Where's the Mass?

Iwas waiting for a gap in the traffic so I might cross the road when an out-of-town car pulled up to ask for directions. The driver was a Catholic priest looking for the church where he was to perform a memorial service. He asked me "Where's the Mass?", and I replied "Some in the Higgs field but mostly in the Gluon Cloud" ;-) That's a quantum physicists' joke, by the way, so let me explain.

When I was at primary school, aged just 7, we had a class teacher who was a big fan of the Austrian philospher Wittgenstein and explained he used Wittgenstein's ladder as his model of education. That is, children are given a simplification as an explanation like a rung in a ladder. When they see the cracks in that simplification they are ready to move up a further rung on the educational ladder to a better explanation. And so on and so forth, moving up the ladder a rung at a time until they get to the top (if there IS a top!) and then can throw the ladder of simplifications away. This ladder idea was rediscovered in 1994 by mathematician Stewart as Lies to Children. A lie-to-children is a simplified explanation of technical or complex subjects as a teaching method for children and laypeople. Both are also how scientists make new discoveries. Here's a ladder of mine : 70 years for 7 rungs!

That primary school teacher sent me to fetch something from a cupboard, warning me that it was heavy. I did so, asking "Why are some things heavy and others not?" and was told that little things are light and big things are heavy (rung 1 of the ladder). After some thought, I objected "The biggest thing here is the air in this room, but it's not heavy!". The teacher promptly moved me up to step 2 of the ladder, explaining that "everything is made up of atoms, that means "indivisible" in Greek, the little atoms are light and the big atoms are heavy - about 250 times heavier than the lightest atom. There are about 100 different sizes of atoms. Think of them as little round balls of matter." This explanation sufficed me for about 5 years.

Skip forward to secondary school, I was about 12, when we taught that the atom (about 1 Angstrom or 100,000 femtometers across) had been split and found to contain a nucleus about 1 femtometer across, made of protons and neutrons, with the electrons orbiting around the nucleus. This was rung 3 of the ladder.

Unfortunately, this explanation was accompanied by misleading diagrams, noone told us they were diagrams and not photos :-(

The diagram on the left is of a lithium atom (three protons and three electrons). Misleadingly it suggests the electrons are in plane orbits perfectly spaced 120 degrees apart and that protons are coloured red and neutrons black. The diagram on the right is of a nitrogen atom (7 protons and 7 neutrons, misleadingly coloured red and yellow respectively). Not only were the colours misleading to me, but the inner and outer electron orbits are shown as coplanar :-( Later our science teachers explained Niels Bohr's model 2D of the atom and so light (colours) came from electrons falling to lower orbits(energy levels). Therefore protons and neutrons did not have colours. I climbed another rung up the ladder. However, I still had my primary school question, now reformulated as "Where's the mass?", and was told it was almost all in the nucleus. Come 1962 and we went to university (Hi John, Hi Derek et al) still with this mental model of the atom and the nucleus as the main mass-carrier. Einstein had showed that E=mc² much earlier, so we could also write m=E/c². So we learned that the mass of the electron is about 0.511 MeV/c² where MeV means Mega-electron-Volt, the proton has a mass of 938 MeV/c² and the neutron is slightly more massive at 939.5 MeV/c² ; so the nucleus has 99% of the mass of the atom. That was the 1966 answer to "Where's the mass?"

But science moves another rung up the ladder since in parallel Murray Gell-Mann - an english physicist - came up with the theoretical idea of Quarks in 1964 which were confirmed experimentally in 1968, so we didn't learn about them at university. So later we learned that a proton is composed of two up quarks, one down quark, and the zero-mass gluons that mediate the forces "binding" them together. The "color" assignment of individual quarks is arbitrary, but all three "colors" must be present. Also "color" is an arbitrary name for a quantum attribute and has nothing to do with the colours we see. Nor are "up" and "down" gravitational directions ;-)

So again I ask "Where's the mass?"; are the quarks massive? Now a proton has a mass of approximately 938 MeV/c², of which the rest mass of its three valence quarks only contributes about 9 MeV/c²; much of the remainder can be attributed to the field energy of the gluons and a bit to the Higgs field. So my current understanding of "Where's the mass?" is "Mostly in the gluon cloud", but I don't know which rung of Wittgenstein's ladder I'm on, nor do I even know how many (more) rungs there are :-(

Comments (9)
Schorsch (D) wrote "I'm still on your rung three :-(" Most people are.
Pergelator wrote " That bit about the rest mass of quarks and the mass of the gluon cloud is news to me. I especially like it since gluons are massless. They must be moving near the speed of light. Zero times infinity must equal 929 MeV/c2. Could it be that the lighter won't light anymore because all the gluons have quit moving?" I'm not sure I even understand what a gluon is. And why are they only in hadrons?
Jenny (Ibiza) asks me to "...explain the third picture...". Okay. The grey circle is a 2D diagram of a proton. It contains 3 quarks, in 3 different "colors". Two of the quarks are labelled U (meaning UP quarks) and one is labelled D (meaning it is a DOWN quark). The white wavy lines represent the Gluons which act as the exchange particles (or gauge bosons) for the Strong force between quarks. Most of the mass of a proton (or neutron) is the result of the Strong force field energy; the individual quarks provide only about 1% of the mass of a proton. So 99% of the mass is in the gluon cloud, as in my joke to the priest ;-)
Cop Car figured that "I note that most of "mass" is in the "ass"." Some schoolchildren here were being taught about fatness and were asked to complete the sentence "People with a BMI over 30 are called ? .....". The expected anwer was "obese" ; one child wrote "Americans" ;-)
Karel (CZ) objected : " That blog article was too, too, heavy. Get back to the lighter stuff please!" Okay.
John (UK), with whom I read physics at university, wrote " 1) The ladder I'm on is one of those telescopic ones which has not been adjusted properly so every step up ends up lower down. 2) You do not record the response of the priest (perhaps he's still confessing)." His response was "What???". We mere physicists have difficulty splitting a tiny atom to make 2 ones of smaller mass; but the priest achieves transubstantiation at every mass ;-) [In theology, transubstantiation is the changing of the elements of the bread and wine, when they are consecrated in the Eucharist, into the real body and real blood of Christ (a doctrine of the Roman Catholic Church). So it's real, non-symbolic cannibalism ;-) ]"
Tanja (Finland), who is a Catholic, sent this cartoon :-)

Ethan (USA) has a blog entry up which points to the next rung up the physics ladder.
Jenny (Ibiza) wrote again, asking "If your sub-nuclear quantum physics is so important, why is it not taught at Hogwarts?" Oh dear :-(

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