A Potentially Unifying Constant of Nature (Brief Note)

Abstract

This brief note describes a method by which numerous empirically-determined quantum constants of nature can be substituted into Einstein’s field equation (EFE) for general relativity. This method involves treating the ratio G/ ћ as an empirical constant of nature in its own right. This ratio is repre- sented by a new symbol, N T . It turns out that the value of N T (which is 6.32891937 × 10 23 m ⋅ kg -2 ⋅ s -1 ) is within 5% of Avogadro’s number N A , although the units are clearly different. Nevertheless, substitutions of N T or N A into the EFE, as shown, should yield an absolute value similar in magnitude to that calculated by the conventional EFE. The method described allows for quantum term EFE substitutions into Einstein’s gravitational constant κ . These terms include ћ , α , m e , m p , R , k B , F, e, M U , and m U . More importantly, perhaps, one or more of the many new expressions given for κ may provide a more accurate result than κ incorporating G . If so, this may have important implications for additional forward progress towards unification. Whether any of these new expressions for Einstein’s field equation can move us closer to quantizing gravity remains to be determined.