this force.