The Upgraded Planck System of Units

Natural systems of units $\{U_i\}$ need to be overhauled to include the dimensionless coupling constants $\{\upalpha_{U_i}\}$ of the natural forces. Otherwise, they cannot quantify all forces in a unified manner. Thus, each force must furnish a system with at least one dimensional and one dimensionless constant. We revisit three natural systems of units (atomic, cosmological, and Planck). The Planck system is easier to rectify, and we do so in this work. The atomic system discounts $\{ G, \upalpha_G \}$, thus it cannot account for gravitation. The cosmological system discounts $\{ \slashed{h}, \upalpha_\slashed{h} \}$, thus it cannot account for quantum physics. Here, the symbols have their usual meanings; in particular, $\upalpha_G$ is the gravitational coupling constant and $\upalpha_\slashed{h}$ is the fine-structure constant. The speed of light $c$ and the impedance of free space $Z_0$ are resistive properties of the vacuum, thus they must be present in all systems of units. The upgraded Planck system $${\rm UPS} \,:=\,\{ c, Z_0, G, \upalpha_G, \slashed{h}, \upalpha_\slashed{h}, \,\dots\,\!\},$$ describes all physical scales in the universe---it is nature's system of units. As such, it reveals a number of properties, most of which have been encountered previously in seemingly disjoint parts of physics, and some of which have been designated as mere coincidences. Based on the UPS results, that relate (sub)atomic scales to the Planck scale and the fine-structure constant to the Higgs field, we can state with confidence that no observed/measured physical properties are coincidental in this universe.