At the risk of getting told I’m an idiot again, I have spent several years pondering (and writing about) the nature of mass. As Tom Moore as pointed out, the *only* self-consistent definition of mass that can be applied both to point-particles as well as to systems of particles, is that “mass” is the magnitude of the four-momentum vector. He has a very elegant “proof” of (argument for?) this that gets overlooked because it is in an introductory textbook. Please note, however, that he set out to write this textbook precisely so that students could learn the nuances of concepts from the very beginning instead of teaching them “watered-down” versions of things and correcting them later.

I once made this argument to Frank Wilczek in a debate that was published in Physics Today but he missed my point.

Edit: I will admit that there are some issues with this in GR, though they are not intractable issues and certainly don’t make this definition any worse than others.

]]>I do not complain that this would be wrong, but that there are several kinds of mass (in GR equivalent) which have profoundly different definition. So one should talk about inertial mass given in terms of dynamics. Note for example the “effective” mass of holes in solid state physics…But I have no time to improve this now. I will be mostly away in next 10 days.

]]>I think “intrinsic energy” is at least a good hint for what mass is.

It’s interesting to notice that only a tiny fraction of the mass of protons and neutrons, hence of atoms and everyhting built from them is rest-mass of the quarks that they consist of. Almost all the mass of the proton is actually in the gluon “gas” that hoids the quarks together. Gluons themselves are massless, so this is all just binding energy.

(And of course, even the tiny fraction of “true rest mass” of the quarks inside the proton is, according to the standard model, just a kind of coupling energy to the Higgs field. )

Recently I read an entertaining article in the otherwise very dry journal of the German Physical Socienty that i am subscribed to, where the author started considering the total mass of the observable universe and then step by step emphasized how it consists mostly of contributions that are not of the kind that we think of as mass in an everyday-sense: first at cosmological scales baryonic mass is just a small fraction among mass of dark matter (according to the standard concordance $\Lambda CDM$ model, at least) (and of course both are just a small fraction of the total energy density, which is mostly “dark energy”). Then among the baryonic mass a huge fraction is really just binding energy of quarks.

So there is surprisingly little “genuine mass” around us, in a way.

]]>The mass of a physical system is its intrinsic energy.

I expect that Zoran will object to some of what I have written there (if not already to my one-sentence definition above), but since I cannot predict how, I look forward to his comments.

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