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Is there an accepted analogy/conceptual aid for the Higgs field?

A video I watched explains the Higgs mechanism as follows.

Take massless particles. These can only ever travel at the speed of light, but they can bounce off things. Now take a particle with mass. Imagine that it can also only travel at the speed of light, but it interacts with the (very dense) Higgs field all the time, by constantly bouncing back and forth off the field. Thus it appears to travel slower than the speed of light.

Would you say this is a reasonable explanation of the mechanism? Does the described process happen in any real sense, or is this one of those interpretations where we can't really pick one over the other because they are mathematically equivalent?

For example, if the particles were really travelling at the speed of light but constantly bouncing off the field, wouldn't GR predict that they would never decay as observed in any frame of reference?

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Roman Starkov
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  • Hm, the video raised another question in me, namely why do massless particles have to travel at the speed of light by default, but maybe that’s a separate question? – Timwi Oct 09 '12 at 17:39
  • Possible duplicate: http://physics.stackexchange.com/q/6450/2451 – Qmechanic Oct 09 '12 at 18:07

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The best non-technical explanation I've seen of this is Matt Strassler's blog article, though even this is still fairly technical, so let me see if I can interpret it a bit.

The key point is that an electron is not a particle. In Quantum Field Theory it's described as an excitation in the electron quantum field. This excitation will propagate in spacetime, and from the way it propagates e.g. the propagation velocity and how much momentum it carries, we can calculate it's mass. And in fact if the electron field has no interaction with the Higgs field the propagation speed would be $c$ so the electron would be massless.

The Higgs field is another quantum field, and the Higgs field and electron field interact. That means you cannot just write an electron just as an excitation of the electron field, but instead it has to be written as an excitation of both the electron and Higgs fields together. Because the interaction is relatively small we can write the excitation as a slightly perturbed electron field excitation, that is we write it as an excitation of the electron field plus a bit of the Higgs field. If we now calculate how this excitation propagates we find it travels at less than the speed of light i.e. the excitation of the combined fields has a mass. The amount of mass is proportional to the strength of the interaction between the electron and Higgs fields.

The idea of an electron bouncing off Higgs bosons is more easily visualised, but it's a very crude analogy, and like all analogies when pushed too far it ceases to be helpful. That's why you're (quite reasonably!) confused about the time dilation the electrons would suffer when moving at light speed in between collisions. It's not correct to think of electrons as intermittently bouncing off Higgs bosons. The electron field and Higgs field mix so the electrons cease to be pure electrons.

This applies to all fermions, i.e. electrons, muons, taus and quarks (and I think neutrinos though I'm not sure about this). The vector bosons like the W and Z particles get their mass through a different interaction. Photons and gluinos remain massless.

John Rennie
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