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Massive elementary particles receive their mass via interaction with the Higgs field. This answer offers some explanation.

But this only accounts for one percent or so of the mass in the Universe. The rest is supplied by the binding energy which pulls the particles together into nucleons and atoms, according to $E = mc^2$.

So mass appears to have a dual nature; part Higgs mass and part relativistic mass. Is this correct, and if so then does Higgs mass contribute to the curvature of spacetime? Or does Higgs mass also derive from $E = mc^2$ via the energy of the Higgs field (in which case it must contribute to the curvature of spacetime)?

Guy Inchbald
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All mass is relativistic in nature, to the extent it is a parameter in all relativistic behavior of everything, including the limit of slowly moving and stationary objects and particles.

The Higgs QFT component is relativistically invariant, like everything else in QFT.

The Higgs quantum field interactions underlie all the mass we know of to the W and Z gauge bosons, and all leptons, like the electron, the μ and τ, and possibly the neutrinos. They also give small masses to all quarks; but the bulk of the mass of all hadrons comes from an elaborate mechanism in QCD, interactions of gluons in a completely independent interaction.

Not just all masses, but all types of energy, as well, couple to gravity, and, as such, contribute to spacetime curvature.

When it comes to cosmic scales, most of the mass of the universe is in mysterious "dark energy" and "dark matter" sectors, (arguably) likely independent of Higgs interactions.

Frankly, I had trouble parsing out the logical trail-map of implications you may well be asking about.

Cosmas Zachos
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    Thank you for your answer. I have deleted the troublesome "sticky". Your trouble parsing my very short question is evident from your expanded paraphrasing of parts of it. Your answer suggests to me that the energy of the Higgs field associates itself with each fundamental particle according to $e = mc^2$, and it is this which gives the particle an apparent mass, analogous to the mass-energy of the gluon fields. Would that be correct? – Guy Inchbald May 08 '21 at 15:36
  • Yes and no... $E=mc^2$ is a dopey static limit for particles just sitting there, and I don't see how it would fit, or not, to what you have in mind... Any particle with any mass would satisfy it in its rest frame. – Cosmas Zachos May 08 '21 at 15:41
  • But the issue here is the other way round: how does the energy equivalence satisfy the rest mass requirement? Specifically, what kind of energy? Just a handwaving "Higgs field energy"? – Guy Inchbald May 08 '21 at 16:37
  • Apologies, like most physicists I follow the math, not handwaving to me...., so I wouldn't dream of another answer. It is all field energy: Nothing else is. – Cosmas Zachos May 08 '21 at 16:45
  • Thank you, I understand better now. I guess that what makes people describe only the Higgs field as "sticky" is another question. – Guy Inchbald May 09 '21 at 11:14
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    I should think so. There is a broad range of mnemonics, metaphors, and analogs, all trying "to dance about architecture"... Turns out I am more confused by them than by the straight mathematical theory. When it comes to its relation to energy and relativity, the Higgs-induced mass is pretty much similar to the QCD-chiral-symmetry-breaking mass that dominates our familiar material world... – Cosmas Zachos May 09 '21 at 11:52
  • "interactions of gluons in a completely independent interaction." Is that interaction completely understood? If it's not the Higgs at work then does that not bring us back to square one as far as understanding the mechanism that causes the hadron to resist acceleration as though 100% of it were interacting with the Higgs field? – Peter Moore Jan 28 '24 at 17:29
  • QCD of the strong interactions is not completely, but effectively, understood. I'm not sure what you are insinuating: QCD interactions give hadrons (in sharp contrast to the leptons and the gauge bosons) more than 99% of their mass, and this beats the Higgs in this function; so you can virtually ignore the Higgs for hadron masses. Both of these mechanisms are relativistic from birth, and comport with mass-energy equivalence. – Cosmas Zachos Jan 28 '24 at 19:42
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A search-term-only answer: if Higgs-field masses didn’t contribute to the curvature of spacetime, it would be a violation of the relativistic “equivalence principle.”

All searches for equivalence-principle violations have been either inconclusive or negative: there is no solid evidence against this bedrock tenet of relativity. But devising new tests is hard. The embarrassingly large uncertainty on the gravitational constant $G$ could (in principle) hide a lot of new physics.

rob
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You are asking "The rest is supplied by the binding energy which pulls the particles together into nucleons and atoms, according to E=mc2. So mass appears to have a dual nature; part Higgs mass and part relativistic mass. Is this correct, and if so then does Higgs mass contribute to the curvature of spacetime?". The answer is yes, in your example, the proton's and neutron's rest mass is 99% binding energy, and only 1% the comes from the rest mass of the constituent quarks, but that 1% still contributes to the stress-energy tensor and creates spacetime curvature.

If you use General Relativity instead you'll find that photons make a contribution to the stress energy tensor, and therefore to the curvature of space.

Does a photon exert a gravitational pull?

Please note that even a single quark, or electron (getting its rest mass from the Higgs mechanism as you say) does create spacetime curvature, and even a photon (being massless) does bend spacetime. Ultimately it is because all of them possess stress-energy.

Árpád Szendrei
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