# List of systems of units

## International System of Units (SI)

The key is to define only the minimum number of measures: if you define more definitions become over constrained and could be inconsistent.
Learning the modern SI is also a great way to learn some interesting Physics.

## Origins of Precision by Machine Thinking (2017)

Great overview of the earlier history of unit standardization.
Gives particular emphasis to the invention of gauge blocks.

## 2019 redefinition of the SI base units

web.archive.org/web/20181119214326/https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf gives it in raw:
• the unperturbed ground state hyperfine transition frequency of the caesium-133 atom is 9 192 631 770 Hz
• the speed of light in vacuum c is 299 792 458 m/s
• the Planck constant h is 6.626 070 15 × J s
• the elementary charge e is 1.602 176 634 × C
• the Boltzmann constant k is 1.380 649 × J/K
• the Avogadro constant NA is 6.022 140 76 × mol
• the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W,
The breakdown is:
• actually use some physical constant:
• the unperturbed ground state hyperfine transition frequency of the caesium-133 atom is 9 192 631 770 Hz
Defines the second in terms of caesium-133 experiments. The beauty of this definition is that we only have to count an integer number of discrete events, which is what allows us to make things precise.
• the speed of light in vacuum c is 299 792 458 m/s
Defines the meter in terms of speed of light experiments. We already had the second from the previous definition.
• the Planck constant h is 6.626 070 15 × J s
Defines the kilogram in terms of the Planck constant.
• the elementary charge e is 1.602 176 634 × C
Defines the Coulomb in terms of the electron charge.
• arbitrary definitions based on the above just to match historical values as well as possible:
• the Boltzmann constant k is 1.380 649 × J/K
Arbitrarily defines temperature from previously defined energy (J) to match historical values.
• the Avogadro constant NA is 6.022 140 76 × mol
Arbitrarily defines the mol to match historical values. In particular, the kilogram is not an exact multiple of the weight of an atom of hydrogen.
• the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W
Arbitrarily defines the Candela in terms of previous values to match historical records. The most useless unit comes last as you'd expect.

## Ampere in the 2019 redefinition of the SI base units

TODO how does basing it on the elementary charge help at all? Can we count individual electrons going through a wire? www.nist.gov/si-redefinition/ampere/ampere-quantum-metrology-triangle by the NIST explains that is it basically due to the following two quantized solid-state physics phenomena/experiments that allows for extremely precise measurements of the elementary charge:

## Kilogram

Unit of mass.
Defined in the 2019 redefinition of the SI base units via the Planck constant. This was possible due to the development of the kibble balance.

## Kibble balance

Measures weight from a voltage.
TODO appears to rely on both quantum Hall effect and Josephson effect

## Candela

Candela is Lumen density per solid angle. A sphere emitting 1 Candela uniformly in all directions produces 4π Lumen total power.

## Lumen (unit)

1 Watt equals 683 Lumens of light power at wavelength 555 nm. At other wavelengths 1 Watt is less Lumens as it takes into account the sensitivity of the average human eye.

## Candela vs lumen

Candela is lumen density per solid angle.

## Hertz (1857-1894, Hz)

Named after radio pioneer Heinrich Hertz.

## Megahertz (MHz)

Mega-Hertz, i.e. a million Hertz.

## Caesium standard (1967, 3.26 cm)

Uses the frequency of the hyperfine structure of caesium-133 ground state, i.e spin up vs spin down of its valence electron , to define the second.
International System of Units definition of the second since 1967, because this is what atomic clocks use.
TODO why does this have more energy than the hyperfine split of the hydrogen line given that it is further from the nucleus?

## Natural units

A series of systems usually derived from the International System of Units that are more convenient for certain applications.

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