# 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:

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

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

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

Where the Compton frequency for the electron is,

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

Rearranging the gravitational coupling constant terms,

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

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

${\displaystyle Force\;Gravity\;Newton=G_{N}\;{\frac {m_{1}\;m_{2}}{r^{2}}}}$
${\displaystyle Force\;Gravity\;Compton={\frac {\hbar \;c}{\nu _{P}^{2}}}{\frac {\;\nu _{C1}\;\nu _{C2}}{r^{2}}}=\color {red}G_{C}\;{\frac {\;\nu _{C1}\;\nu _{C2}}{r^{2}}}}$

Where Compton's gravitational constant GC is;

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

Compton's gravitational force energy form;

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

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

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