Natural units (Part 1)

Most units of measurement are based on specific physical qualities or tangible reference objects. But they don’t have to be. [1 of 2]

Back in 2019 I promised to write about Planck units in a post on the largest number. At the time, I called the Planck volume “as small as volume gets.” While it’s accurate to say that this volume is absurdly small, 4.2217 x 10−105 m3, the truth of it and the other Planck units is a little more complicated.

All units of measurement have to connect to some common standard in order to be useful as measurements. In antiquity these often aligned to observable natural phenomena: the width of an average human thumb (the inch) or the time from noon until noon (the day). When standardisation hit units became more specific, like one ten-millionth of the distance between the North Pole and the Equator (the metre). Sometimes they referred to a specific object that served as the reference point for the measurement (the kilogram), which was handy except when those objects were stolen by pirates.

Today most serious measurements are defined by some rather obscure standards. The second, for example, has the following definition:

The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ΔνCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9,192,631,770 when expressed in the unit Hz, which is equal to s-1.

Definitions of the SI base units

Fortunately, we only need a few of these basic units to construct a huge system of measurements, because you can take just a few basic units and derive all the rest from them.

In the metric system, the seven base units (metre, second, kilogram, ampere, kelvin, mole, and candela) can be used to construct twenty more units. The measurement for force, for example, is the Newton. Its definition doesn’t involve any weird vibrating caesium, but instead uses a specific combination of three of the base units: the metre, the second, and the kilogram.

The dirty secret at the heart of all these units of measurement is this: they are arbitrary. We didn’t choose 9,192,631,770 periods of caesium-133 because that particle or that number carried any fundamental significance. It’s just a convenient way to be precise about the duration of the second. It is anthropocentric, a human measurement made by humans.

The physicist Max Planck, in 1899, proposed something a little different. He suggested a system of units that did not rely on arbitrary human decisions at all.

[Part 2 comes tomorrow.]