From Newton to universal Planck natural units – disentangling the constants of nature - Andrew Wutke (Journal of Physics Communications, 2023)
This study exploits a historical gap in the evolution of metric systems that resulted from the incomplete implementation of the ‘rationalization’ concept published by Heaviside in 1893 and by ignoring the suggestion of Maxwell in 1873 to use the simplest form of Newton’s gravitational law expression with no proportionality constant. Bridging this gap required deriving an experimental Rationalized Metric System (RMS) and a corresponding Universal Planck Natural Unit System (UPNUS) in [ LT ] units. The described solution combines Heaviside’s rationalization of Newton’s law and makes the unit of mass dimensions [ L ^3 T ^−2 ], as suggested by Maxwell. Consequently, the modified Coulomb’s law, changes the unit of electric charge to the same dimensions as those of mass. The elimination of the kilogram and ampere has a disentangling effect on the dependencies among the constants of nature and opens new horizons. New systems have the potential to become powerful exploratory tools in fundamental research and education because of the simplification of the relationships among physical quantities. Some highlights from the analyzed examples are worth mentioning. The well-known expression for the Stoney mass ( m _S ) when converted to RMS units is reduced to the electron charge quantity, whereas traditional metric systems entangle the charge, speed of light, and gravitational constant, forming an entity in the dimension of mass, as first presented by Stoney in 1874. Furthermore, a well-substantiated conjecture is proposed, wherein the Stoney energy E _S = m _S c ^2 is likely the long-sought, finite electric field energy of the electron, and the gravitational constant appears to be the limiting factor. In UPNUS, the most disentangled fundamental expression, apart from the Stoney mass, is the elementary charge $\mathop{{\boldsymbol{e}}}\limits^{\unicode{x0030C}}$ as the function of the fine structure constant α and the Planck mass ${\mathop{{\boldsymbol{m}}}\limits^{\unicode{x0030C}}}_{{\boldsymbol{P}}},$ namely $\check{{\boldsymbol{e}}}{\boldsymbol{=}}{\check{{\boldsymbol{m}}}}_{{\boldsymbol{P}}}\sqrt{{\boldsymbol{α }}}{\boldsymbol{≈ }}1.073476469,$ with $\mathop{{\boldsymbol{e}}}\limits^{\unicode{x0030C}}$ and ${\mathop{{\boldsymbol{m}}}\limits^{\unicode{x0030C}}}_{{\boldsymbol{P}}}$ of the same [ L ^3 T ^−2 ] dimensions in Planck units, where ${\mathop{{\boldsymbol{m}}}\limits^{\unicode{x0030C}}}_{{\boldsymbol{P}}}{\boldsymbol{=}}{\boldsymbol{4}}{\boldsymbol{π }}.$