The Interaction Strength and Implications For Microphysics

Since $\tilde{G}$ has a different dimensionality than G, we can now use it instead of G, to form the standard units of m, r, and t by combining $\tilde{G}$ with h and c. So doing yields:

$$\tilde{m} = (\frac{h^{2}}{\tilde{G}})^{1/3} = 1.4 \cdot 10^{-24} g$$

$$\tilde{r} = (\frac{\tilde{G}\cdot h}{c^{3}})^{1/3} = 1.8 \cdot 10^{-13} cm$$

$$\tilde{t} = (\frac{\tilde{G}\cdot h}{c^{6}})^{1/3} = 6 \cdot 10^{-24} s$$ (6)

Note that although both $\tilde{m}$ and $\tilde{r}$ agree quite well with the classical definition of the nuclear mass and radius, the two are coupled together; any value of G (or $\tilde{G}$) that yields the correct m will perforce yield the corresponding r. Nonetheless, the similarity of $\tilde{m}$ to the observed nuclear mass is remarkable.

Another interesting result is obtained when the classical electrostatic force is equated with the $\tilde{M}$ interaction at the distance $\tilde{r}$, using $\tilde{m}$ as one of the masses, and solving for the other mass. We get:

$$\frac{\tilde{G}\tilde{m}m_{x}}{\tilde{r}^{3}} = \frac{q_{1}q_{2}}{\tilde{r}^{2}}$$ (7)

so

$$m_{x} = \frac{\tilde{r}q_{1}q_{2}}{\tilde{G}\tilde{m}} = \fr... ...t 10^{19} \cdot 1.4 \cdot 10^{-24}} \approx 1 \cdot 10^{-27} g$$ (8)

This, of course, is very close to the value for the electron's rest mass. Thus, we apparently have a way to uniquely determine both the proton and electron rest masses. While these results could be considered as merely chance numerical coincidences, it is possible that this result could point toward some sort of exchange interaction, whereby quantum mechanical operators allow interchanges between fundamental M and ``particles".