The proton

If you look around the internet you can find articles like Matt Strassler’s what’s a proton anyway? He says the proton isn’t made up of three quarks joined together by three gluons. He says that’s a lie, a white lie, but a big one. Instead he said there’s “zillions of gluons, antiquarks, and quarks in a proton”, and gives a picture of a whole host of quarks and gluons, all mixed up together like beans in a bag. All rushing around as fast as possible, at nearly the speed of light”. You can also find the physorg article physicists zoom in on gluons’ contribution to proton spin. It quotes John Lajoie saying this: “the more we zoom in, the more ‘quantum fluctuations’ we can observe”. He also says “inside the proton, there’s a sea of quarks and antiquarks and gluons changing and evolving”. Here’s a picture from the article, it shows how the quark model has evolved over the years:

Image credit PhysOrg

When the quark model was proposed in 1964 the proton was said to be composed of three quarks and nothing else. Now the proton is said to be composed of zillions of quarks, all subject to the strong force mediated by zillions of gluons. Rather conveniently you can never ever see these quarks or gluons. That’s because of asymptotic freedom, which is sometimes known as the bag model of quark confinement. The story goes that if you try to pull a quark out it gets more and more difficult, as if the gluonic bag is made of some kind of strong elastic. Some kind of strong rotating elastic. Note the curved white arrows in the “now” picture above right. Two of them point up and one points down. They’re trying to depict the gluon contribution to proton spin. For more on that see the underlying Physical Review D paper, which is on the arXiv. John Lajoie is one of the authors. He’s a member of the PHENIX collaboration, and the gluon contribution to proton spin is all to do with the proton spin crisis.

The proton spin crisis

See the 2014 Sci-Am article proton spin mystery gains a new clue. Daniel de Florian talks about “the naïve idea 25 years ago”. That’s where two of the proton’s three quarks were thought to have equal and opposite spins cancelling each another out, such that the proton’s net spin ½ is all down to the third quark. Daniel de Florian is one of the authors of evidence for polarization of gluons in the proton. He talks about the 1987 EMC experiment, saying this: “By the end of the 80s it was possible to measure the contribution of the spin of the quarks to the spin of the proton, and the first measurement showed it was 0 percent. That was a very big surprise”. Other measurements since then have suggested a figure of 25%, but nevertheless there’s a lot of spin missing, and it’s a problem. As John Hansson points out in the proton spin crisis – a quantum query, the whole idea of the quark model was to account for 100 percent of hadron spin, solely in terms of quarks. That’s why color was added to the movable feast, because in the much-vaunted omega-minus baryon, three strange quarks all had the same spin, driving a coach and horses though the Pauli exclusion principle.

Who assumed the quark is a spherically symmetric s-wave?

On the Wikipedia proton spin crisis article you can read this: “The ruling assumption was that since the proton is stable, then it exists in the lowest possible energy level. Therefore, it was expected that the quark’s wave function is the spherically symmetric s-wave with no spatial contribution to angular momentum”. Who assumed the quark is a spherically symmetric s-wave? That doesn’t tie in with what Paul Matthews said in the 20th February 1964 issue of New Scientist. He said the masses of the various particles were analogous to the energy levels of atomic systems. And what he said ties in with that 2014 Sci-am article proton spin mystery gains a new clue. It says quarks and gluons have angular momentum that comes from their movement around the center of the proton. Hence those curved white arrows on the previous page. So the quarks and gluons together are starting to sound a little like the electron. Especially since Matt Strassler said the zillions of quarks and gluons were  rushing around as fast as possible, at nearly the speed of light”. But since gluons are said to be massless, shouldn’t that be at the speed of light for the gluons? And should that be around and around? And what about the quarks? What’s their mass and how fast do they go around?

Quark mass

On the Wikipedia proton-to-electron mass ratio article you can read that the proton mass is composed primarily of gluons, and of quarks. The gluons come first. That’s a bit of a surprise, because gluons didn’t feature in the original quark model. So, how much of the proton mass is down to the quarks? In his 2009 book A Zeptospace Odyssey, CERN physicist Gian Guidice, now head of theory, says the constituent quarks account for only about 1% of the proton mass:

Fair use excerpt of copyrighted material by Oxford University Press

So, the quark isn’t responsible for much proton spin, and it isn’t responsible for much proton mass either. A quark certainly isn’t one third of a proton, it’s more like one three-hundredth, if that. In the Wikipedia quark article we can read that the up quark mass is 2.3 ± 0.7 MeV, and the down quark mass is 4.8 ± 0.5 MeV. That’s really not very much compared to the proton mass of 938.272046(21) MeV. Moreover the quark-mass error margin is huge, even after forty years, which suggests they aren’t sure. Maybe that 1% is wrong? By 1%? Either way it can’t count for much so let’s move on to the gluons. In the Wikipedia proton article we can read that the gluons have zero rest mass. That’s OK because we know about the photon in the box. So there’s no problem when the Wikipedia article goes on to say this: ”the rest mass of a proton is the invariant mass of the system of moving quarks and gluons that make up the particle, and, in such systems, even the energy of massless particles is still measured as part of the rest mass of the system”. OK. We know that gluons are supposed to be bosons like photons are bosons. We know that when you trap a massless photon in a mirror-box you increase the mass of the system. The Wikipedia article continues: “most of a proton’s mass comes from the gluons that bind the current quarks together, rather than from the quarks themselves. While gluons are inherently massless, they possess energy… and it is this that contributes so greatly to the overall mass of protons (see mass in special relativity)”.

Let’s open the box

That matches what we know about the photon in the box. When you open the box, the photon departs at c, and the box is a radiating body that loses mass, just like Einstein said in his E=mc² paper. We can then say that electron-positron annihilation is rather like opening one box with another, whereupon each is a radiating body that loses all its mass and then there’s no boxes left. Because the electron is like a photon in a box of its own making. Photon momentum is a measure of resistance to change-in-motion for a wave moving linearly at c, whilst electron mass is a measure of resistance to change-in-motion for a wave going around and around at c. And electron charge is what you get when you wrap a field-variation into a spin ½ standing-wave spinor configuration. Standing wave, standing field. OK, that hangs together. So, let’s break the proton open and take a look at all those zillions of quarks and gluons spilling out like beans from a bag. Get your bubble chamber ready, let’s open the box.

Proton-Antiproton annihilation

Just as we can annihilate an electron with its antiparticle the positron, we can annihilate a proton with its antiparticle the antiproton. Ideally we would perform low-energy annihilation to keep things as simple as we can. So, do we see sprays of quarks and gluons? Jets consisting of “zillions” of fundamental particles flying out in three or more directions? Since the gluons are massless bosons they’d presumably fly away at c, whilst the quarks would presumably depart at some slower speed. Can we track all these zillions of particles in a bubble chamber? No we can not, because what we see instead, is two photons:

Image credit CSIRO, see The Big Bang & the Standard Model of the Universe

You might protest and say annihilation to gamma photons is rare, and mesons such as pions are more likely. But see Claude Amsler’s 1998 proton-antiproton annihilation paper where you can read that the fraction of annihilations decaying to photons is 3.9%. That isn’t that rare. And remember that neutral pions last for only 10-16 seconds. Their lifetime is so brief that they don’t even leave tracks in the bubble chamber. Then note this on the Wikipedia annihilation article: “when a proton encounters an antiproton, one of its constituent valence quarks may annihilate with an antiquark, while the remaining quarks and antiquarks will undergo rearrangement into a number of mesons (mostly pions and kaons), which will fly away from the annihilation point. The newly created mesons are unstable, and will decay in a series of reactions that ultimately produce nothing but gamma rays, electrons, positrons, and neutrinos”. Forget the neutrinos for now. Instead note that those mesons leave you with nothing but gamma photons, electrons, and positrons. And note this too: you can annihilate the electrons with the positrons. Then you have rendered all those zillions of quarks and gluons down to a handful of photons. What happened to all that color charge and strong force? What happened to all those fundamental quarks and gluons? We didn’t see any quarks and gluons come spilling out like beans from a bag. Why not? Because it’s another little white lie?

Quark confinement

Or would that be a big black lie? The long-standing issue with quarks is that we’ve never seen one. This is said to be due to quark confinement. The particle adventure quark confinement article says this: If one of the quarks in a given hadron is pulled away from its neighbors, the color-force field ‘stretches’ between that quark and its neighbors. In so doing, more and more energy is added to the color-force field as the quarks are pulled apart. At some point, it is energetically cheaper for the color-force field to ‘snap’ into a new quark-antiquark pair”.

Image from the particle adventure

So, you can’t see a free quark because when you pull two quarks apart you create two more? Pull the other one. We no longer believe in spontaneous creation like worms from mud. It is not acceptable, particularly since as Ofer Comay points out on page 154 of Science or Fiction, two quarks in the guise of a neutral pion have no problem escaping their neighbours. Quark confinement is not scientific, it is non-falsifiable. You can’t see the angels dancing on the pin because they’re invisible angels. Yes, you can find people saying things like a free quark is like the free end of an elastic band. Stretch the elastic and eventually it snaps, and now you’ve got four quarks. But the analogy fails like a solenoid fails when you stretch it until it snaps. There are no magnetic monopoles, just as there are no one-sided coins. Such things do not exist. They are not real. And surprise surprise, nor are gluons. Yes, gluons are another “little white lie” too.

Gluons in ordinary hadrons are virtual

Google on gluons, and you can find articles that say the quarks in a hadron madly exchange gluons. You can find articles that say gluons are the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles. You can read that the strong interaction is mediated by the exchange of massless particles called gluons. There’s just one problem: hydrogen atoms don’t twinkle, and magnets don’t shine. There are no photons streaming out of the end of a solenoid. That’s because the messenger particles of the electromagnetic interaction are virtual photons. They aren’t short-lived real photons that pop in and out of existence, they only exist in the mathematics of the model. The electron has an electro-magnetic field, and so does the proton. Those fields interact, and that interaction is modelled using virtual particles. But the electron and the proton are not throwing photons back and forth. So, why is that relevant to the gluon? Take a look at the Wikipedia gluon article and you can read this: “there are also conjectures about other exotic hadrons in which real gluons (as opposed to virtual ones found in ordinary hadrons) would be primary constituents”. The gluons in a proton are virtual. As in not real. They only exist in the mathematics of the model. All those fairy stories about gluons flying back and forth between quarks are lies to children. Little “white” lies to children. Only there a whole pack of them, because sea quarks are virtual too.

Sea quarks are virtual too

Check out sea quarks: Hadrons contain, along with the valence quarks that contribute to their quantum numbers, virtual quark–antiquark pairs known as sea quarks”. Sea quarks are virtual quarks. As in not real quarks. The space where a hydrogen atom is, is not full of photons popping in and out of existence. Or electrons and positrons popping in and out of existence. The space where a proton is, is not full of quarks and antiquarks popping in and out of existence. The sea quarks in a proton are virtual rather than real, they only exist in the mathematics of the model too. And yet In the Wikipedia parton article, you can read that at low energies the scattering particle only sees the valence partons, but that at higher energies it also detects the sea partons:

Images by AnonyScientist, see Wikipedia

That’s neat. A particle is able to detect particles that only exist in the mathematics of the model? Bjorken scaling is said to provide evidence of the pointlike structure of a whole host of sea quarks and gluons, when those sea quarks and gluons are virtual. Something doesn’t add up here. The whole is greater than the sum of the partons, and somebody is missing the trick.

Elastic fantastic

I think you spot the trick when you understand the photon, and pair production, and the wave nature of matter, and the electron. And of course the Einstein-de Haas effect and Einstein’s general relativity. Einstein’s stress-energy tensor features a shear stress term. Stress is directional pressure and tension is negative stress, a pull rather than a push. But it takes two to tango and light waves are transverse waves. If there was no elastic tension to oppose the stress there wouldn’t be any transverse waves. What is that tensile attribute that keeps a light wave propagating at c? And what is it that keeps the standing-wave electron in one piece? Space waves, because it has an elastic quality. In Frank Close’s book quantum theory you can read how “in 1970, a young physicist named Leonard Susskind got stuck in an elevator with Murray Gell-Mann, one of physics’ top theoreticians, who asked him what he was working on. Susskind said he was working on a theory that represented particles ‘as some kind of elastic string, like a rubber band’. Gell-Mann responded with loud, derisive laughter”. What’s so funny? After all, Rutherford scattering is elastic scattering.

You can’t fit a longer-wavelength 2.3 MeV quark inside a smaller-wavelength 938.27 MeV proton

Imagine I lead you blindfolded into a classroom and put a rock in your hand. Then I guide you by the shoulders and point you towards the whiteboard. You throw the rock and it bounces right back and hits you on the head. You think it bounced back because it hit some other rock? And that the room is somehow studded with rocks, and these rocks increase in number when you throw harder? That’s got to be the wrong picture. It’s quantum field theory, not quantum point-particle theory. The electron is not some point particle. The electron has spin and a magnetic moment and can be diffracted, because it has a wave nature. Ditto for the proton. Things wave because of some elastic quality, so for a better picture, let me take your blindfold off. The room isn’t studded with rocks. Instead there’s this big old rubber band two feet wide and a hundred feet long, all festooned back and forth across the room in front of you. Throw your rock and it bounces back. If you couldn’t see it you might think the proton was made up of an infinite number of point-like partons. But it can’t be, because of the wave nature of matter. And as Martin van der Mark said in on the nature of stuff and the hierarchy of the forces: smaller mass means bigger wavelength, so you can’t fit a longer-wavelength 2.3 MeV quark inside a smaller-wavelength 938.27 MeV proton. The quark is not some point-particle, the proton isn’t some point-particle either, and nor is it some infinity of point particles. It’s something else. What can it be? As Matt Strassler said “First and foremost, it’s a mess. A total mess”. George Zweig said the standard model is a mess. An “ugly kludge”. But oranges are not the only fruit, and the standard model is not the only theory.

Topological quantum field theory

There’s also topological quantum field theory, also known as TQFT. It’s related to knot theory, and there is such a thing as a knot zoo. That ought to remind you of the particle zoo. Ed Witten was involved in knot theory. See his knots and quantum theory. He’s better known for string theory, which is what Susskind in the elevator was talking about. String theory features closed strings and open strings, rather like a rubber band and a rubber strip. The electron is arguably something like a rubber band. The Poynting vector goes around and around. It goes round twice all Möbius-style, a double-loop 720°, which is why the electron is a spin ½ spinor. If you undo it, you now have a linear wave with a linear Poynting vector. What’s not to like? Unfortunately string theory missed the trick, and TQFT got sidelined. When I look on the Edinburgh geometry and topology web page, I see this:

Image from Edinburg University School of Mathematics

I recognise that. That’s the double-loop spin ½ spinor. That’s the trivial-knot electron. A sinusoidal field variation is wrapped round twice Möbius-style, and then you’ve got a dynamical spinor in frame-dragged space. Sir Michael Atiyah has been at Edinburgh since 2005. He knows all about tying light in knots. He was at the 2011 ABB50/25 conference in Bristol. That’s where Qiu-Hong Hu had a poster entitled the electron, twisted photon, and knotted light. What’s the next knot in the knot zoo? The trefoil. There’s a picture of one on the Lisbon TQFT mini-workshop web page. A trefoil knot is tricolourable, like the traditional tricoloured proton picture:

 CCASA image by Arpad Horvath see Wikipedia             Public domain image by Jim Belk, see Wikipedia

It’s chiral, you can tie a knot left over right or right over left. Find a picture of a trefoil knot. Imagine it’s all wrapped round twice and twisted Möbius-style. Imagine it’s elastic, like a fat rubber band. It’s elastic so if you throw rocks at it, the rocks bounce back. It’s elastic so if you could grab hold of two of the loops and try to pull them apart, it would be more and more difficult, like the bag model. It’s a thing of “frantic motion” too. Not at nearly the speed of light. At the speed of light, such that the Poynting vector goes around and around and around the three loops in different directions like those white arrows in the physorg picture. Like this:

Based on a GNUFDL trefoil image by Ylebru, see Wikipedia

But it’s a spin ½ spinor, so it goes round twice, so it goes around and around and around, and around and around and around. It goes round six times, or nearly six times. We perhaps ought to inflate the trefoil to three congruent spherically-symmetric spheres, and then do some subtle shading to make it clear that there are no surfaces, because everything is fields and waves. But even without that, this picture is a better picture. Undo this thing and your Poynting vector exits stage left at 299,792,458 m/s. What is a quark? Just a loop, so when you break this thing you don’t see quarks racing away. You see pions. What is a pion? Just two loops, like a figure of eight. What is a proton? Just a spherically-symmetric three-loop trefoil “knot” of field-variation configured as a standing-wave particle. Light moving through light moving through light. Standing wave, standing field. Why do I think this? Because the proton g factor is 5.585. And because you can trace around that trefoil anticlockwise from the bottom left calling out the crossing-over directions: up down up. Now what are the chances of that?

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