Today, the ‘discovery’ of the elusive Higgs Boson was announced at CERN. ‘Discovery’ in scare quotes, because when dealing with the criteria for new discoveries in fundamental physics, there is always some arbitrariness, which I will explain in a moment. I’ve just watched the live webcast of the talks at CERN today, and as expected, they were built around the announcement that the Higgs has been discovered at ~125 GeV.

There are plenty of excellent resources in the internet explaining the significance of the Higgs boson, and the ramifications that the discovery has for future physics. CERN has a sort of FAQ about the Higgs here. In addition, see for instance Richard Ruiz’s post ‘What Comes Next’ in the Quantum Diaries blog, or Matt Strassler’s ‘Why the Higgs Particle Matters’ in his Of Particular Significance blog. Both blogs are full of interesting and useful posts on the Higgs and related matters. But as interesting as all these posts from the point of view of physicists are, they leave open several questions that might be of interest to philosophers. In this post I will attempt to address some of those questions, and analyse the philosophical significance of the Higgs.

As a disclaimer, I have to emphasise that I’m by no means an expert on particle physics, and a lot of what I say below builds on the material from the mentioned sources. I also wrote this rather hastily while listening to the talks, so I apologise for any errors in the science. However, these should have little effect on my philosophical analysis in any case.

The facts, in my understanding, are as follows:

• Both of the independent groups, ATLAS and CMS, presented strong results to the effect that there is a Higgs boson near 125 GeV.
• Although all the data is compatible with the discovered boson being the Standard Model Higgs, there is no confirmation of this yet.
• The picture could be much more complicated than what has been seen so far; there may be a number of other Higgs bosons, corresponding to different Higgs fields.
• What was discovered is most likely a scalar particle (with a spin of zero), and helps to explain electroweak symmetry breaking, but the details remain open.

Now, to begin with, something should be said about what constitutes a “discovery”. As I understand it, particle physics has an accepted definition for what is sufficient to claim a discovery: 5.0 sigma significance, i.e. level of certainty up to five standard deviations. In statistical terms, this means a probability of less than one in a million that the observed phenomenon is produced by something else than the postulated Higgs, namely statistical fluctuation. The reason for this type of talk is of course that the Higgs cannot be observed directly. Rather, we can observe decay products, such as photons, which could be produced by a number of phenomena that have to be ruled out. This also makes it quite clear that there is always an aspect of fallibility in these types of results.

We have a discovery! (Ripped off from Joe Incandela’s (CMS) talk today.)

Interestingly, at the press conference after the talks at CERN, the journalists (most of whom asked pretty idiotic questions) kept asking whether it is the Higgs that has been discovered, clearly not quite understanding what they even mean by the Higgs. Part of the problem, I think, is that the people answering the questions were experimental physicists, not theoretical. They could’ve done a better job explaining the theory. To put it simply, we’re looking for an explanation for the electroweak symmetry breaking familiar from the Higgs mechanism. The Higgs mechanism postulates the Higgs field which is responsible for the masses of elementary particles. In some sense, the Higgs is just whatever serves the purpose of explaining this phenomenon. But in effect I think that people are associating this with the Standard Model Higgs, i.e. the Higgs that has the properties compatible with the standard model (among other things, a spin of zero). Right now, this question remains open. Emphasising the words of Rolf Heuer, I would say that there is a Higgs, because whatever has been discovered, it’s at least a part of the explanation for the electroweak symmetry breaking, but it might not be the explanation fully compatible with the Standard Model.

In the interviews at CERN aired after the main event, Philip Warren Anderson, who postulated the Higgs mechanism in 1962, said something quite interesting about the original modelling of the Higgs mechanism and the postulation of the Higgs. He indicated that back in the sixties they didn’t expect that the model was anything more than that: an interesting model which probably has little to do with real physics. In particular, Anderson praised ‘imagination’ as the source of the modelling, emphasising that it’s ‘simple ideas’ that we have to explore. This aligns nicely with the methodology of scientific reasoning (and indeed “discovery”) that I’ve proposed in a couple of papers, ‘A New Definition of A Priori Knowledge: In Search of a Modal Basis‘ and ‘A Priori and A Posteriori: A Bootstrapping Relationship‘ in particular. In short, what Anderson describes as ‘imagination’ is what I consider to be a priori modelling of the space of metaphysically possible scenarios that could explain the data (the a posteriori basis) we currently have. Now, this is where the Higgs (mechanism) gets interesting, it’s a theoretical model that has now, after 50 years, been virtually confirmed with an enormous experimental effort. But I think it is a mistake to focus on the ‘discovery of the Higgs particle’. Instead, we should congratulate the teams at CERN about the confirmation of a possible explanation (a model) for one of the central questions in physics, not the discovery of a particle.

Physicists already knew that there must be something like the Higgs field which is responsible for the mass of things like W and Z bosons. They want to study the properties of this field, which can be done by finding and studying the corresponding Higgs particle. But: the Higgs field may not be elementary, it could be composed of several other fields, each of which would have a corresponding Higgs boson. So, we know of a number of possible combinations of particles and fields that would explain our current empirical data — and many of these options are still live.

In fact, even in the now unlikely event (less than one in a million) that the boson confirmed by the data were just a statistical fluctuation, or that something else is responsible for the observed deviations in the decay products, we could say something interesting. Whatever the arrangement of elementary fields and particles is, we do know that it manifests itself in such a way that we observe massive particles (that is, particles that have mass) like W and Z bosons. Hence, when we quantify over the Higgs boson by asking: ‘Does the Higgs boson exist?’, we are primarily interested in an explanation for previous data, that is, we want to understand the mechanism which is responsible for the emergence of massive particles. To this end, it makes little difference whether there exists such a thing as the Higgs boson. The experiments at the LHC are designed to reveal us something more about the nature of the Higgs field or fields, and we already know of the existence of something like the Higgs field(s). Now it seems very likely that at least one such field exists, and it’s the decay products of a boson corresponding to that field that ATLAS and CMS have been studying.

Philosophical analysis

Philosophically, perhaps the most interesting question is this: how do we know that the physicists are talking about the same thing when they debate the properties and the existence of the Higgs boson? There is certainly some common ground between the disputants, such as the Standard Model of quantum mechanics, but that is hardly sufficient to ensure that the disputants are indeed talking about the same thing, since the discovered boson may not even be the Standard Model Higgs (we will hopefully know in a couple of months). Building on Matt Strassler’s Higgs FAQ, here are the options (assuming that the announced results are not a mere statistical fluctuation):

1. There is a Standard Model Higgs, with a mass of ~125 GeV.
2. There is a Standard Model Higgs, but some other yet unknown particles and/or forces cause it to behave in unexpected ways, making it difficult to observe.
3. There are several Higgs bosons, which are probably more difficult to observe than a Standard Model Higgs.
4. There is no Standard Model Higgs boson, but rather something completely different: new particles and/or forces.

From what was announced today, there is no deciding between these options, but it seems that a lot of people are hoping for (1). I gather that (2) is unlikely, but it’s not impossible: the boson that we have discovered could turn out to be one of these unknown particles that mask the Standard Model Higgs. I don’t think that this is an option that will be seriously entertained from now on though, at least insofar as the properties of the discovered boson don’t turn out to be really strange. (3) is certainly a live option, as the observed boson may not be the Standard Model Higgs, in which case there could be other Higgs bosons that are difficult to observe. (4) is also live, but it appears that the discovered boson fits the Standard Model to such an extent that it must have some relevance to the Higgs mechanism, which would suggest that “something completely different” is unlikely.

Given the variety of options, how do we know that theoretical physicists are talking about the same thing when they talk about the Higgs boson? After all, there might be no Standard Model Higgs. There may even be several things. Or there might be some other phenomena responsible for the observed decay products. In fact, physicists might not even agree about what the options are — the list above is certainly simplified. It is not beyond the realm of possibility that even large portions of the Standard Model have to be abandoned. The philosophical upshot is that there is no clear sense of what enables us to determine whether the debate is even substantial. At the extreme end of the scale, it could be claimed that we simply do not know what it is that we are debating about. And I don’t think that this is an exception, it happens all over the place.

But clearly there is something substantial at issue here! Despite even fundamental disagreements about the background, physicists have been able to design experiments to test the various options. There must be something that is shared here. But it’s a mistake to think that it is the existence of something — something that we can quantify over with the existential quantifier — that has to be shared.

Let me venture a positive proposal: we know that the Higgs debate is substantial because we know what the Standard Model Higgs would be like if it were to exist, that is, we have a previous grasp of its nature or essence. This is what I take Philip Warren Anderson to have been hinting at. What does this previous grasp of essence entail? It entails that we have an idea as to what would explain the empirical data that we currently have. Among other things, we have already observed W and Z bosons and other heavy particles. It turns out that unless something like the Higgs field(s) is postulated, the Standard Model will have to be abandoned. So, the need to postulate the Higgs field(s), or the Higgs mechanism in its entirety, stems from the need to explain how elementary particles get their mass. The options listed above exhaust the logical space, or most of it at any rate, that fits the empirical data.

When the search for the Standard Model Higgs began, its possible mass range was fairly wide. The LHC ruled out chunks of it little by little, finally arriving at ~125GeV. But each of the specific masses in that original range were possible for the kind of thing that we are looking for. My suggestion is that we must know what kind of thing(s) would explain the data before we can ‘imagine’ possible models, like Anderson seems to think. It may turn out that it is a merely possible kind of thing, as it could for instance turn out that the Higgs field is not elementary and in fact consists of a number of other fields. But even in this case, we had a previous grasp of the natures or essences of the other possible kinds of things that would have explained the data, even though no such things exist. This story does not reflect a fundamental quantificational structure (contra Ted Sider’s suggestion in his Writing the Book of The World (2011, OUP)), it reflects a fundamental natural kind structure.

Well, there’s a lot more to say about all this, and especially about the process of scientific modelling via ‘imagination’, but I’ll leave that for a paper! I find the case of the Higgs to be a fascinating example of scientific modelling and the effort to verify these models has been impressive, but my reading of what the basis of scientific modelling is may seem controversial to many. I’ve used the Higgs as an example in many papers and talks and will certainly continue to do so; I’m encouraged by Anderson’s comments in particular. I think that a lot of the confusion surrounding the issue (and evident from the press conference questions, among other things) has to do exactly with the red herring of trying to identify with a single, quantifiable particle, THE Higgs boson, whereas we should really focus our attention on the wider explanatory effort and process of modelling itself.