Fashion for naturalness
So almost everyone who is building his or her interest in fundamental physics on accessible experiments seems to be frustrated these days. The discovery of the Higgs boson may have made those emotions even worse, see e.g. Jester at Resonaances, in agreement with the "nightmare scenario" people would talk about 5 years ago and we seem to be living through now, so far (the scenario is that the LHC only finds the Higgs boson and nothing else). Those of us who don't think that physics ends at \(8\TeV\) or \(14\TeV\) – and this includes most formal theorists, I would guess – are largely unaffected by this particular spleen, of course. ;-)
Note that patience is sometimes needed. Peter Higgs hasn't spent 50 years in depressions even though he had to wait for the discovery of "his" goddamn particle for 48 years – despite the fact that it's a very trivial quantum of a field that is more mundane than any other field we have found in Nature (it's spinless, stupid). That's a reason to think that the problem is with the people, not with the actual progress in physics. People just don't like physics as much as our predecessors did. They keep on whining, complaining, and I am annoyed by them because the current physics' image of the world is richer and more accurate than it has been at any moment in the past.
There are clearly many important physics questions whose characteristic energy is higher than \(14\TeV\) and that still need to be resolved because they're essential for the inner workings of our Universe. Careful theoretical arguments and calculations must obviously play a crucial role in this process. Much like formal theorists don't care about the absence of new physics too much, experimenters don't care about theoretical arguments much. ;-)
Let me discuss an interesting example. Dr Lily Asquith of ATLAS wrote an interesting blog entry at the Guardian blogs today,
Desperately seeking SUSY.Her title was inspired by an old paper by Ginsparg and Glashow.
The picture above was originally placed beneath the subtitle. It shows Brad Pitt with someone who is definitely not Angelina Jolie but this combination was claimed to show a "perfect symmetry". Later, the picture was replaced by a less blasphemous picture of Madonna as Susan:
If the writer posted her own picture, it wouldn't really hurt! ;-)
But let's return to the content. Asquith expressed some degree of skepticism about supersymmetry, an attitude that is somewhat widespread among the experimenters. This asymmetry isn't shocking: experimenters are focusing on what they see and they don't think "too much ahead of time" because it's simply not their job.
She seems to be aware of the basic "naturalness" arguments although her detailed ideas about this principle are often incorrect. For example, we learn that it's unnatural for the up-quark to be twice lighter than the down-quark. Well, this ratio isn't unnatural because it's of order one.
The LHC has already ruled out many explanations of naturalness – such as the Higgs compositeness or technicolor – and "some corners of supersymmetric theories' parameter spaces" are really the only surviving candidates to explain naturalness. If these soldiers fall in coming years, "naturalness" as defined by 't Hooft is simply not a good guide to understand the unbearable lightness of the God particle's being.
Only recently, I realized how many people in particle physics – and which people – were deeply affected by the particular 't Hooft's paper that introduced naturalness. The paper contains many important conceptual ideas but when it comes to the question whether they're justified, it's a mixed bag. He really predicted some strong coupling near the electroweak scale, some compositeness or technicolor – and today we know that the prediction is almost certainly wrong.
The people whom I referred to in the previous paragraph – which includes various undergraduate and even graduate particle physics instructors that were teaching me – viewed the "new strong dynamics" at the electroweak scale to be "generic", "almost certain", and so on. I was never forced to read the paper in its entirety so I wasn't brainwashed. Maybe I am not alone in this "different generation" but I have always considered any ideas about the compositeness of the Higgs etc. to be totally awkward, contrived, unnatural, and unlikely. String theory seems to produce elementary scalar fields without any problems so it has always seemed unjustifiable to try to insert another layer of the onion in between the Higgs and more fundamental physics. The Higgs boson may also be light due to cancellations and other new principles (SUSY is the best example), something that was implicitly assumed to be impossible in 't Hooft's paper.
But imagine that there's just an elementary Higgs boson whose lightness is protected by no new physics at nearby scales. The anthropic explanation would get much more convincing but I think that strictly speaking, it would still not be established. It's still plausible that the underlying high-energy fundamental theory produces light fields for a certain mathematical reason to be understood – while this reason doesn't actually have to imply the existence of any new light fields.
Fine. Let me not go into it. The anthropic explanation of the light Higgs may in principle be right, too. The Higgs is fine-tuned to be light simply because it's needed for stars to be long-lived and, consequently, for life to exist. Ms Asquith doesn't like the anthropic principle, either. But because she doesn't seem to like any other explanation of the Higgs' lightness either, you may worry that she is an example of a permanent, habitual naysayer who has no solution but denounces all other attempted solutions.
Some people, like Nima Arkani-Hamed, think that this "anthropic vs non-anthropic" question is a defining, polarizing issue of contemporary physics, a crossroad that must send physics into one of two possible, vastly separated roads. This "extreme crisis moment" is intriguing and comments about it may be linked to Nima's immense temperament. But I, for one, have some doubts whether this polarization is as sharp as Nima is imagining. In fact, it seems plausible that the truth is somewhere in between.
Of course that it's wrong if someone proposes to use the anthropic slogans as an answer to – or as an excuse for – every currently open problem in physics. Many questions in the past – well, almost all of them – turned out to have non-anthropic explanations and there is no verse in the Bible that would imply that right after the year 2000 or 2012, a phase transition has to occur and all questions must be answered anthropically. This is, of course, nonsense. Currently open questions may allow for "conventional" physical explanations much like the questions open in the past turned out to have such explanations.
On the other hand, the laws and parameters of our Universe clearly have to be such that they allow life to exist because life does exist, after all. And whenever some features of Nature seem to be chosen "randomly", we must care about the probability distributions. While Nature may offer some cold hard lifeless distributions, it's clear that we only want to pick those that seem relevant to us. If Nature predicts zillions of universes – or a vast majority of universes – that don't allow life, it's not necessarily a contradiction.
The real question isn't whether the anthropic principle gives us a non-trivial explanation of something: it never does. All anthropic explanations are just tautologies or particular projections or aspects of the trivial observation that we're here. They're filters applied to the set of possible theories by looking at some function of the observed facts (even though the anthropic champions want to make their "existence of stars and life" sound more canonical than what they are, namely just some observed facts among many others). The real question is whether there exists a conventional physical explanation for a physics mystery. For many physics mysteries, we know that the answer is Yes: that's why they're no longer real mysteries. For others, it may be No.
Asquith mentions some of the other "unnaturally small numbers" that are known to have a conventional physics explanation. In particular, she reminds us that the proton and the neutron have very similar masses. They only differ by a small percentage of the proton mass. This approximate degeneracy is also needed for the existence of stars and life but we don't refer to those things when we explain the approximate degeneracy. Instead, we say that the proton and the neutron are two components of a doublet under an approximate symmetry, the flavor symmetry mixing two light quarks, namely up and down.
While the lightness of any quark may be unnatural, if two of them happen to be light at the same moment, it doesn't look excessively more unnatural. After all, whatever mechanism makes the up-quark light may make the down-quark light, too. So the explanation of the approximate degeneracy based on the approximate flavor symmetry seems to remove most of the mystery from the question.
However, we could perhaps find more complicated examples of "apparent fine-tuning" that still has some conventional explanation but where we may be tempted that the right explanation is "partly anthropic", anyway. For example, some of these "approximate degeneracies required for life" may depend on the detailed values of the quarks' bare masses. If such "approximate degeneracies (or other numerical accidents) needed for life" exist, we can't say that the right explanation is purely conventional because it still relies on the detailed values of the quarks' bare masses which we can't calculate at this moment.
You may see that I am proposing that the transition from conventional to anthropic explanations could be continuous and gradual. If that's the case, I would like to know what is the parameter that controls the "percentage" – the parameter that decides whether the right explanation to a mystery is more conventional or more anthropic.
Some clues.
Whenever you adopt the assumption that some mystery may be explained anthropically, it allows you – and perhaps encourages you – to imagine that our visible Universe is fundamentally very messy, awkward, a Rube Goldberg machine. The anthropic principle is an excuse that allows some people to say that many things must simply be separately adjusted because that's needed for life. This description of a universal property of the anthropic principle also makes it clear that creationism is one of the extreme versions of the anthropic principle (regardless of the pro-God or anti-God rhetoric that may sound diametrically opposite: but I am trying to analyze the logical framework of the ideologies, not some superficial religious affiliations).
On the other hand, physics based on conventional explanations always tries to make the world as "unified" as possible – explain a maximum number of observed features of Nature as consequences of the same, small number of assumptions. A possible problem with this "opposite extreme", conventional physics as we've known it, is that it may seem incapable of explaining certain things such as the tiny cosmological constant or the very small Higgs mass.
A relevant quantity is the probability that a world that qualitatively agrees with ours follows from a conventional explanation or from the anthropic explanation. To be able to decide which explanation is more likely, we must guarantee that all these probabilities are numbers in between 0 and 1 – but they're never 0 or 1. For example, it is illegitimate to use the "extreme anthropic reasoning" that would allow you "solve any problem". With this perspective, Christian creationism – but, to disappoint my Christian readers, every other miraculous story about the Universe as well – would be possible.
Nima Arkani-Hamed would say that it is legitimate to use the anthropic explanations to demystify the mysteries and consider probabilities such as \(10^{-400}\), i.e. ten to the power of a "few hundreds", acceptably large. There are many universes in the multiverse and their number is comparable to these numbers. On the other hand, creationism is invalid because it requires to consider processes (known as miracles) whose probabilities are \(\exp(-10^{400})\) or so – even exponentially smaller – to be acceptable.
While it's true that \(\exp(-10^{400})\) is "qualitatively" smaller than \(10^{-400}\), you may still be worried about the discrimination against one of them. After all, both of these numbers are small and the transition between them is continuous. To defend Arkani-Hamed's perspective, you may try to refer to string theory that apparently allows us to estimate that the number of semirealistic vacua is of order "ten to the hundreds" – which arises from the fact that the most complicated Calabi-Yau manifolds have Hodge numbers of order "a few hundreds" as well.
Maybe it's a right argument. Maybe the counting of cycles of Calabi-Yau manifolds implies that "universe-creating" events with probabilities "ten to the minus few hundred" are acceptably likely while events whose probabilities are "ten to ten to minus few hundreds" are unacceptable miracles. But I have some problems with this conclusion. After all, \(10^{-400}\) is still an extremely small number. The anthropic ideology de facto tells you to treat numbers such as \(10^{-400}\) to be numbers of order one. But if that's the case, all the values of observables – and even probabilities of "individual events" – we may ever measure are of order one! (It's because we can't really measure anything with the accuracy \(\exp(-10^{400})\) or detect similarly small effects.) That would mean that no explanations are needed for anything that will ever become a part of science: the anthropic ideology is enough. This conclusion would clearly be invalid.
So if we try to find a demarcation line between the conventional and anthropic explanations, we simply can't afford to declare the anthropic explanations the winner whenever the probabilities we need to explain are as small as \(10^{-400}\). These are already very small probabilities and even though the anthropic principle wants to claim it's able to "explain all these small miracles", we must resist and we must still give a chance to conventional explanations.
What's the right quantitative procedure to estimate – and to justify the estimate – whether it is legitimate to rely on the anthropic non-explanation? Is there a procedure at all? Do you have any ideas?
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