I have been musing for a while on the idea of writing about Naturalness in science, particularly as it applies to the radial acceleration relation. As a scientist, the concept of Naturalness is very important to me, especially when it comes to the interpretation of data. When I sat down to write, I made the mistake of first Googling the term. The top Google hits bear little resemblance to what I mean by Naturalness.

So the radial acceleration relation is a new law of nature. What does it mean? One reason we have posed it as a law of nature is that it is interpretation-free. It is a description of how nature works – in this case, a rule for how galaxies rotate. Why nature behaves thus is another matter.

Flat rotation curves were the first clear evidence that the dynamics of galaxies do not follow the same rules as planetary systems. But they do follow rules. These include asymptotic flatness, Tully-Fisher, the luminosity-size-rotation curve shape relation (aka the `universal‘ rotation curve), Renzo’s rule, and the central density relation.

Previously I noted how we teach about Natural Law, but we no longer speak in those terms. All the Great Laws are already know, right? Surely there can’t be such things left to discover! That rotation curves tend towards asymptotic flatness is, for all practical purposes, a law of nature. It is tempting to leap straight to the interpretation (dark matter!), but it is worth appreciating the discovery for itself.