The structure of physical constants, Planck units, natural formulas, and unit invariance
Compute the Sun’s luminosity from the Planck-decomposed Stefan-Boltzmann law: four factors spanning 202 orders of magnitude — from 10⁻¹¹⁴ to 10⁸⁸ — combine to match the IAU value to four significant figures.
Decomposed into Planck-scale factors, the Stefan-Boltzmann constant separates into a geometric efficiency, a temperature ratio, and the Planck power per Planck area — and the same factors compute the Sun’s luminosity from numbers spanning 202 orders of magnitude.
The Planck constant appears in every quantum formula. But what is it, physically? When expressed in Planck units, ℏ reveals itself as a composite of three recognizable quantities — the Planck length, the Planck mass, and the speed of light — and the formulas of quantum mechanics become statements about ratios to the Planck scale.