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General strategy of naturalness is just plain logical inference

Backreaction has launched another crusade against naturalness in high-energy physics.

Who is crazy now? (In which I am stunned to encounter people who agree with me that naturalness is nonsense.)
It may be appropriate to start with an answer to the question in that title. Sabine Hossenfelder isn't crazy. Instead, these statements are yet another almost rigorous proof that she is a 100% incompetent, fake physicist – a layman who has no clue about modern physics. It's something else than being crazy. Over 7.5 billion people in the world misunderstand naturalness but they're not "crazy".

We're offered a picture of white teeth with the rhetorical question: Are they natural? Well, sometimes one can feel that the whiteness has been enhanced (but sometimes by very natural procedures and stuff!). But lots of people have really natural white teeth. And things like fillings are surely a symptom of unnatural, artificial interventions into the teeth, aren't they? So if the dental context were discussed cleverly, it could provide us with good enough analogies to particle physics: violations of the "beauty" such as the dental fillings surely betray an unnatural intervention. But she doesn't want to do that.

I won't discuss her suggestions that some hassles with her tooth crown demonstrate a point in particle physics. They don't and the suggestion is so dumb that I won't honor it with a response. The color and slope of the teeth follow from some (statistical) laws of biology, chemistry, and physics. And these laws may be discussed from the viewpoint of naturalness, too. The idea that naturalness fails in these contexts is as wrong as all of her other statements about contemporary particle physics.

Naturalness is an argument in favor of a physical theory – and against other, unnatural theories. There are various detailed meanings of the word "naturalness" that differ by their precision. One may talk about naturalness at a very general level – something that allows us to distinguish whether something has evolved in nature or whether it has been created through the human creation or modified by human interventions or engineering. We want the laws of physics to be natural in this sense because we assume that they weren't constructed by a human engineer.

The most general meaning of naturalness may be an expression of someone's feelings and emotions which lacks any definition that could be written in terms of mathematical symbols or at least words.

But particle physicists tend to use a more special type of naturalness. The dimensionless parameters that determine the natural theory – a theory that gets a good grade from naturalness, and this grade matters – shouldn't be extremely large or extremely small in comparison with one: they should be of order one. The most precise, technical naturalness formulates these requirements more accurately and takes the assumed global symmetries into account. One may insert some reasoning that has led most phenomenologists to assume that for every massive scalar particle such as the Higgs boson, there should exist additional particles whose masses are of the same order as the Higgs mass and that help to keep the Higgs boson comparably light. I've always had doubts about this "strongest" form of naturalness – scales may be hypothetically generated as exponentially small by various mechanisms etc. – but it was still true that these arguments have increased the probability that the simple picture with "additional light enough particles" is right – increased but not to 100%.

Let me provide you with an unnatural theory that I will call Leo Vuyk 2020 theory. He hasn't invented this precise theory yet but he's free to plagiarize me. The theory says that the world is a giant strawberry whose vital characteristic, the Vyukness, is a real number, a parameter known as \(LV\). It defines the ratio of the diameters of the strawberry and its pit. Strawberries usually don't have pits but Leo Vyuk's strawberry has one.

Now, the parameter \(LV\) contains the answer to all questions in the world. It's approximately equal to \(42.05121973\dots\). Fourty-two was explained in the Hitchhiker's Guide. But it's the other digits that matter. If you divide the decimal expansion of \(LV\) to 10-digit segments, the segments are equal to the results of all chronologically sorted quantitative experiments ever done by the scientists. So if you read it carefully, there will be the digits \(0000000125\) that mean that the Higgs boson mass is \(125\GeV\), and so on.

It's a theory that contains the answers to all quantitative questions about Nature.

What is wrong with that theory? It's not predictive, some people would say. But it's just because we haven't found a good enough way to calculate the precise value of \(LV\), Leo could object, and such a formula for \(LV\) could perhaps materialize in the future. A more lasting problem is that the theory is not natural because the constant \(LV\) contains too many zeroes – many more zeroes than a random number of the same type. So it's extremely unlikely that Nature would pick this value by accident.

That's the actual, logical, technical explanation why we "don't like" such a theory. For the theory to be right, some parameters – its only parameter \(LV\) – has to have values or a value that is very unlikely to emerge from a hypothetical calculation that Leo Vuyk may dream about. (The theory also seems to require a preferred reference frame where the measurements are ordered chronologically, it requires one to objectively divide processes to measurements and non-measurements, and it has other big problems.)

By construction, I needed the value of \(LV\) to be fine-tuned. The example was chosen as an extreme form of fine-tuning. As long as physicists will remain physicists, they will need to refuse theories that are as unnatural as the Leo Vyuk 2020 theory above. This is not something that can go away after null results coming from the LHC after 5 or 10 years.

The reason why we refused the 2020 theory as an unnatural one wasn't formulated as a rigorous proof. It was evidence that had the probabilistic character. But that's exactly how natural science almost always works. Science is a method that allows us to say that certain things are more likely and certain things are less likely. If a theory needs to be extremely lucky with the digits in its parameter(s), in order to agree with the empirical data (and in order to be logically consistent), the validity of the theory itself is less likely.

What we're doing isn't really a consequence of some assumed laws of physics – that could be replaced with other laws of physics. The probabilistic reasoning above only assumes pure mathematics – well, the probabilistic calculus or Bayesian inference, if you wish. And pure mathematics can't ever go away. So some kind of naturalness will always be assumed because it's absolutely inseparable from any rational thinking.

What has arguably failed after the null results from the LHC isn't naturalness as a principle. What has failed is an extreme version or simplification of the naturalness that says that the absolute value of a random number \(x\) normally distributed around \(0\) with the standard deviation \(1\) cannot be greater than \(2\) (in combination with another assumption, namely that the field content that is sufficient for a discussion of the value of parameters is as minimal as MSSM or something like that). Well, such a recipe works approximately 95% of the time. But it doesn't always work. Statistics happens. Sometimes this rule-of-thumb, like all rules-of-thumbs, is unavoidably violated.

So the people who built all their research on the bet that the normal distribution may be assumed to be squeezed between \(-2\leq x \leq 2\) were never guaranteed to win that bet, and they have arguably lost this particular one. I have always been among those who have criticized the selective belief in the "new physics around the corner" which was always driven by a wishful thinking, not by solid evidence (it's a wishful thinking because the early new discoveries they believed in are more exciting and they wanted it – and they wanted to get the prizes for boldly guessing those in advance). Numbers like \(1/137\) are still "of order one", although barely so. (The fine-structure constant may be calculated from more fundamental constants at the more relevant, higher energy scales and they're "closer to be of order one" than \(1/137\).) Values of parameters like that may occur – and they have already occurred.

But such failures of the LHC to find new physics after several years can never "debunk" the principle of naturalness in its general form – because no physical experiment can ever refute the laws of mathematics.

I had to laugh when I read her comments about the changing Zeitgeist:
[Everyone has always politely informed me that I was a stupid crank.]

But this time it’s different. One day into the conference I notice that all I was about to say has already been said. The meeting, it seems, collected the world’s naturalness skeptics...
Well, there's a simple explanation why "this time it's different". It's because she has attended a conference that unnaturally collected various people – overwhelmingly third-class physicists such as Hossenfelder herself – who were skeptical about naturalness. As I mentioned, such people aren't rare, well over 7 billion people in the world wouldn't support naturalness with a logical defense. ;-) When you apply filters like that, what you get is a group that is skeptical towards naturalness. What a surprise. But there is no way to deduce anything from a poll taken among these cherry-picked people.

On top of that, these people generally have nothing to say. They may refuse modern physics but they have nothing to replace it with. Hossenfelder herself has admitted that she had nothing to say at the conference. She has nothing to say anywhere. She just emits irrational anti-science tirades and it's apparently enough for her brain-dead readers.

That conference took place in Aachen. It became a politically important city (on the German-Benelux border) during Pepin the Short, a Frankish ruler. At school, as kids, we would always laugh hysterically when Pepin the Short was mentioned because his name sounds as if he had a short penis. Aachen is named "Cáchy" in Czech which arose from a degeneration of "z Aachen" i.e. "from Aachen" in Czech.

When people completely lose it – and lose their ability to rationally think – they may start to build on the very existence of similar losers who gather in a scientifically irrelevant city, and on dumb and illogical analogies with tooth crowns. But scientists actually need to work with ideas that make some sense – and in the case of physical theories, it always includes the condition that the theories have to embrace some kind of naturalness at one level or another.

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