## Wednesday, August 10, 2016 ... /////

### Naturalness, a null hypothesis, hasn't been superseded

Quanta Magazine's Natalie Wolchover has interviewed some real physicists to learn

What No New Particles Means for Physics
so you can't be surprised that the spirit of the article is close to my take on the same question published three days ago. Maria Spiropulu says that experimenters like her know no religion so her null results are a discovery, too. I agree with that. I am just obliged to add that if she were surprised she is not getting some big prizes for the discovery of the Standard Model at $\sqrt{s}=13\TeV$, it's because her discovery is too similar to the discovery of the Standard Model at $\sqrt{s}=1.96\TeV$, $\sqrt{s}=7\TeV$, and $\sqrt{s}=8\TeV$, among others. ;-) And the previous similar discoveries were already done by others.

She and others at the LHC are doing a wonderful job and tell us the truth but the opposite answer – new physics – would still be more interesting for the theorists – or any "client" of the experimenters. I believe that this point is obvious and it makes no sense to try to hide it.

Nima Arkani-Hamed says lots of things I appreciate, too, although his assertions are exaggerated, as I will discuss. It's crazy to talk about a disappointment, he tells us. Experimenters have worked hard and well. Those who whine that some new pet model hasn't been confirmed are spoiled brats who scream because they didn't get their favorite lollipop and they should be spanked.

Yup. But when you look under the surface, you will see that there are actually many different opinions about naturalness and the state of physics expressed by different physicists. If you're strict enough, many of these opinions almost strictly contradict each other.

Nathaniel Craig whom I know as a brilliant student at Harvard says that the absence of new physics will have to be taken into account and addressed but he implicitly makes it clear that he will keep on thinking about theories such as his "neutral naturalness". Some kind of naturalness will almost certainly be believed and elaborated upon by people like him in the future, anyway. I think that Nathaniel and other bright folks like that should grow balls and say some of these things more clearly – even if they contradict some more senior colleagues.

Aside from saying that the diphoton could have been groundbreaking (yup), Raman Sundrum said:
Naturalness is so well-motivated that its actual absence is a major discovery.
Well, it is well-motivated but it hasn't been shown not to exist. This claim of mine contradicting Sundrum's assertion above was used in the title of this blog post.

What does it mean that you show that naturalness doesn't exist? Well, naturalness is a hypothesis and you want to exclude it. Except that naturalness – while very "conceptual" – is a classic example of a null hypothesis. If you want to exclude it, you should exclude it at least by a five-sigma deviation! You need to find a phenomenon whose probability is predicted to be smaller than 1 in 1,000,000 according to the null hypothesis.

We are routinely used to require just a 2-sigma (95%) exclusion for particular non-null hypotheses that add some new particles of effects. But naturalness is clearly not one of those. Naturalness is the null hypothesis in these discussions. So you need to exclude it by the five-sigma evidence. Has it taken place?

Naturalness isn't a sharply defined Yes/No adjective. As parameters become (gradually) much smaller than one, the theory becomes (gradually) less natural. When some fundamental parameter in the Lagrangian is fine-tuned to 1 part in 300, we say that $\Delta=300$ and the probability that the parameter is this close to the special value (typically zero) or closer is $p=1/300$.

(The precise formula to define $\Delta$ in MSSM or a general model is a seemingly technical but also controversial matter. There are many ways to do so. Also, there are lots of look-elsewhere effects that could be added as factors in $\Delta$ or removed from it. For these reasons, I believe that you should only care about the order of magnitude of $\Delta$, not some precise changes of values.)

The simplest supersymmetric models have been shown to be unnatural at $\Delta \gt 300$ or something like that. That means that some parameters look special or fine-tuned. The probability of this degree of fine-tuning is $p=1/300$ or so. Does it rule out naturalness? No because we require a five-sigma falsification of the null hypothesis e.g. $p=1/1,000,000$ or so. We're very far from it. Superpartners at masses comparable to $10\TeV$ will still allow naturalness to survive.

Twenty years ago, I wasn't fond of using this X-sigma terminology but my conclusions were basically the same. If some parameters are comparable to $0.01$, they may still be said to be of order one. We know such parameters. The fine-structure constant is $\alpha\approx 1/137.036$. We usually don't say that it's terribly unnatural. The value may be rather naturally calculated from the $SU(2)$ and $U(1)_Y$ electroweak coupling constants and those become more natural, and so on. But numbers of order $0.01$ only differ from "numbers of order one" by some 2.5 sigma.

My taste simply tells me that $1/137.036$ is a number of order one. When you need to distinguish it from one, you really need a precise calculation. For me, there's pretty much "no qualitative realm in between" $1$ and $1/137.036$. Numbers like $0.01$ have to be allowed in Nature because we surely know that there are dimensionless ratios (like $m_{\rm Planck}/m_{\rm proton}$) that are vastly different from one and they have to come from somewhere. Even if SUSY or something else stabilizes the weak scale, it must still be explained why the scale – and the QCD scale (it's easier) – is so much lower than the Planck scale. The idea that everything is "really" of the same order is surely silly at the end.

OK, assuming that $\Delta\gt 300$ has been established, Sundrum's claim that it disproves naturalness is logically equivalent to the claim that any 3-sigma deviation seen anywhere falsifies the null hypothesis, and therefore proves some new physics. Well, we know it isn't the case. We had a 4-sigma and 3-sigma diphoton excess. Despite the fact that the Pythagorean combination is exactly 5 (with the rounded numbers I chose), we know that it was a fluke.

Now, the question whether naturalness is true is probably (even) more fundamental than the question whether the diphoton bump came from a real particle. But the degree of certainty hiding in 3-sigma or $p=1/300$-probable propositions is exactly the same. If you (Dr Sundrum) think that the observation that some $\Delta \gt 300$ disproves naturalness, then you're acting exactly as sloppily as if you consider any 3-sigma bump to be a discovery!

A physicist respecting that particle physics is a hard science simply shouldn't do so. Naturalness is alive and well. 3-sigma deviations such as the observation that $\Delta \gt 300$ in some models simply do sometimes occur. We can't assume that they are impossible. And we consider naturalness to be the "basic story to discuss the values of parameters" because this story looks much more natural or "null" than known competitors. If and when formidable competitors were born, one could start to distinguish them and naturalness could lose the status of "the null hypothesis". But no such a convincing competitor exists now.

As David Gross likes to say, naturalness isn't a real law of physics. It's a strategy. Some people have used this strategy too fanatically. They wanted to think that even $\Delta \gt 10$ was too unnatural and picked other theories. But this is logically equivalent to the decision to follow research directions according to 1.5-sigma deviations. Whenever there's a 1.5-sigma bump somewhere, such a physicist would immediately focus on it. That's simply not how a solid physicist behaves in the case of specific channels at the LHC. So it's not how he should behave when it comes to fundamental conceptual questions such as naturalness, either.

Naturalness is almost certainly a valid principle but when you overuse it – in a way that is equivalent to the assumption that more than 3-sigma or 2-sigma or even 1.5-sigma deviations can't exist – you're pretty much guaranteed to be sometimes proven wrong by Mother Nature because statistics happens. If you look carefully, you should be able to find better guides for your research than 1.5-sigma bumps in the data. And the question whether $\Delta\lt 10$ or $\Delta \gt 10$ in some model is on par with any other 1.5-sigma bump. You just shouldn't care about those much.

While I share much of the spirit of Nima's comments, they're questionable at the same moment, too. For example, Nima said:
It’s striking that we’ve thought about these things for 30 years and we have not made one correct prediction that they have seen.
Who hasn't made the correct predictions? Surely many people have talked about the observation of "just the Standard Model" (Higgs and nothing else that is new) at the LHC. I've surely talked about it for decades. And we had discussions about it with virtually all high-energy physicists who have ever discussed anything about broader physics. I think that the Standard Model was by far the single most likely particular theory expected from the first serious LHC run at energies close to $\sqrt{s}=14\TeV$.

The actual adjective describing this scenario wasn't "considered unlikely" but rather "considered uninteresting". It was simply not too interesting for theorists to spend hours about the possibility that the LHC sees just the Standard Model. And it isn't too interesting for theorists now, either. A hard-working theorist would hardly write a paper in 2010 about the "Standard Model at $\sqrt{s}=13\TeV$". There's simply nothing new and interesting to say and no truly new calculation to be made. But the previous sentence – and the absence of such papers – doesn't mean that physicists have generally considered this possibility unlikely.

I am a big SUSY champion but even in April 2007, before the LHC was running, I wrote that the probability was 50% that the LHC would observe SUSY. Most of the remaining 50% is "just the Standard Model" because I considered – and I still consider – the discovery of all forms of new physics unrelated to SUSY before SUSY to be significantly less likely than SUSY.

So I think that the statement that "we haven't made any correct prediction" to be an ill-defined piece of sloppy social science. The truth value depends on who is allowed to be counted as "we" and how one quantifies these voters' support for various possible answers. When it came to a sensible ensemble of particle physicists who carefully talk about probabilities rather than hype or composition of their papers and who are not (de facto or de iure) obliged to paint things in more optimistic terms, I am confident that the average probability they would quote for "just the Standard Model at the LHC" was comparable to 50%.

I want to discuss one more quote from Nima:
There are many theorists, myself included, who feel that we’re in a totally unique time, where the questions on the table are the really huge, structural ones, not the details of the next particle. We’re very lucky to get to live in a period like this — even if there may not be major, verified progress in our lifetimes.
You know, Nima is great at many things including these two:
1. A stellar physicist
2. A very good motivational speaker
I believe that the quote above proves the second item, not the first. Are we in a totally unique time? When did the unique time start? Nima has already been talking about it for quite some time. ;-) If the young would-be physicists believe it, the quote may surely increase their excitement. But aren't they being fooled? Is there some actual evidence or a rational reason to think that "physics is going through a totally unique time when structural paradigm shifts are around the corner"?

I think that the opposite statement is much closer to be a rational conclusion of the available evidence. Take the statements by Michelson or Kelvin over 100 years. Physics is almost over. All that remains is to measure the values of the parameters with a better precision.

Well, I think that the evidence is rather strong that this statement would actually be extremely appropriate for the present situation of physics and the near future! This surely looks like a period in which no truly deep paradigm shifts are taking place and none are expected in coming months or years. I think that Nima's revolutionary proposition reflects his being a motivational speaker rather than a top physicist impartially evaluating the evidence.

We should really divide the question of paradigm shifts to those that demand an experimental validation; and those that may proceed without an experimental validation. These two "realms of physics" have become increasingly disconnected – and this evolution has always been unavoidable. And it's simply primarily the first one, the purely theoretical branch, where truly new things are happening. When you only care about theories that explain the actual doable experiments, the situation is well-described by the Michelson-Kelvin quote about the physics of decimals (assuming that Michelson or Kelvin become a big defenders of the Standard Model).

Sometimes motivational speeches are great and needed. But at the end, I think that physicists should also be grownups who actually know what they're doing even if they're shaping their opinions about big conceptual questions.

For years, Nima liked to talk about the unique situation and the crossroad where it's being decided whether physics will pursue the path of naturalness or the completely different path of the anthropic reasoning. Well, maybe and Nima sounds persuasive but I have always had problems with these seemingly oversimplified assertions.

First, the natural-vs-anthropic split is just a description of two extreme philosophies that may be well-defined for the theories we already know but may become inadequate for the discussion of the future theories in physics. In particular, it seems very plausible to me that the types of physics theories in the future will not "clearly fall" into one of the camps (natural or anthropic). They may be hybrids, they may be completely different, they may show that the two roads discussed by Nima don't actually contradict each other. At any rate, I am convinced that when new frameworks to discuss the vacuum selection and other things become persuasive, they will be rather quantitative again: they will have nothing to do with the vagueness and arbitrariness of the anthropic principle as we know it today. Also, they will be careful in the sense that they will avoid some of the naive strategies by the "extreme fans of naturalness" who think that 2-sigma deviations or $\Delta \gt 20$ are too big and can't occur. Future theories of physics will be theories studied by grownups – physicists who will avoid the naivite and vagueness of both the extreme naturalness cultists as well as the anthropic metaphysical babblers.

Even if some new physics were – or had been – discovered at the LHC, including supersymmetry (not sure about the extra dimensions, those would be really deep), I would still tend to think that the paradigm shift in physics would probably be somewhat less deep than the discovery of quantum mechanics 90 years ago.

So while I think that it's silly to talk about some collapse of particle or fundamental physics and similar things, I also think that the talk about the exceptionally exciting situation in physics etc. has become silly. It's surely not my obsession to be a golden boy in the middle. But I am in the middle when it comes to the question whether the future years in physics are going to be interesting. We don't know and the answer is probably gonna be a lukewarm one, too, although both colder and hotter answers can't be excluded. And I am actually confident that the silent majority of physicists agrees that the contemporary physics and fundamental physics in the foreseeable future is and will be medium-interesting. ;-)