The higgs mechanism is a mechanism by which gives gauge bosons their mass, by absorbing the goldstone bosons appearing in the goldstone theorem. I found this mechanism very mathematically beautiful, but what philosophical implications can you draw from this mechanism, as this mechanism seems a very deep physical principle.
There are some philosophical issues with the Higgs mechanism, but they are not the types of things considered in any traditional sense part of philosophy. The issue here is which type of language is appropriate for describing the phenomenon, particle language or field language. The two are very subtly dual, and it is difficult to make a precise particle description out of a field description. But to fully understand the Higgs mechanism, you need both, and it is not clear to what extent the particle picture is available.
In field language, the Higgs mechanism is when a scalar field which is charged has an expectation value in the vacuum, so that the lowest energy state gives a vacuum which is full of charge condensate which is not invariant under gauge transformations. When this happens, the associated photon (the particle carrying the interactions appropriate to this charge) becomes short range. The phenomenon is completely described by field Hamiltonians, and is easy to calculate and straightforward to understand in this classical field language. For electromagnetism, this was understood by Stueckelberg, but it wasn't appreciated fully until it was done for nonabelian gauge fields by Brout/Englert, by Higgs and by Guralnik/Hagen/Kibble in this order in 1964, following Nambu's ideas about fields in a vacuum having expectation values, something which was suggested earlier by Heisenberg, who was the first to understand and formulate the notion of spontaneous symmetry breaking, something which emerged from Heiseberg's work in the early days of quantum mechanics with Neville Mott regarding a more traditional philosophical problem of how measurement works.
The philosophical issues however come from the fact that the Higgs mechanism was first discovered using a different language, where it is not natural or straightforward, in the language of particles, not quantum fields. The Higgs mechanism was first discovered by (arguably) Landau, Bardeen/Cooper/Schreifer, or by Anderson, all of whom were thinking about coherent condensates of charged particles like electron-pairs inside a metal. When you have a coherent superposition state of many nonrelativistic particles which are charged, the end result is that the nonrelativistic quantum field describing these particles has a vacuum expectation value, so that there is a Higgs mechanism, and the electromagnetic photon gets a mass. This is the Meissner effect of superconductivity, the fact that photons can't penetrate a superconductor to a given length.
All the philosophical issues come from the question of particle-field duality. To what extent is it appropriate to describe the quantum field in particle langauge?
When you have a nonrelativistic quantum field, there is no philosophical issue. The quantum particle language and the quantum field language are entirely mathematically equivalent, and a many-identical-particle wavefunction evolving according to the many-particle Schrodinger equation with additional interactions can be equally well described by a quantum field evolving according to a nonlinear Schrodinger equation in space. This duality is described on Wikipedia under "Schrodinger field".
But when you have relativity, the particle and field pictures are only dual if the particles are allowed to propagate back in time. The scale at which this happens is the Compton wavelegth, which, even for the electron, is very small compared to atoms. So the relativistic complication doesn't appear in condensed matter systems, and the nonrelativistic theory, where the duality is mathematically fully worked out, is applicable.
But in the relativistic context, the field picture is well defined, but the particle picture is only defined in a Feynman expansion through perturbation theory, and it isn't fully clear what the description is outside of the perturbation series. You can't give a wavefunction for the particles at one time, because the particles can turn around later and come back to the same time "later". So your description of the wavefunction for the particles must be either on an asymptotic incoming trajectory, where this problem is sidestepped because the effective fields are free, this is the point of view of scattering theory, or alternatively by using additional parameters for the proper times of the intermediate particles and describing the wavefunction as a function of these new unobservable proper times.
The issue with introducing intermediate proper times is that the interactions happen when the particles are at the same position, not at the same proper time. So that if a particle at one proper time hits a particle with another proper time, they can interact. This means that the description doesn't have a one-way time where interactions happen only in the future direction, and this makes the description a mess. The mess is only simplified in a perturbation series, and this doesn't give one confidence that the formalism is completely consistent.
Anyway, putting the well-definedness aside, in particle picture, the Higgs mechanism is a condensation of relativistic charged particles in the vacuum which make a charged condensate, a superconductor, just like an ordinary material superconductor. The superconductivity picture of the Higgs mechanism is hard to make precise, because one usually defines the particles relative to a given vacuum. For the superconductor, the particles are defined relative to a symmetric uncharged vacuum that does not exist. To the extent that relativistic particle field duality makes sense (and it should make perfect sense), the Higgs mechanism is a condensation of the charged space-time localizable particles corresponding to the quantum field with an expectation value.
So the philosophical issue that I see is to what extent the particle field duality is true, that is to what extent is the quantum field theory also a theory of point particles interacting at points. The resolution to this philosophical question will come with a better formalism that gives a consistent particle description of field theory, which allows you to fully make sense of the wavefunction of a photon, or the wavefunction of an up quark, two particles that are never nonrelativistic. Such a formalism is only half-way developed always.
In addition to this question, which is investigated by physicists, there are other questions which physicists do not consider real questions, because they aren't logically positivistically well defined.
- Ontology: Is quantum field theory about particles or fields?
This question asks whether the objects in the theory are "really" particles making a superconductor, or "really" fields making a charged condensate. This question is nonsense to a logical positivist, so I won't consider it further. All questions of ontology are generally meaningless to a positivist, and in my opinion, the subject is closed forever. You can take any ontology you like that is consistent with experience, and the result is just a change in point of view, a change in philosophical gauge, and to debate which gauge is real is no more meaningful than debating which gauge is real in electromagnetism, or which coordinate system is real in relativity. The answer is clearly "none of them".
- Epistemology: How can we be sure that there is really a charged condensate, and not just terms in a Lagrangian fooling us into thinking that there is stuff in the vacuum?
This has to do with the fact that we don't see the condensate directly, rather we see the oscillations of the condensate, which have their own interactions which can be defined without direct reference to the condensate. This is again positivistically meaningless, since the two ideas of a conspiratorial Lagrangian and an actual condensate can't be distinguished by experience, since they are mathematically identical.
The fact that philosophers don't accept logical positivism anymore makes it so that it is generally impossible for physicists and philosophers to communicate anymore. The philosophers ask all sorts of questions that make no sense as questions, and do not accept that these questions make no sense. This is why physicists always do their own philosophy, and this will not change until philosphers accept positivism as a principle for sorting out the meaningless from the meaningful questions.
-What are the philosophical implications of the Higgs mechanism?
Developments in science have philosophical implications to the extent they force us to refine philosophical positions we take. Embryonic stem cell research, for instance, is forcing us to refine arguments about when a group of cells become human.
A development in our understanding of matter would hopefully affect our understanding of consciousness.
Questions within physics aren't, strictly speaking, philosophical questions. Whether an idea can be translated from one theoretical language to another is a philosophical question, and positivism is a dubious answer.
If the question is what are the philosophical implications of the Higgs mechanism for theoretical physics then the answer has to do with how physicists handle the translating.
But if the question is asking for the philosophical implications in the general sense, that is, to the extent our understanding of matter is affected by the understanding of the theory of the Higgs mechanism, then the answer is wait and see. The role of causality in consciousness is the philosophical question and the Higgs theory does not seem to be developed enough to help us refine our conception of consciousness.