The key thing in a good system of units is to define units in a way that depends only on physical properties of nature.

Ideally (or basically necessarily?) the starting point generally has to be discrete phenomena, e.g.

- number of times some light oscillates per second
- number of steps in a quantum Hall effect or Josephson junction

What we don't want is to have macroscopics measurement artifacts, (or even worse, the size of body parts! Inset dick joke) as you can always make a bar slightly more or less wide. And even metals evaporate over time! Though the mad people of the Avogadro project still attempted otherwise well into the 2010s!

Standards of measure that don't depend on artifacts are known as intrinsic standards.

A dimension in a system of units is something like length, weight or time, without considering how to assign numerical values ot them, which requires units of measurement such as the meter, kilogram or second.

Talking about dimensions can be useful when explaining new derived units without worrying about the exact units involved. See e.g. this table: en.wikipedia.org/w/index.php?title=Lumen_(unit)&oldid=1233810964#SI_photometric_units

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.

Great overview of the earlier history of unit standardization.

Gives particular emphasis to the invention of gauge blocks.

web.archive.org/web/20181119214326/https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf gives it in raw:
The breakdown is:

- the unperturbed ground state hyperfine transition frequency of the caesium-133 atom $Δv_{Cs}$ 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 × $10_{−34}$ J s
- the elementary charge e is 1.602 176 634 × $10_{−19}$ C
- the Boltzmann constant k is 1.380 649 × $10_{−23}$ J/K
- the Avogadro constant NA is 6.022 140 76 × $10_{23}$ mol
- the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W,

- actually use some physical constant:
the unperturbed ground state hyperfine transition frequency of the caesium-133 atom $Δv_{Cs}$ 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 × $10_{−34}$ J s

Defines the kilogram in terms of the Planck constant.the elementary charge e is 1.602 176 634 × $10_{−19}$ 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 × $10_{−23}$ J/K

Arbitrarily defines temperature from previously defined energy (J) to match historical values.the Avogadro constant NA is 6.022 140 76 × $10_{23}$ mol

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.

Unit of electric current.

Affected by the 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:

- quantum Hall effect, which has discrete resistances of type:
for integer values of $ν$.$R_{xy}=I_{channel}V_{Hall} =e_{2}νh $
- Josephson effect, which provides the Josephson constant which equals:
$K_{J}=h2e $

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.

Measures weight from a voltage.

www.bipm.org/documents/20126/28432564/working-document-ID-11315/8532173e-8bae-2bdf-b74a-cb48296b4e67

TODO appears to rely on both quantum Hall effect and Josephson effect

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

Bibliography:

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 is lumen density per solid angle.

Bibliography:

Named after radio pioneer Heinrich Hertz.

Uses the frequency of the hyperfine structure of caesium-133 ground state, i.e spin up vs spin down of its valence electron $6s_{1}$, 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?

Why caesium hyperfine structure is used:

Highlighted at the Origins of Precision by Machine Thinking (2017).

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

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