Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 10 January 2023 / Approved: 12 January 2023 / Online: 12 January 2023 (06:08:29 CET)
Version 2 : Received: 24 February 2023 / Approved: 27 February 2023 / Online: 27 February 2023 (02:04:10 CET)

How to cite: Christodoulou, D.M.; Kazanas, D. The Upgraded Planck System of Units that Reaches from the Known Planck Scale All the Way Down to Subatomic Scales. Preprints 2023, 2023010211. https://doi.org/10.20944/preprints202301.0211.v2. Christodoulou, D.M.; Kazanas, D. The Upgraded Planck System of Units that Reaches from the Known Planck Scale All the Way Down to Subatomic Scales. Preprints 2023, 2023010211. https://doi.org/10.20944/preprints202301.0211.v2.

Abstract

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 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 $\{ G, \upalpha_G \}$, 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 Dirac's fine-structure constant. The speed of light $c$ and the impedance of free space $Z_0$ 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 $${\rm UPS} \,:=\,\{ c, Z_0, G, \upalpha_G, \slashed{h}, \upalpha_\slashed{h}, \,\dots\,\!\},$$ 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. 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 only $K$.

Keywords

Atomic processes; Cosmological parameters; Cosmology: theory; Early Universe; Elementary particles; Galaxies: kinematics and dynamics; Gravitation.

Subject

PHYSICAL SCIENCES, Particle & Field Physics

Comment 1
Received: 27 February 2023
Commenter: Dimitris Christodoulou
Commenter's Conflict of Interests: Author
Comment: We have revised the manuscript following referee reports. We clarified the role of dimensionless constants, we rewrote the part about the descriptive unit "radian" that cannot be dropped from e.g. angular velocity, and we explained the necessity for deflation factor of 1/30. We also wrote a new subsection in Appendix A, section A.3, in which we calculated particle g-factors and the Weinberg angle using the empirical mass ladder that we had listed in the original Table A.1. These calculations show how we can reduce the number of free parameters of the Standard Model to just a handful.
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