Magnetic Gravity

this wikiversity original research on
 * how gravity and inertia emerge from electromagnetic formulae

and
 * how they might be large-number electromagnetic interactions

has just started and you are about to read sketch notes unripe for print until this very warning is altered because the argument became more elaborated:

Sanchez Exponential
In his horribly typeset but brilliantly

helpful paper

 * http://vixra.org/pdf/1609.0217v3.pdf
 * Calculation of the gravitational constant G using electromagnetic parameters
 * 2016-09-14 ©©-by jesus.sanchez.bilbao@gmail.com

peer reviewed, printed, and republished in
 * http://file.scirp.org/pdf/JHEPGC_2016122915423655.pdf
 * Journal of High Energy Physics, Gravitation and Cosmology, 2017, 3, 87-95

independent researcher Jesús Sánchez discovered

the equation

 * $$\frac{\alpha_g}{(2\pi\alpha)^2}

=\frac{G m_e^2}{2\pi\alpha^2 c h} =\frac{G m_e^2\epsilon_0}{\alpha \pi q_e ^ 2} =\frac{G m_e^2 c h}{\frac{\pi}2 q_e^4\epsilon_0^{-2}} $$

=\frac{G h}{8\pi^3c^3r_e^2} =\frac{G h}{(2\pi c)^3r_e^2} =\frac{r_s r_c}{(4\pi r_e)^2} =\frac{\ell_P ^ 2}{2\pi r_e^2} $$

=\exp(\frac{\sqrt2\alpha\pi}4-\frac1{\sqrt2\alpha}) =\sqrt[-\sqrt2]e^{\frac1{\alpha}-\frac{\alpha\pi}2} =e^{-96.891} $$

=2^{-139.784} =10^{-42.079} =\texttt{8.33E-43} $$

====using $ \exp(\ln(x))=x $ ====
 * on $$\exp(\ln(\frac{r_s r_c}{(4\pi r_e)^2}))

=\exp(\frac{\sqrt2\alpha\pi}4-\frac1{\sqrt2\alpha})$$

====using $ \exp(x)=\exp(x) $ ====
 * on $$\ln(\frac{r_s r_c}{(4\pi r_e)^2})

=\frac{\sqrt2\alpha\pi}4-\frac1{\sqrt2\alpha}$$

====using $ x=0+x $ ====
 * on $$0=

\frac{\sqrt2\alpha\pi}4 -\ln(\frac{r_s r_c}{(4\pi r_e)^2}) -\frac1{\sqrt2\alpha}$$

====using $ \alpha = r_e/r_c $ ====
 * on $$0=

\frac{\sqrt2r_e\pi}{r_c4} -\ln(\frac{r_s r_c}{(4\pi r_e)^2}) -\frac{r_c}{\sqrt2r_e} $$

====using $ t_c = \int_0^c\sqrt{1^2-(\frac{v(t)}{c})^2}\partial t=\frac{\pi}4t_e $ ====
 * on $$0=

\frac{\sqrt2t_cr_e}{r_ct_e} -\ln(\frac{r_s r_c}{(4\pi r_e)^2}) -\frac{r_c}{\sqrt2r_e}$$

====using $ \int^{r_e}_{\partial r} \frac{q'(r)}{q(r)} =\int^{q(r_e)}_{\partial q} \frac1q =\ln(q(r_e)) $ ====
 * on $$0=

\int^{r_e} \frac{\sqrt2t_c}{r_ct_e}\partial r -\frac {\frac{-\frac{2r_s}r r_c}{(4\pi r)^2}} {\frac{r_s r_c}{(4\pi r)^2}}\partial r +\frac{r_c}{\sqrt2r^2}\partial r $$

====using $ \frac{\partial r^2}{\partial s^2} =\frac{\partial r}{\partial s^2}\partial r =\int\frac{4\pi\frac{r_c} {\sqrt2}}{4\pi r^2}\partial r =\frac{-r_c}{\sqrt2r} $ ====
 * on $$0=

\int^{r_e} -\frac{\tau\partial s^2}{r\partial r^2}\partial r -\frac {\frac{-\frac{2r_s}r r_c}{(4\pi r)^2}} {\frac{r_s r_c}{(4\pi r)^2}}\partial r -\frac{\partial r^2}{\partial s^2}r^{-2}\partial r $$

====using $ \frac{\partial\tau^2}{\partial t^2} =1-\frac{r_s}r =-\frac{\partial r^2}{\partial s^2} $ ====
 * on $$0=

\partial r\int^{r_e} \frac{\tau\partial t^2}{r\partial\tau^2}\partial r -\frac {\frac{-\frac{2r_s}r r_c}{(4\pi r)^2}} {\frac{r_s r_c}{(4\pi r)^2}} -\frac{\partial r^2}{\partial s^2}r^{-2} $$

====using $ ... $ ====
 * on $$0=\int^{r_e}

\frac{\partial t^2-\partial s^2-\partial r^2} {\partial s^2}\partial r $$

====using $ (\phi,\theta):=(0,0) $ ====
 * on $$

ds^2= ({R\choose d\Omega}\mapsto{\sqrt[3]{r^3+r_s^3} \choose d\theta^2+\sin^2\theta d\phi^2}) (\frac{dt^2}{\frac{R}{R-r_s}} -\frac{dR^2}{\frac{R-r_s}R} -R^2d\Omega) $$