The unnatural desire for naturalness

There's a particle called the muon that's almost like the electron, except it's about 206.768 times heavier. Nobody knows why. The number 206.768 is something we measure experimentally, with no explanation so far. Theories of physics tend to involve a bunch of unexplained numbers like this. If you combine general relativity with Standard Model of particle physics, there are about 25 of these constants.

Many particle physicists prefer theories where these constants are not incredibly huge and not incredibly tiny. They call such theories natural. Naturalness sounds good - just like whole wheat bread. But there's no solid evidence that this particular kind of naturalness is really a good thing. Why should the universe prefer numbers that aren't huge and aren't tiny? Nobody knows.

For example, many particle physicists get upset that the density of the vacuum is about

0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001

Planck masses per Planck volume. They find it 'unnatural' that this number is so tiny. They think it requires 'fine-tuning', which is supposed to be bad.

I agree that it would be nice to explain this number. But it would also be nice to explain the mass of the muon. Is it really more urgent to explain a tiny number than a number like 206.768, which is neither tiny nor huge?

+Sabine Hossenfelder say no, and I tend to agree. More precisely: I see no a priori reason why naturalness should be a feature of fundamental physics. If for some mysterious reason the quest for naturalness always led to good discoveries, I would support it. In science, it makes sense to do things because they tend to work, even if we're not sure why. But in fact, the quest for naturalness has not always been fruitful. Sometimes it seems to lead us into dead ends.

Besides the cosmological constant, another thing physicists worry about is the Higgs mass. Avoiding the 'unnaturalness' of this mass is a popular argument for supersymmetry... but so far that's not working so well. Sabine writes:

Here is a different example for this idiocy. High energy physicists think it’s a problem that the mass of the Higgs is 15 orders of magnitude smaller than the Planck mass because that means you’d need two constants to cancel each other for 15 digits. That’s supposedly unlikely, but please don’t ask anyone according to which probability distribution it’s unlikely. Because they can’t answer that question. Indeed, depending on character, they’ll either walk off or talk down to you. Guess how I know.

Now consider for a moment that the mass of the Higgs was actually about as large as the Planck mass. To be precise, let’s say it’s 1.1370982612166126 times the Planck mass. Now you’d again have to explain how you get exactly those 16 digits. But that is, according to current lore, not a fine-tuning problem. So, erm, what was the problem again?

Sabine explains things in such down-to-earth terms, with so few of the esoteric technicalities that usually grace discussions of naturalness, that it may be worth reading a more typical discussion of naturalness just to imbibe some of the lore.

This one is quite good, because it includes a lot of lore but doesn't try too hard to intimidate you into believing in the virtue of naturalness:

• G.F. Giudice, Naturally speaking: the naturalness criterion and physics at the LHC, available at https://arxiv.org/abs/0801.2562.

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