mathman said:
You are to some extent mixing up two issues. The rest mass of particles and the effects of relativity.
Higgs field gives an explanation for the rest mass of some particles, but it is not the whole story. For example, Higgs accounts for only a small part of the mass of a proton, the rest is due to internal energy from gluons and virtual quarks.
Relativity is concerned with the effects of motion etc. on mass, such as what happens to protons in the LHC.
For example, I just now found the highly respectable BBC at the top of my Google: higgs boson mass search, wherein is the following explanation:
"Mass is, quite simply, a measure of how much stuff an object - a particle, a molecule, or a Yorkshire terrier - contains. If not for mass, all of the fundamental particles that make up atoms and terriers would whiz around at light speed, and the Universe as we know it could not have clumped up into matter. The Higgs mechanism proposes that there is a field permeating the Universe - the Higgs field - that allows particles to obtain their mass. Interactions with the field - with the Higgs bosons that come from it - are purported to give particles mass. This is not unlike a field of snow, in which trudging through impedes progress; your shoes interacting with snow particles slows you down."
and:
" The Higgs boson came about because although the Standard Model holds together neatly,
nothing requires the particles to have mass; for a fuller theory, the Higgs - or something else - must fill in that gap" (emph. added)
http://www.bbc.co.uk/news/science-environment-16116236
It sounds like you're saying "yes, the Higgs boson has little to do with why things are massive in a macroscopic everyday sense". But they are talking both of particles and terriers—ensembles of particles, and moreover they introduce motion into the question quite clearly as though there were more involved than simply rest mass. Allowing that they are talking loosely about the contribution of the Higgs mechanism to the totality of rest mass of particles, and supposing we fortify the Higgs mechanism with other like mechanisms, and mechanisms of internal kinetic energy of gluons and quarks, could we say that would explain all the mass of all particles individually, and collectively in large objects?
My 'relativistic' and 'relativistic mass' were poorly chosen. What I meant was mass pertaining to Einstein's relativity in which space, time, mass, energy, and...inertia are bound together in a unified whole. There must be a reason why, when our car battery is dead we have push it hard to get it rolling at a reasonable speed, but once it gets going we can ease off a bit.
This inertia is somehow explained by the distortion (with respect to observers in differing reference-frames, not absolutely) of the 4-space field that doesn't care to be distorted ('...tends to stay at rest', but doesn't appreciate being undistorted ('...tends to stay in motion'). I'm putting it in the crudest layperson's terms, but I think someone in the spirit of Feynman can repair it.
In sum, it sounds to me like a fully amplified microscopic description of mass is in competition with the mass fully explained by Einstein, and there has to be some kind of unification that couples both, to explain the rest mass of a proton over that of a muon in terms of the energy needed to accelerate each to the same speed.