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

${\frac {\alpha _{g}}{(2\pi \alpha )^{2}}}={\frac {Gm_{e}^{2}}{2\pi \alpha ^{2}ch}}={\frac {Gm_{e}^{2}\epsilon _{0}}{\alpha \pi q_{e}^{2}}}={\frac {Gm_{e}^{2}ch}{{\frac {\pi }{2}}q_{e}^{4}\epsilon _{0}^{-2}}}$

$={\frac {Gh}{8\pi ^{3}c^{3}r_{e}^{2}}}={\frac {Gh}{(2\pi c)^{3}r_{e}^{2}}}={\frac {r_{s}r_{c}}{(4\pi r_{e})^{2}}}={\frac {\ell _{P}^{2}}{2\pi r_{e}^{2}}}$

$=\exp({\frac {{\sqrt {2}}\alpha \pi }{4}}-{\frac {1}{{\sqrt {2}}\alpha }})={\sqrt[{-{\sqrt {2}}}]{e}}^{{\frac {1}{\alpha }}-{\frac {\alpha \pi }{2}}}=e^{-96.891}$

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

using ${\textstyle \exp(\ln(x))=x}$

on $\exp(\ln({\frac {r_{s}r_{c}}{(4\pi r_{e})^{2}}}))=\exp({\frac {{\sqrt {2}}\alpha \pi }{4}}-{\frac {1}{{\sqrt {2}}\alpha }})$

using ${\textstyle \exp(x)=\exp(x)}$

on $\ln({\frac {r_{s}r_{c}}{(4\pi r_{e})^{2}}})={\frac {{\sqrt {2}}\alpha \pi }{4}}-{\frac {1}{{\sqrt {2}}\alpha }}$

using ${\textstyle x=0+x}$

on $0={\frac {{\sqrt {2}}\alpha \pi }{4}}-\ln({\frac {r_{s}r_{c}}{(4\pi r_{e})^{2}}})-{\frac {1}{{\sqrt {2}}\alpha }}$

using ${\textstyle \alpha =r_{e}/r_{c}}$

on $0={\frac {{\sqrt {2}}r_{e}\pi }{r_{c}4}}-\ln({\frac {r_{s}r_{c}}{(4\pi r_{e})^{2}}})-{\frac {r_{c}}{{\sqrt {2}}r_{e}}}$

using ${\textstyle t_{c}=\int _{0}^{c}{\sqrt {1^{2}-({\frac {v(t)}{c}})^{2}}}\partial t={\frac {\pi }{4}}t_{e}}$

on $0={\frac {{\sqrt {2}}t_{c}r_{e}}{r_{c}t_{e}}}-\ln({\frac {r_{s}r_{c}}{(4\pi r_{e})^{2}}})-{\frac {r_{c}}{{\sqrt {2}}r_{e}}}$

using ${\textstyle \int _{\partial r}^{r_{e}}{\frac {q'(r)}{q(r)}}=\int _{\partial q}^{q(r_{e})}{\frac {1}{q}}=\ln(q(r_{e}))}$

on $0=\int ^{r_{e}}{\frac {{\sqrt {2}}t_{c}}{r_{c}t_{e}}}\partial r-{\frac {\frac {-{\frac {2r_{s}}{r}}r_{c}}{(4\pi r)^{2}}}{\frac {r_{s}r_{c}}{(4\pi r)^{2}}}}\partial r+{\frac {r_{c}}{{\sqrt {2}}r^{2}}}\partial r$

using ${\textstyle {\frac {\partial r^{2}}{\partial s^{2}}}={\frac {\partial r}{\partial s^{2}}}\partial r=\int {\frac {4\pi {\frac {r_{c}}{\sqrt {2}}}}{4\pi r^{2}}}\partial r={\frac {-r_{c}}{{\sqrt {2}}r}}}$

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 ${\textstyle {\frac {\partial \tau ^{2}}{\partial t^{2}}}=1-{\frac {r_{s}}{r}}=-{\frac {\partial r^{2}}{\partial s^{2}}}}$

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 ${\textstyle ...}$

on $0=\int ^{r_{e}}{\frac {\partial t^{2}-\partial s^{2}-\partial r^{2}}{\partial s^{2}}}\partial r$

using ${\textstyle (\phi ,\theta ):=(0,0)}$

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