The Higgs Boson in Context

I ran across this recently while looking for something else, and was reminded of it by this discussion of jargon. It’s an attempt to explain the general historical context of the whole Higgs Boson thing, and why it’s important. I improvised this in response to somebody’s question about how I would explain that, drawing mostly on my recollection of a couple of history-of-field-theory books. I kept it in case I needed to bust it out when they discovered the Higgs, but that fell during the time when I wasn’t able to blog, so I never used it. I’m never going to use it for anything else, though, so I might as well throw it up here to be mocked and reviled for my ignorance of theoretical physics.

If you want to understand the importance of the Higgs, you really need to go back to the start of quantum physics, when people started to think seriously about how to treat electromagnetic interactions. Classically, you just sort of assert that particles have charges, and as long as you don’t think too much about that, it works reasonably well– you can do a very good job of calculating the spectrum of light emitted by simple atoms, for example. If you start to look closely, though, there are some big problems. Specifically, if you try to calculate things like the energy of a single electron by itself, you get utter nonsense– the simple calculation gives you an infinite answer. The problem is, basically, that you’re trying to pack a finite amount of charge into an infinitesimally small space, and it ought to take an infinite amount of energy to do that. On the experimental side, there are some problems as well– the simple calculation for the energies of an electron inside a hydrogen atom is very, very good, but doesn’t quite get everything. In particular, there’s a thing called the “Lamb shift,” a slight difference in the energy of a particular state that nobody could explain.

This was a big crisis for theoretical physics, and some very smart people spent a lot of time beating on it. Eventually, nearly simultaneously on different sides of the planet, Richard Feynman, Julian Schwinger, and Shin-Ichiro Tomonaga hit on the solution, the theory that’s now called “quantum electro-dynamics,” or QED for short. The new theory had some surprising elements, in particular the fact that empty space is no longer empty– it’s filled with a fluctuating electromagnetic field, that can manifest as “virtual particles” popping out of nowhere, then disappearing again. This is deeply weird, but fixes the problems with the simplest models– having these virtual particles pop into existence tends to sort of smear out the charge of the electron, so it’s not packed so tightly, which lets you get rid of the infinite energy for an electron by itself. And the interaction between electrons in an atom and these particles popping out of empty space has a tiny but measurable effect on the energy of those electrons, which shows up in things like the Lamb shift.

So, QED fixes the problems with putting electromagnetism into quantum mechanics by filling empty space with virtual particles. This sounds bizarre, but it’s fantastically successful– for one particular property, the “g-factor” of the electron, which determines the energy of an electron interacting with a magnetic field, the QED prediction and the experimental measurement agree with each other to about 14 decimal places. It’s probably the best tested theory in the history of testable theories.

The next big problem to face physics was the need to incorporate some new forces, in particular the “weak nuclear force,” which is called that because it mostly acts on particles found in the nucleus of an atom, and it’s not as strong as the “strong nuclear force.” Physicists suck at names. when you try to add the weak force into the theory, you once again find yourself getting nonsensical results– particles that ought to exist don’t, or particles that do exist shouldn’t.

Once again, the solution is to change the nature of empty space. Where QED took empty space and filled it with virtual particles acting through the electromagnetic field, incorporating the weak force into the picture adds another field permeating all of space. A bunch of different people came up with the idea at around the same time, but for various reasons Peter Higgs’s name has gotten attached to this thing, so they call it the “Higgs field.” Like the virtual particles from QED, this can occasionally pop up as a particle from nowhere, which is the Higgs boson.

As with QED, filling empty space with a whole new thing seems pretty weird, but it works very well to get rid of the nonsensical answers. In particular, it interacts with some particles in a way that makes them behave as if they have mass, when the simplest attempt at a theory of the weak force says they shouldn’t.

This “Higgs mechanism” is one of the central elements of the Standard Model of particle physics. Again, physicists suck at names. It manages to successfully incorporate the weak force into quantum mechanics, and sets the basic parameters for all the particles making up that theory. every one of them has been found, with the exception of the Higgs boson itself, which has proven trickier to track down than people would’ve liked. Once they find that– and nobody seriously doubts that they will– the Standard Model will be complete, which is why it’s a big deal.

(The “featured image” is a picture of Feynman, Schwinger, and Tomonaga, because I already had it, and it was easy to add to the post, and these things look better with an image of some sort. If you’re reading via RSS, you’re not missing much.)

8 thoughts on “The Higgs Boson in Context

  1. That’s all great but the approach of solving theoretical problems by inventing ad-hoc fields with just the right properties feels somewhat like cheating. Yeah I know those new fields constitute a better, more efficient description so it’s not completely cheating but still.

    Photon field, electron field, muon field, taon field, gluon field, electron neutrino field, muon neutrino field, taon neutrino field, up quark field, down quark field, charm quark field, strange quark field, top quark field, bottom quark field, W+ boson field, W- boson field, Z0 boson field, Higgs boson field…

    That’s a shitload of fields. Epicycles come to mind. There has to be a better more unified picture then this disjointed mess of fields. Yes I know, people have been searching for a better explanation for centuries without success. Still I find it much more plausible that this mediocrity is due to our feeble intellect than that it’s inherent in Nature.

  2. @Paul: It’s not like there were no order in all these fields. The fermions are arranged in three families, each containing one neutrino, one lepton, one up-type-quark and one down-type-quark. The force bosons photon, gluon and W/Z0 are most likely more or less the same with a broken symmetry differentiating them. With electro-weak unification it is already demonstrated, that photon and W/Z0 are really members of a larger symmetry (U(1)xSU(2)), consisting of 1+3 extremely simmilar fields, that got broken (most likely by the Higgs-field) and mixed to form the weak and electromagnetic force with rather different behaviors. For the unification with the gluons, the symmetry and mechanism hasn’t yet been found, but scientist are looking for this grand unified theory. And for the fermions, many physicist think that they are also related by a broken symmetry or something similar, which would explain why electron (a lepton) and proton (consisting of quarks with non-integer electric charge) have exactly the same, although opposite, electric charge, which is still a conundrum. The number of families is still a mystery, but at least we have good evidence that there are only these three and not more.

  3. I’m not sure you can really call all of those fields “ad hoc.” I mean, electrons, photons, muons, and neutrinos were known to exist well before QED came along, and the “fields” associated with them are an inevitable consequence of quantization.

  4. @Paul: What would be ad hoc is if some of these particles had associated fields and others did not. It’s definitely not ad hoc to say that if the electron has a field, then the up quark, etc., also have to have fields. It’s also not ad hoc when people predict in advance the properties of a particle that is later discovered–on the contrary, that is how you test theories. The Standard Model would have long since been discarded if the W/Z0 had not existed, or turned out to have significantly different properties (including rest mass) from what the Standard Model predicted (and they actually have).

    Likewise the Higgs boson. Its properties were not as well constrained by theory as the W/Z0, but there is a region of parameter space allowed by the Standard Model, and the Higgs boson’s actual properties are inside that region. Again, we would have to discard the Standard Model if the Higgs boson were outside that region.

  5. @Paul:
    To reinforce what Eric said @#4, you might not realize that the hunt for the W and Z was not at all like the hunt for the Higgs. The masses of each had been very definitely predicted by previously measured values of the model that linked the photon with the Z and W. The Nobel Prize was for pulling off the search, not finding something that was completely unexpected. It would have been an astounding discovery if they had not been there!

    The Higgs, on the other hand, only had to exist with properties that did not contradict what was known. They really had to look for it.

    And lets not forget that epicycles often get a bad rap. They make excellent predictions once the parameters are determined because they are basically an expansion of an ellipse in terms of circles. The inefficiency is that you have to add another cycle instead of tweaking the n-th digit of parameters of an ellipse. With that perspective, the few parameters of a field theory are like the size and eccentricity of an ellipse replacing a much larger number of seemingly arbitrary numbers for a set of epicycles. An ellipse might not be as neat and clean as a circle, but it works better.

  6. Has there been any reconciliation between string theory and the Higgs field? With the idea being that string resonance is what dictates the actual manifestation of a particle? For example, the reason an electron is an electron is because of the resonance of its strings and the reason that particles “appear” in the Higgs field is because electro-magnetic resonance, at any given time, matches the resonance of certain particle types (and when that resonance changes, those particles “disappear”). Obviously this is wild conjecture but I’m curious if anyone has even made the conceptual connection.

  7. I don’t think I ever registered that the virtual particles in QED come from a fluctuating EM field that exists everywhere. Most descriptions of it just mention that space isn’t empty and has virtual particles, borrow energy, Heisenberg, borrow time, etc.

    That made it sound like empty space has virtual particles, but if I understand what you wrote, space has an EM field and it is the EM field that creates the virtual particles. A subtle difference, but a difference none the less.

    So the Higgs field is really the equivalent for the weak force. A property of empty space is that it has a “weak field” everywhere which we call the “Higgs Field” and its the Higgs Field which causes the bosons to pop in and out of existence in ways that I only partly understand, but is similar to how things work in QED.

    Am I on the right track?

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