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. The closest match is specific to a particular, rather narrow concept in theoretical particle physics. I mean something much more general. I know many scientific colleagues who share this ideal. I also get the impression that this ideal is being eroded and cheapened, even among scientists, in our post-factual society.

I suspect the reason a better hit for Naturalness doesn’t come up more naturally in a Google search is, at least in part, an age effect. As wonderful a search engine as Google may be, it is lousy at identifying things B.G. (Before Google). The concept of Naturalness has been embedded in the foundations of science for centuries, to the point where it is absorbed by osmosis by students of any discipline: it doesn’t need to be formally taught; there probably is no appropriate website.

In many sciences, we are often faced with messy and incomplete data. In Astronomy in particular, there are often complicated astrophysical processes well beyond our terrestrial experience that allow a broad range of interpretations. Some of these are natural while others are contrived. Usually, the most natural interpretation is the correct one. In this regard, what I mean by Naturalness is closely related to Occam’s Razor, but it is something more as well. It is that which follows – naturally – from a specific hypothesis.

An obvious astronomical example: Kepler’s Laws follow naturally from Newton’s Universal Law of Gravity. It is a trivial amount of algebra to show that Kepler’s third Law, P^{2} = a^{3}, follows as a direct consequence of Newton’s inverse square law. The first law, that orbits are ellipses, follows with somewhat more math. The second law follows with the conservation of angular momentum.

It isn’t just that Newtonian gravity is the simplest explanation for planetary orbits. It is that all the phenomena identified by Kepler *follow naturally* from Newton’s insight. This isn’t obvious just by positing an inverse square law. But in exploring the consequences of such a hypothesis, one finds that one clue after another falls into place like the pieces of a jigsaw puzzle. This is what I mean by Naturalness.

I expect that this sense of Naturalness – the fitting together of the pieces of the puzzle – is what gave Newton encouragement that he was on the right path with the inverse square law. Let’s not forget that both Newton and his inverse square law came in for a lot of criticism at the time. Both Leibniz and Huygens objected to action at a distance, for good reason. I suspect this is why Newton prefaced his phrasing of the inverse square law with the modifier *as if*: “*Everything happens… as if the force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.” *He is not claiming that this is right, that it has to be so. Just that it sure looks that way.

The situation with the radial acceleration relation in galaxies today is the same. Everything happens *as if* there is a single effective force law in galaxies. This is true regardless of what the ultimate reason proves to be.

The natural explanation for the single effective force law indicated by the radial acceleration relation is that there is indeed a unique force law at work. In this case, such a force law has already been hypothesized: MOND. Often MOND is dismissed for other reasons, though reports of its demise have repeatedly been exaggerated. Perhaps MOND is just the first approximation of some deeper theory. Perhaps, like action at a distance, we simply don’t yet understand the underlying reasons for it.

Nice piece! As I see it simplicity is often the key. MOND offers a simple explanation but how can gravity ‘know’ where to behave in different ways? What coould the mechanism be? As for DM a particle we haven’t yet discovered could explain some phenomena but where the *ˆ#&! is it? Based on my limited knowledge I feel there is something fundemental we are missing. Perhaps we are trying to use one explanation for several different phenomena?

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Thanks. I agree that it feels like we are missing something fundamental. But what? Whatever it is, I would hope that it sensibly unites disparate phenomena. But that sort of thing is only obvious in hindsight.

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As much as I think the RAR is a breakthrough of the first order, I would point out that the notion of universal law given here is not the same as that in the abstract of the RAR paper. In this post you emphasize the fecundity of the law and what one might call the “aha!-ness” of it. In the abstract though, it is the extremely low scatter in the observation that is emphasized, along with the wide range of galaxies to which the relation applies. I think the abstract got it right. A universal law is strictly enforced everywhere. The deeper the better of course, but I’d say that’s secondary. To return to your example, I don’t think that Kepler’s laws should be demoted from this status simply because Newton found deeper ones (and of course the same can be said about Newton and Einstein’s GR).

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(to say it better, I’d argue that universal laws are valid to a high degree of approximation everywhere, but they can be more or less fundamental, cf. the Kepler < Newton < GR example.)

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Sure. I don’t mean to demote Kepler, and didn’t think I had done so. Just giving an example of what a natural result looks like.

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“Perhaps MOND is the first approximation to some deeper theory.” No perhaps — MOND has too many empirical successes — MOND is undoubtedly the first approximation to some deeper theory, Consider 8 possibilities for Newton’s 3 laws of motion: (± 1st law, ± 2nd law, ± 3rd law), where + means true and – means false. The string theorists like (+ 1st law, + 2nd law, + 3rd law) and supersymmetry. I say that supersymmetry needs to be replaced by MOND-compatible supersymmetry. From the point of view of Witten, Green, & Schwarz, this might be the deeper theory.

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