Einstein Probabilistic Units/Compton Gravity

Compton Gravity

Based on Dimension Balancing we know gravitational forces can be expressed in terms of frequency squared, Poisson-Newton equation for gravity:

$\Delta \;\phi =\Delta {\frac {m^{2}}{s^{2}}}=4\pi G\rho ={\frac {1}{s^{2}}}=D_{T}^{-2}$

In addition we know the gravitational coupling constant for two electrons can also be expressed in terms of Compton frequency squared and Planck frequency squared

$\alpha _{G_{e}}={\frac {G\;m_{e}^{2}}{\hbar \;c}}={\frac {\nu _{C_{e}}^{2}}{\nu _{P}^{2}}}$

Where the Compton frequency for the electron is,

$\nu _{C_{e}}={\frac {m_{e}\;c^{2}}{h}}={\frac {E_{e}}{h}}$

Rearranging the gravitational coupling constant terms,

$G\;m_{e}^{2}=\hbar \;c{\frac {\nu _{C_{e}}^{2}}{\nu _{P}^{2}}}={\frac {\hbar \;c}{\nu _{P}^{2}}}{\frac {\;\nu _{C1}\;\nu _{C2}}{r^{2}}}$

Next we will derive Compton's gravitational force equation and Compton's gravitational constant G_C

$Force\;Gravity\;Newton=G_{N}\;{\frac {m_{1}\;m_{2}}{r^{2}}}$

$Force\;Gravity\;Compton={\frac {\hbar \;c}{\nu _{P}^{2}}}{\frac {\;\nu _{C1}\;\nu _{C2}}{r^{2}}}=\color {red}G_{C}\;{\frac {\;\nu _{C1}\;\nu _{C2}}{r^{2}}}$

Where Compton's gravitational constant G_C is;

$G_{C}\;={\frac {\hbar \;c}{\nu _{P}^{2}}}={\frac {\hbar ^{2}}{F_{P}}}=G\left({\frac {\hbar ^{2}}{c^{4}}}\right)=9.2\times 10^{-113}\;{\frac {N\;m^{2}}{\nu ^{2}}}$

Compton's gravitational force energy form;

$Force\;Gravity={\frac {G\;m_{1}\;m_{2}}{r^{2}}}={\frac {h^{2}\;\nu _{C1}\;\nu _{C2}}{F_{P}\;r^{2}}}=\color {red}{\frac {E_{C1}\;E_{C2}}{F_{P}\;r^{2}}}$

The Compton's gravitational force equation is comparable to the Newton's gravitational force equation. From this we can develop additional gravitational modules based on frequency

$Force\;Gravity=G_{N}\;{\frac {m_{1}\;m_{2}}{r^{2}}}=G_{C}\;{\frac {\nu _{C1}\;\nu _{C2}}{r^{2}}}$

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