Fundamental

by Tim James

  By analysing the masses, charges, spins and lifetimes of the abundant particles being discovered, Gell-Mann showed that all of them could be explained as combinations of kworks, which came in two varieties he named up and down.

  Up kworks have a positive charge of +⅔ while down kworks have a negative charge of −⅓. If you combine two up kworks with a down you get +⅔, +⅔ and −⅓ which adds to +1… a proton. If instead you combine two down kworks with one up kwork you have −⅓, −⅓, and +⅔ which cancel to zero, giving us the neutron.

  Three up kworks becomes a particle called a delta. An up kwork with an antimatter down kwork becomes the pion and so on. The particle zoo was an illusion, and protons and neutrons were composite particles, not fundamental. Kworks were what mattered because they made up matter.

  Oh, and that is how you can have anti-neutrons, by the way. While a regular neutron is chargeless, its constituent kworks are not. You can have two anti-downs with an anti-up totalling to zero, but an antimatter zero rather than a matter zero. Ain’t life grand?

  CRY OF THE SEAGULL

  One evening, while reading a copy of the novel Finnegans Wake by the Irish modernist James Joyce, Gell-Mann came across a poem opening with the phrase: ‘Three quarks for Muster Mark.’

  He was immediately struck by this nonsense-word ‘quark’ because it described something occurring in a group of three, just like his proposed particles often did. The spelling matched the sound he had picked – sort of – and he adopted it from then on. Joyce probably intended the word quark to rhyme with Mark but Gell-Mann decided it should rhyme with quartz instead.6

  In the poem, the word represents the noise a seagull makes and presumably seagulls in California, where Gell-Mann lived, make a ‘kwork’ sound rather than a ‘kwark’.

  In Britain, people usually pronounce the word as ‘kwark’ but that is not what Gell-Mann wanted. You have to pronounce it kwork or face the wrath of Californian seagulls.

  Besides, naming a particle after a bird noise is hardly the weirdest thing out there. The physicist Alan Guth named a hypothetical particle of his invention an inflaton after its supposed ability to inflate the universe, while Frank Wilczek named a particle of his invention the axion after a brand of laundry detergent.7

  COLOURFUL LANGUAGE

  Quarks were discovered experimentally, a few years after Gell-Mann proposed them, in a process that fires leptons (electrons, muons and tauons) at a neutron and watches their paths. If the neutron was a single chunk of matter in a ‘neutron field’ then electrons would recoil at a sharp angle, but if a neutron was made from a quark sub-structure, as Gell-Mann predicted, the leptons would instead be deflected, pulled off their course by the quarks’ partial charges.8

  The outcome of these experiments matched Gell-Mann’s predictions, giving us a new type of particle and a quantum field theory for the nucleus in the process.

  Protons and neutrons are composed of three quarks, plus thousands of virtual quarks popping up around them thanks to Heisenberg uncertainty. The three quarks that remain constant are called ‘valence quarks’ and they determine the overall identity.

  We know quarks interact with the photon field since they have an electric charge but the obvious question is why two up quarks, which are both positive, do not repel. Two like-charged particles never hang out together so someone needed to explain why the nucleus of every atom does not blast itself to pieces within moments of forming.

  The Japanese physicist Hideki Yukawa proposed a force much stronger than electromagnetism that kept protons in one piece, as well as holding protons and neutrons together. This force could overpower charge repulsion because it was quite strong, so he named it (brace yourself for this) the strong force.

  The difference in magnitude between the electromagnetic and strong forces is pretty vast. Electromagnetic interactions are the kind that move electrons around atoms and get chemical reactions going, e.g. they start fires. The energies involved in the strong force are about moving protons and neutrons in the core of an atomic nucleus. They start nuclear explosions.

  Since the electromagnetic force is all about particles coupling to the photon field and communicating via virtual photons, logically the strong force should have its own field for the quarks to couple to, which Gell-Mann called the gluon field. Y’know, cos it glues things.

  Next, we need a property to go with it. A particle’s ability to couple to the photon field is called its electric charge. Gell-Mann needed a name for the property that allowed quarks to couple to the gluon field and he chose the rather unhelpful word, colour.

  Stickiness might feel a more intuitive name, but Gell-Mann did have a reason. Unlike electric charge, which comes in two varieties (positive and negative), colour comes in three, reminiscent of the three primary colours of light.

  Quarks with red, green and blue ‘colours’ bind together via gluons and the colours cancel out to make a proton or neutron ‘white’ overall. Quarks are not literally red, blue or green (they do not have colour actually – see Appendix V) but we usually draw them that way just to confuse things as much as we possibly can.

  Feynman’s quantum field theory for electrons and photons was quantum electro-dynamics so Gell-Mann called his theory for quarks and gluons quantum chromo-dynamics (QCD for short), from the Greek word chroma meaning colour.

  LOOKS LIKE WE’RE STUCK THIS WAY

  The big difference between Feynman’s QED theory for leptons and Gell-Mann’s QCD theory for quarks is that in QED everything can be described in terms of opposites. Attraction and repulsion, positive and negative, matter and antimatter, etc. All these things can be handled by reversing stuff in your equations and diagrams. But with the strong force there are three kinds of colour so it is no longer a matter of back-pedalling. When there are three varieties available the word ‘opposite’ does not even apply.

  Also, antimatter quarks have anti-colours named anti-red, anti-blue and anti-green, so really there are six colour charges we have to explain if QCD is going to make sense. Electric charges are the result of photons behaving in opposing ways but gluons are different and it was their quirky (or quarky) behaviour that Gell-Mann would have to rationalise.

  A more complicated type of Feynman diagram was needed, in which colour could be transferred.

  Electrons and positrons hold their electric charge but quarks can swap colour back and forth between them. If you have two quarks, let’s say red and blue, the gluon field can exchange their colours so red becomes blue and blue becomes red.

  The diagrams for QCD use coiled lines to represent gluons and the interaction between two quarks can be calculated/drawn like this:

  The gluon that moves between them is carrying blue charge to the left and red charge to the right, meaning virtual gluons are multicoloured as they shuttle back and forth.

  This colour exchange also explains why the strong force is always attractive whereas electromagnetism can both attract and repel. Since virtual gluons are multicoloured, there always has to be a quark at each end. Gluons, by definition, are transferring colour from one quark to another so if you delete one of the quarks the gluon is left with some colour charge and nowhere to put it.

  Quarks have colour, which is another way of saying they couple to the gluon fields and thus they never exist on their own because part of their identity is ‘being bound to other quarks via gluons’. The strong force is always attractive.

  The term for this is ‘quark confinement’. Quarks are always found in pairs (called mesons), trios (baryons), quartets (tetraquarks) and so on. We never observe quarks ‘naked’ – genuine term – although physicists being perverts have desperately tried to catch a glimpse.

  We can take two quarks at the end of a gluon thread (a meson) and spin them inside a magnetic field until the gluon tube snaps.

  Unfortunately, when we run this experiment the gluons wind up with excess energy and transfer it instantly into the quark field, creating new quarks at each end of the rip. One mes
on becomes two. Quarks do not exist on their own even if we try to pull them apart.

  In Feynman’s QED, photons do not possess a charge (they cause it) but in Gell-Mann’s QCD, gluons do possess colour as well as their quarks, meaning gluons will self-interact, swapping quantum rainbows back and forth at will.

  Originally it made sense to think of a proton as a trio of quarks with gluons moving between them to form a triangle, but because gluons talk to each other and cling together, the gluon tubes between quarks are now thought to form a Y-shape.

  This also means gluons can stick together without needing quarks at all, forming their own tangled gluon-gluon bird’s-nest structures called glueball particles.

  In some ways, all these additional complications make QCD a more impressive and intricate theory than Feynman’s. On the other hand, QED is far more elegant, requiring only one exchange particle while QCD requires several (eight types of gluon to exchange all the colour combinations). Thank God there are only two types of quark. Right?

  STRANGELY CHARMING

  Gell-Mann’s up/down quarks are great. By combining them in the right order we can account for almost all the known particles in the particle zoo. The key word there being ‘almost’.

  One particle in particular, the kaon, cannot be described as a combination of up and down quarks. It acts more like an up quark glued to a heavier version of a down quark.

  Given that electrons were known to have more massive counterparts (the muon and tauon), Gell-Mann decided the down quark must be the same. The behaviour of kaons was undeniably strange, so Gell-Mann used that as his name for the third quark, giving us a list of all required quarks in QCD:

  But come on. Look at it.

  Gell-Man used complicated mathematics to predict the up and down quarks, but it does not take a Nobel Prize winner to see something is missing there. If the down quark has a heavier partner does it not seem likely the up quark should have one too? Would it not be a whole lot neater and prettier if there was a fourth?

  The physicist Sheldon Glashow believed in this fourth type of quark and worked out what properties it was likely to have. There was some minor evidence to suggest its existence (particles called K+ and K0 were expected to turn into lighter particles in a way which did not happen, even though Gell-Mann’s three-quark theory predicted they ought to), but Glashow was largely going on a gut feeling that the universe should be pretty.

  A lot of the time, scientists are hard-nosed sceptics who refuse to entertain any idea without evidence but sometimes they are human and they have hope.

  Glashow believed nature was beautiful in a deep way and named his hoped-for particle the charm quark because its charming nature completes the quark symmetry. For his optimism, he was rewarded with its discovery in 1974. A reminder that sometimes in physics you can hope that maybe nature knows what she is doing.

  THREE IS A MAGIC NUMBER… APPARENTLY

  In the Arthur C. Clarke science-fiction masterpiece Rendezvous with Rama (1973), humanity discovers an abandoned alien structure built by a species obsessed with the number three. They find alien suits with three limbs, structures built in trios and every decision the mysterious species made seems to have been copied three times. Nature has a similar obsession.

  The year before the charm quark was validated and, in fact, the same year Rendezvous with Rama was published, Makoto Kobayashi took the idea of symmetry and neatness one step further. QED had three matter particles – electrons, muons and tauons – so maybe a similar trend should be repeated in QCD.

  The up quarks heavier sister was the charm quark and the down quarks was the strange. Might there be a third generation? Kobayashi, who did not believe in no-win scenarios, called these mega-quarks the ‘bottom’ and ‘top’ to complete the set. They were both discovered, in 1977 and 1995 respectively.

  The humans in Rendezvous with Rama are left at the end of the novel with a lot of questions about who the aliens were and why they chose to do everything in threes. In particle physics, the story is the same.

  Why are there three generations of quark and lepton? Nobody knows. Could there be a fourth of each kind? Nobody knows. Are the three generations somehow linked to the three colours? Nobody knows.

  Maybe one day we will be able to overcome the gluon-thread confinement and analyse an isolated quark to get more insight into their behaviour. Maybe one day we will get our hands on a naked charm, a naked strange or a naked up quark. And maybe one day, if we are very lucky, we will catch a glimpse of a naked bottom.

  CHAPTER FOURTEEN Honey, Where’s My Higgs?

  HER MAJESTY, THE QUEEN OF PHYSICS

  On 4 July 2012 newspapers around the world proclaimed a momentous day for science. The Independent front-page headline was ‘Scientists prove existence of God particle’, CBC news reported a ‘missing cornerstone of particle physics’ had been found and the New York Times ran with ‘physicists find elusive particle seen as key to Universe’.

  It was the monumental discovery of the Higgs boson and everyone was scrabbling to explain what the fuss was about. The Higgs boson is pretty complicated, however, and cannot be summed up in a newsworthy soundbite.

  So complicated is the Higgs that in 1993 the UK science minister William Waldegrave offered a bottle of champagne to any scientist in the country who could summarise what the Higgs did on a single side of paper.1 That is not what we are going to do here (I would rather have a milkshake) but we will try and get a feel for what the Higgs is all about.

  What makes it important is that it validates a prediction made by physicists almost fifty years prior, requiring construction of the Large Hadron Collider – the largest machine ever built.

  But how did we know it was worth the effort? I could invent a particle right now called the timon, the particle that makes you want to check your watch during a boring movie. Are we going to build a machine for that?

  Come to think of it, how do theoretical physicists know any hypothesis is worth investigating? There are so many particles/fields and interactions between them, how do we figure out if our equations are sensible? Is there some ultimate law for making new physics laws?

  The answer is yes and it comes from one of the most brilliant and criminally unheard of physicists of all time: Amalie ‘Emmy’ Noether.

  At the beginning of the twentieth century, Noether was one of two women permitted to attend the University of Erlangen in Germany and had to get permission from every lecturer whose classes she wished to attend. Believe it or not, her uterus did not prevent her from understanding mathematics (how about that?) and she wrote a series of outstanding papers, which caught the attention of the well-respected mathematician David Hilbert.

  Hilbert helped Noether get a job as a lecturer at Gottingen University, where she was the solitary female member of staff. The position was unpaid, of course, and her lectures had to be advertised under Hilbert’s name but, regardless, she had a foot in the door of academia.2

  What finally turned the tide was when she discovered what is probably the most important guiding principle in theoretical physics: Noether’s theorem. In a way, it is a shame that to be treated as equal a woman had to triumph over every male physicist in the world, but also… it make her kind of badass. Men were not giving her enough respect, so she out-mathed every one of them with a theorem so far-reaching it forms a cornerstone of QED and QCD, and solves puzzles in relativity even Einstein could not figure out.

  Noether’s theorem is about finding what physicists call ‘symmetry’, an idea with which we have vaguely been toying. When we are studying an event or a particle we use equations that tell us about the kinetic energy (movement) and the potential energy (location in a field). The difference between these two energies is called a Lagrangian and every physical law has one.

  But we can always change the details of whatever scenario we are studying. If we perform our experiment near a strong magnet say, or change the mass of the particle, this will sometimes alter the Lagrangian and sometimes leav
e it untouched. If our changes do not change the Lagrangian, all the equations are identical and we call our theory symmetric. If changing something does impact the Lagrangian, the equations change too and our theory contains a ‘broken symmetry’.

  Noether’s theorem says that if you have symmetry in a theory, there has to be an associated property of particles that does not change either.

  For example, suppose we are studying a particle and decide to shift it 1 metre to the right. The particle behaviour will be identical. Our theory is therefore symmetric with respect to location.

  Noether’s theorem says this change in location is the result of the particle travelling with momentum from one place to the other, so momentum has to be ‘conserved’, i.e. it cannot be created or destroyed. Particles can transfer momentum during collisions but the total before and after is the same no matter what.

  Another example of Noether’s theorem is that when we move a particle forward through time the laws of physics are again invariant. Laws of physics are symmetric with respect to time so there must be a conserved property to go along with it – it turns out to be energy (since we are talking about cause/effect). Émilie du Châtelet had already proven energy is never created or destroyed but Noether’s theorem gave us the underlying reason.

  Charge is another conserved quantity, originating from the way a particle’s wavefunction vibrates. That is why photons of light always create antimatter and matter particles in tandem. Charge has to be conserved so a chargeless photon cannot make an electron without making an anti-electron to keep the overall charge zero. And these are just a few examples.

  Noether’s theorem tells us what properties we can and cannot change for a law of physics and it was integral for Dirac, Feynman and Gell-Mann when figuring out how quantum field theories ought to work. Noether gave us a law for physics laws and it is hard to overstate how important that is.