this post was submitted on 26 Oct 2025
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There are various systems of units where select physical constants are set to 1. A handy comparison chart is on Wikipedia: https://en.wikipedia.org/wiki/Natural_units?wprov=sfla1
It turns out you can't harmonize all the physical constants. Some will necessarily end up as some non-round number.
Most of them have speed of light = 1, but some have it as 1/α where α is the fine-structure constant (α = e² / 4πε₀ħc ≈ 0.007297)
IMO it might be better to only look at natural units that don't depend on the specific properties of matter (i.e. proton mass, electron charge, ...)
arguably, there could be an alien civilization in our universe that is purely made of exotic matter somewhere really far away, we simply haven't found it yet. It's purely made of exons and kaions and yppsons and particles that don't exist on earth, where an exon has a positive charge of 1.456... proton charges and an yppson has a negative charge of -4.132... proton charges and so on.
therefore i consider physical constants such as ħ and c and G more fundamental than e and such, because those numbers would be the same even for exotic matter, i claim.
then, is that reduced set of natural constants harmonizable?
A quick glance at the summary table can answer that. Planck units seem to do the trick.
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