## Friday, 27 April 2012

### How to explain the Higgs mechanism

Time and again I read/hear popular-level descriptions of the Higgs mechanism in which it is proclaimed that the Higgs field is "like molasses", offering resistance to particles moving through it. This is an awful analogy, and makes me cringe every time. Even non-physicists should immediately see why: a particle moving through molasses feels a drag force which will ultimately bring it to rest with respect to the molasses (in the absence of some persistent driving force). But the Higgs field fills all of spacetime, and thanks to Galileo and Newton, we know that in empty space, in the absence of forces, particles move with an arbitrary constant velocity (up to the speed limit imposed by Einstein, of course!).

The big difference is that the background value of the Higgs field is Lorentz-invariant — it doesn't define any absolute standard of rest. This is difficult to explain to somebody who doesn't know what a Lorentz transformation is, but it must be possible. Even without knowing mathematics, it is at least plausible that there could be a 'substance' which appears exactly the same to any two observers, regardless of their relative velocity. In fact, this applies to empty space, and it is not unreasonable to say that the value of the Higgs field is just a property of empty space. The problem, of course, is that none of this gives people any idea of what the Higgs field has to do with mass (but in my opinion, neither does the molasses analogy).

So I set a challenge to anybody who happens upon this blog: how does one explain the Higgs mechanism to 'laymen' in a way which is not completely misleading, yet is non-vacuous? Answers in the form of links to good popular-level expositions are perfectly acceptable.

I should acknowledge that at a more technical level, there is a big conceptual difference between the mass of the $W^\pm$ and $Z^0$ bosons, which comes from the true 'Higgs mechanism', and that of the fundamental fermions, which comes from their Yukawa couplings to the Higgs field. This is another level of complexity altogether, and I think it is perfectly okay to leave it out.

1. I sympathise with your annoyance, but I don't know of a better explanation. In fact, I don't see any reason to believe that a more correct popular-level explanatory analogy should exist. There are many concepts in physics - like the spin of an electron, or the effect of gravity on the curvature of space time - for which the layman analogies we use are flawed in some respect, but can't be improved upon without actually learning the theory, because human intuition doesn't work at that level. I don't see why the Lorentz-invariance of the Higgs 'molasses' should be any different.

This is rather apposite here: http://xkcd.com/895/

2. Can I take a shot at this? I'm going to, perhaps annoyingly, start with the rubber sheet analogy complained about in the xkcd comic, but hear me out. (I'll also address only the Yukawa-coupling part of the story and not the real "Higgs mechanism." In fact, I'll just refer to anything getting mass from the Higgs as the "Higgs mechanism" for the moment out of laziness.)

Okay, you (and presumably your audience) has heard of the analogy of the rubber sheet? The analogy is that a massive object bending spacetime is like a bowling ball on a rubber sheet -- other things "fall" toward dents in the sheet, and, in a similar way, real things in the universe fall toward massive objects. Anyway, there are problems with the analogy, but "mass distorts (curves) spacetime" is a good way to think about it. And gravitational lensing makes sense as light being curved around a massive object because the object is curving the spacetime the light is travelling through.

Back to the Higgs: There is a field pervading all space called the Higgs field. Since the Higgs field is responsible for all the mass that any particle has, you can (without too much loss of accuracy) say that the Higgs field is the thing that allows particles to distort spacetime. You can think of it like a mediator -- if you don't talk to the Higgs, you can't distort spacetime. So, let's say you're a photon, and you're moving through spacetime and through the Higgs field. You can be deflected by distortions of spacetime, and you can be delayed by moving through distorted spacetime, but since you don't couple to the Higgs field, you can't distort spacetime yourself. But if you're a massive particle, like an electron, when you move through spacetime and through the Higgs field, your coupling to the Higgs field allows you to distort spacetime. And because distorted spacetime takes longer to go through, you are continually delaying yourself with respect to a photon that's travelling *without* distorting spacetime. You're moving slower only because you're going through more space, not because you're experiencing some kind of drag force.

Of course, the cocktail-party analogy (here: http://www.hep.ucl.ac.uk/~djm/higgsa.html) is actually a pretty good one, tried and true, and doesn't seem to suffer from the drag/energy-loss problem. So maybe it's better to just stick with that one and not bother with molasses or curved spacetime at all.

1. I'm not sure I like bringing curved spacetime into the mix; the Higgs mechanism really has nothing to do with gravity.

I either hadn't heard, or had forgotten about, the cocktail party analogy. That's actually a pretty good one, and probably the best I know.

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