README: add reference to specific unit system

[waldyrious]

The "natural units" Wikipedia page describes multiple unit systems that bear this name, and although it mentions Planck units, it doesn't make a reference to its rationalized version.

This PR adds a link to the latter and the specific name to make the reference more explicit.

[coveralls]

Pull Request Test Coverage Report for Build 1239365228

• 0 of 0 changed or added relevant lines in 0 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage decreased (-5.6%) to 82.609%

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Totals
Change from base Build 1238626672:	-5.6%
Covered Lines:	19
Relevant Lines:	23

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[coveralls]

Pull Request Test Coverage Report for Build 1239365228

• 0 of 0 changed or added relevant lines in 0 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage decreased (-5.6%) to 82.609%

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Totals
Change from base Build 1238626672:	-5.6%
Covered Lines:	19
Relevant Lines:	23

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💛 - Coveralls

[coveralls]

Pull Request Test Coverage Report for Build 1239365228

• 0 of 0 changed or added relevant lines in 0 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+1.2%) to 89.474%

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Totals
Change from base Build 1238626672:	1.2%
Covered Lines:	17
Relevant Lines:	19

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💛 - Coveralls

[MasonProtter]

Hmm, this is actually a little strange. None of the unit systems listed in these wikipedia pages are what most practitioners I know would call natural units and instead are either Planck units, or some problem specific adapted unit systems.

In the Planck style units, one too many constants have been set to unity, so everything is unitless and so one can actually just give up on dimensional analysis. Every quantity is convertible to eachother. What most people I know mean when they use natural units is to set

ħ = c = ϵ₀ = kb = 1

so that every quantity is measurable in terms of powers of energy or length. If you also set G=1, then lengths have the same units as volumes, energy has the same units as inverse energy, etc.

Perhaps I should just remove the links to wikipedia altogether..

[MasonProtter]

Interestingly, the wikipedia page even says

In this case, the reinsertion of the correct powers of e, c, etc., can be uniquely determined.[1][2]

but this is just untrue for most of the unit systems described in the page. The entry for

Natural units (particle and atomic physics)

would be standard if they didn't set the electron mass to unity.

[waldyrious]

What most people I know mean when they use natural units is to set

ħ = c = ϵ₀ = kb = 1

so that every quantity is measurable in terms of powers of energy or length. If you also set G=1, then lengths have the same units as volumes, energy has the same units as inverse energy, etc.

That's precisely what's described in the link added in this PR. 🙂 Note that it points to a specific section on the "Plank units" article, titled "Alternative choices of normalization", which says:

a substantial body of physical theory developed since Planck (1899) suggests normalizing not G but 4πG (or 8πG) to 1.
(...)
The rationalized Planck units are defined so that c = 4πG = ħ = ϵ₀ = kb = 1.

That's why I used the term "rationalized Planck units", rather than just "Planck units", to make this explicit. Although perhaps it wasn't explicit enough? 😅

[MasonProtter]

No, the choice of 4πG is not what I'm talking about. If you set any multiple of G to 1, then you collapse the unit system and have no unit scales in the system. I'm explicitly not letting G be a unitless number because I want a unit in the problem.

julia> natural(Unitful.G)
6.708830746231457e-57 eV⁻²

otherwise there is no unique conversion to and from natural units.

[waldyrious]

Ah, sorry, then. Is there any reference you would recommend instead to provide context? And/or perhaps another term, more specific than "natural units" but different from "rationalized Planck units", which could be used to help people find the right resources for background?

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 86.95%. Comparing base (2d24a37) to head (904dded).

Additional details and impacted files

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  Lines          23       23           
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[mo8it]

That spam with codecov…