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:

$\mathrm{\Delta }\varphi =\mathrm{\Delta }\frac{m^2}{s^2}=4\pi G\rho =\frac{1}{s^2}=D_T^{-2}$

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

${\alpha }_{G_e}=\frac{G{m}_e^2}{\hslash c}=\frac{{\nu }_{C_e}^2}{{\nu }_P^2}$

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,

$G{m}_e^2=\hslash c\frac{{\nu }_{C_e}^2}{{\nu }_P^2}=\frac{\hslash c}{{\nu }_P^2}\frac{{\nu }_{C1}{\nu }_{C2}}{r^2}$

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

$ForceGravityNewton=G_N\frac{m_1{m}_2}{r^2}$

$ForceGravityCompton=\frac{\hslash c}{{\nu }_P^2}\frac{{\nu }_{C1}{\nu }_{C2}}{r^2}=G_C\frac{{\nu }_{C1}{\nu }_{C2}}{r^2}$

Where Compton's gravitational constant G_C is;

$G_C=\frac{\hslash c}{{\nu }_P^2}=\frac{{\hslash }^2}{F_P}=G\left(\frac{{\hslash }^2}{c^4}\right)=9.2\times 10^{-113}\frac{N{m}^2}{{\nu }^2}$

Compton's gravitational force energy form;

$ForceGravity=\frac{G{m}_1{m}_2}{r^2}=\frac{h^2{\nu }_{C1}{\nu }_{C2}}{F_P{r}^2}=\frac{E_{C1}{E}_{C2}}{F_P{r}^2}$

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

$ForceGravity=G_N\frac{m_1{m}_2}{r^2}=G_C\frac{{\nu }_{C1}{\nu }_{C2}}{r^2}$

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