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, NT. It turns out that the value of NT (which is 6.32891937 × 1023 m⋅kg-2⋅s-1) is within 5% of Avogadro’s number NA, although the units are clearly different. Nevertheless, substitutions of NT or NA 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, me, mp, R, kB, F, e, MU, and mU. 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.
Highlights
Introduction and BackgroundThere are a myriad of difficulties in attempting to unite gravity with the other fundamental forces of nature
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 represented by a new symbol, NT
Substitutions of NT or NA into the EFE, as shown, should yield an absolute value similar in magnitude to that calculated by the conventional EFE
Summary
There are a myriad of difficulties in attempting to unite gravity with the other fundamental forces of nature. Not the least of these is that our best gravity theory, general relativity, has classical deterministic features, whereas quantum theory is anti-deterministic, probabilistic, and built upon the foundation of Hei-. To unite gravity with the other forces using these two theories, without some modifications to one or both theories, is a bit like mixing oil and water. An “emulsifier” approach, successfully combining certain features of both theories, is needed
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