A few days ago, on November 16, 2018, the General Conference on Weights and Measures (CGPM) voted to approve a set of revisions to the International System of Units, common known as the SI units (or metric system). There has been numerous revisions to the SI unit system in the past, but this particular one, scheduled to become effective on May 20, 2019, was special. For the first time, all 7 base units (from which all other SI units can be derived) are to be defined by physical constants. Prior to this, the kilogram, along with a few other base units that depend on it, was the last to still be defined by an actual object.

I’ve always been quite fascinated by the definitions of the SI base units, for reasons that I couldn’t really explain. As a result of my personal interest though, I have been following the development of the kilogram re-definition effort (the main point of this revision) over the last few years. So naturally when the CGPM vote (which was more of a ceremonial event) passed last week, I was excited to read the new definitions. I then noticed something interesting, right on the first page of the official document for the definition revisions.

Here are the first three statements in the new description of the SI unit system (taken from the CGPM Draft Resolution):

• The unperturbed ground state hyperfine transition frequency of the caesium 133 atom $∆ν_{Cs}$ is $9192631770$ Hz.
• The speed of light in vacuum $c$ is $299792458 m/s$.
• The Planck constant $h$ is $6.62607015 × 10^{-34} Js$.

Each of the 3 points specifies a base unit of the SI unit system: the second, the meter, and the kilogram, respectively. But note that none of the statements defines the related unit directly. This is true for all 7 statements describing the SI unit system, including the ones not listed above. In fact, the direct definitions (with the more expected phrasing of “the second is …”) of the units are not in the main document at all, and can only be found on the last page of the draft, in Appendix 3.

This struck me as odd at first, that the document specifying the revisions to the SI base unit definitions does not seem to want to directly state what the units are. I then realized the reason. The descriptions on the first page of the document are all inverses of the unit definitions, phrased as factual statements about the physical world we live in.

This realization actually helped me understand the source of my fascination with these seemingly mundane scientific definitions. Units of measurement are constructs of the human mind to make sense of the universe, and there are no units more fundamental than the 7 SI base units. The statements that inversely define these base units sit simultaneously at the foundations of modern science and at the edge of our current understanding of the world. In a sense, these descriptions, though they do not directly define the units, encapsulates the core constituents of reality that each of the unit measures. This, to me, is a much more elegant way to define the SI base units.