The Upgraded Planck System of Units That Reaches from the Known Planck Scale All the Way Down to Subatomic Scales

Abstract

Natural systems of units {Ui} need to be overhauled to include the dimensionless coupling constants {αUi} of the natural forces. Otherwise, they cannot quantify all the forces of nature in a unified manner. Thus, each force must furnish a system of units 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,αG}, thus it cannot account for gravitation. The cosmological system discounts {h,αh}, thus it cannot account for quantum physics. Here, the symbols have their usual meanings; in particular, αG is the gravitational coupling constant and αh is Dirac’s fine-structure constant. The speed of light c and the impedance of free space Z0 are resistive properties imposed by the vacuum itself; thus, they must be present in all systems of units. The upgraded Planck system with fundamental units UPS:={c,Z0,G,αG,h,αh,…} 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, which 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 or measured physical properties are coincidental in this universe. Furthermore, we derive from first principles Koide’s K=2/3 enigmatic constant and additional analogous quark and vector boson constants. These are formal mathematical proofs that justify a posteriori the use of geometric means in deriving the quark/boson mass ladder. This ladder allows us to also calculate the Higgs couplings to the vector bosons and the Weinberg angle in terms of K only, and many of the “free” parameters of the Standard Model of particle physics were previously expected to be determined only from experiments.