It's clear, from reading pop-science articles about the Higgs boson, that particle physicists have something very specific in mind when they say "mass". In classical physics the mass of a particle is just a given value, but in the context of particle physics you hear things like "computing the mass" or "such and such interaction gives some mass".
What does "mass" mean to a particle physicist? How does it relate-to/explain the classical notion of mass, and how does it differ?
I'm not sure what level of explanation I'm looking for. I don't know particle physics, obviously, so any grad-level equations are likely to go way over my head. But explanations like "bouncing back and forth all the time" from this minute physics video are too simplified. I'm left wondering, for example, how coupling with the Higgs field makes electrons bounce back and forth? And why wouldn't it just scatter them? And how is this process Lorentz invariant? And why does the bouncing resist/react-to forces?
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