Everything we call real is made of things that cannot be regarded as real.
Niels Bohr
At the end of the 1920s it seemed as if the basic building blocks of matter had been tracked down. The atoms of the periodic table could all be built by taking combinations of electrons, protons and neutrons. The electron has withstood any attempts to divide it further. But revelations over the next decades would lead scientists to believe that there was another layer of reality hiding below the other two building blocks.
The principal reason for the realization that protons and neutrons might not be as indivisible as the electron came not from more sophisticated technology but from the mathematics of symmetry. It is striking that time and again mathematics appears to be the best microscope we have to look inside my casino dice. A mathematical model began to emerge to explain the proton and the neutron, and it was built on a mathematical concept that could be divided. If the mathematics came apart into smaller pieces, the feeling was that the same should apply to the proton and the neutron.
The mathematical model responsible for this belief in the divisibility of the proton and neutron arose because physicists discovered that there were a lot more particles out there than just the three believed to be the constituents of stable atoms.
The discovery of these new particles was a result of collider experiments. Not human-constructed colliders like the LHC, but naturally occurring collisions that happen in the upper atmosphere when cosmic rays strike the atmosphere.
The first evidence of new particles was found in the cloud chambers that experimenters had built in their labs to record the paths of charged particles. Cloud chambers consist of a sealed tank full of a supersaturated vapour of water and alcohol. The supersaturation is such that any charged particle passing through leaves a trail of condensation behind it.
Carl Anderson, a physicist working at Caltech, had used these cloud chambers in 1933 to confirm the existence of a strange new sort of matter called antimatter that had been predicted some years earlier by British physicist Paul Dirac. Dirac’s attempt to unify quantum physics and the theory of electromagnetism had successfully explained many things about electrons, but the equations seemed to have a complete mirror solution that didn’t correspond to anything anyone had seen in the lab.
Dirac’s equations were a bit like the equation x2 = 4. There is the solution x = 2, but there is another mirror solution, namely x = –2, because –2 × –2 is also equal to 4. The mirror solution in Dirac’s equations implied that there was a mirror version of the electron with positive charge. Most thought this was a mathematical curiosity that emerged from the equations, but when, four years later, Anderson spotted in his cloud chamber traces of a particle behaving like an electron in a mirror, antimatter went from theory to reality. Anderson’s positrons, as they came to be known, had been created in the particle interactions happening in the upper atmosphere. And they weren’t the only new things to appear.
Even stranger particles that had not been predicted at all were soon leaving trails in Anderson’s cloud chamber. Anderson started to analyse these new paths with his PhD student Seth Neddermeyer in 1936. The new particles corresponded to negatively charged particles passing through the cloud chamber. But they weren’t electrons. The paths these new particles were leaving indicated a mass much larger than that of the electron. Just as Thomson had done, mass can be measured by how much the particle is deflected under the influence of a magnetic field. The particle seemed to have the same charge as the electron but was much harder to deflect.
Now called the muon, it was one of the first new particles to be discovered in the interactions of cosmic rays with the atmosphere. The muon is unstable. It quickly falls apart into other particles, most often an electron and a couple of neutrinos. Neutrinos were another new particle that had been predicted to explain how neutrons decayed into protons. With almost no mass and no charge, it took until the 1950s before anyone actually detected these tiny particles, but they theoretically made sense of both neutron decay and the decay of this new muon. The decay rate of the muon was on average 2.2 microseconds, which is sufficiently slow that enough particles won’t have decayed by the time they reach the surface of the Earth.
The muon helped to confirm Einstein’s prediction from special relativity that time slows down as you approach the speed of light. Given its half-life, far fewer muons should be reaching the surface of the Earth than were being detected. The fact that time slows down close to the speed of light helps explain this discrepancy. If a clock was attached to the muon, it would show that a smaller interval of time had elapsed before it hit the Earth. Thus more muons would therefore survive, as revealed by experiment. I will return to this in the Fifth Edge when I consider pushing time to the limits of knowledge.
The muon appeared to behave remarkably like the electron but had greater mass and was more unstable. When the American physicist Isidor Rabi was told of the discovery, he quipped: ‘Who ordered that?’ It seemed strangely unnecessary for nature to reproduce a heavier, more unstable version of the electron. Little did Rabi realize how much more there was on the menu of particles.
Having realized that cosmic ray interactions with the upper atmosphere were creating new forms of matter, physicists decided that they better not wait for the particles to reach the cloud chambers in the labs, by which time the particles might have decayed into traditional forms of matter. So the cloud chambers were moved to high-altitude locations in the hope of picking up other particles.
The Caltech team chose the top of Mount Wilson near their home base in Pasadena. Sure enough, new tracks indicated that new particles were being picked up. Other teams placed photographic plates in observatories in the Pyrenees and the Andes to see if they could record different interactions. Teams in Bristol and Manchester also saw traces of new particles in their own photographic plates. It turned out that the muon was the least of Rabi’s worries. A whole menagerie of new particles started showing up.
Some had masses about one-eighth that of a proton or neutron. They came in positively or negatively charged varieties and were dubbed pions. An electrically neutral version that was harder to detect was later discovered. In Manchester two photographs from their cloud chamber showed what appeared to be a neutral particle decaying into pions. The mass of these new particles was roughly half that of a proton. The cloud chamber at the top of Mount Wilson recorded more evidence to support the discovery of what would become known as kaons, four in number.
As time went on, more and more particles were uncovered, so much so that the whole thing became totally unwieldy. As Nobel Prize winner Willis Lamb quipped in his acceptance speech of 1955: ‘The finder of a new elementary particle used to be rewarded by a Nobel Prize, but such a discovery now ought to be punished by a $10,000 fine.’ The hope was that the periodic table would be simplified once scientists had discovered how it was put together using electrons, protons and neutrons. But these three particles turned out to be just the tip of the iceberg. Now there were over a hundred particles that seemed to make up the building blocks of matter. As Enrico Fermi admitted to a student at the time: ‘Young man, if I could remember the name of these particles, I would have been a botanist.’
Just as Mendeleev had managed to find some sort of order with which to classify and make sense of the atoms in the periodic table, the search was on for a unifying principle that would explain these new muons, pions, kaons and other particles.
The underlying structure that finally seemed to make sense of this menagerie of particles – the map, as it were, to find your way around the zoo – ultimately came down to a piece of mathematics.
When you are trying to classify things, it helps to recognize the dominant characteristics that can gather a large mess of objects into smaller groups. In the case of animals, the idea of species creates some order in the animal kingdom. In particle physics one important invariant that helped divide the zoo into smaller groups was the idea of charge. How does the particle interact with the electromagnetic force? Electrons would bend one way, protons the other, and the neutron would be unaffected.
As these new particles emerged from the undergrowth, they could be passed through the gateway of the electromagnetic force. Some would join the electron’s cage, others would head towards the proton, and the rest would be put together with the neutron – a first pass at imposing some order on the menagerie of particles.
But the electromagnetic force is one of four fundamental forces that have been identified at work in bringing the universe together. The other forces are gravity, and the strong nuclear force responsible for binding protons and neutrons together at close quarters inside the nucleus, and finally the weak nuclear force that controls things like radioactive decay.
The key was to identify other characteristics similar to the idea of charge that could distinguish the different behaviours of these particles with the other fundamental forces. For example, the mass of a particle was actually quite a good way of establishing some hierarchy in the particle zoo. It collected pions and kaons together as particles that were a factor lighter than the protons or neutrons that made up ordinary matter. A new collection of particles called Sigma, Xi and Lambda baryons had masses larger than the proton and neutron and often decayed into protons or neutrons.
Often particles with very similar masses got the same Greek names. Indeed, the proton and neutron have such similar masses that they were believed to be intimately related, so much so that the German physicist Werner Heisenberg (whose ideas will be at the heart of the next Edge) rechristened them nucleons. But mass was a rather rough and ready way of sorting these particles. Physicists were on the lookout for something more fundamental: a pattern as effective as the one Mendeleev had discovered to order atoms.
The key to finding patterns to make sense of the onslaught of new particles was a new property called strangeness. The name arose due to the rather strange behaviour demonstrated by some of these new particles as they decayed. Since mass is equivalent to energy via Einstein’s equation E=mc2, and nature favours low-energy states, particles with larger mass often try to find ways to decay into particles with smaller mass.
There are several mechanisms for this decay, each depending on one of the fundamental forces. Each mechanism has a characteristic signature which helps physicists to understand which fundamental force is causing the decay. Again it’s energy considerations that control which is the most likely force at work in any particle decay. The strong nuclear force is usually the first to have a go at decaying a particle, and this will generally decay the particle within 10–24 of a second. Next in the hierarchy is the electromagnetic force, which might result in the emission of photons. The weak nuclear force is the most costly in energy terms and so takes longer. A particle that decays via the weak nuclear force is likely to take 10–11 seconds before it decays. So by observing the time it takes to decay, scientists can get some indication of which force is at work.
For example, a Delta baryon decays in 6 × 10–24 seconds to a proton and a pion via the strong nuclear force, while a Sigma baryon takes 8 × 10–11 seconds to decay to the same proton and pion. The longer time of decay indicates that it is controlled by the weak nuclear force. In the middle we have the example of a neutrally charged pion decaying via the electromagnetic force into two photons, which happens in 8.4 × 10–17 seconds.
Imagine a ball sitting in a valley. There is a path to the right which, with a little push, will take the ball over the hill into a lower valley. This path corresponds to the strong nuclear force. To the left is a higher hill which is also a path to a lower energy state. This direction represents the work of the weak nuclear force.
A Delta baryon ∆ decays via the strong nuclear force to a proton and a pion. In contrast, a Sigma baryon ∑ decays via the weak nuclear force.
So why did the Delta baryon find a way over the easy hill while the Sigma baryon went the long way? This seemed rather strange. There appeared to be certain particles that encountered a barrier (represented in the figure by a broken line) that prevented them from crossing via the easy route to the lower valley.
The physicists Abraham Pais, Murray Gell-Mann and Kazuhiko Nishijima came up with a cunning strategy to solve this puzzle. They proposed a new property like charge that mediated the way these particles interacted or didn’t interact with the strong nuclear force. This new property, called strangeness, gave physicists a new way to classify all these new particles. Each new particle was given a measure of strangeness according to whether or not its decay would have to take the long route.
The idea is that the strong nuclear force can’t change the strangeness of a particle, so if you have two particles with different strangeness, the strong nuclear force can’t decay one into another. There is a barrier blocking the route to the lower valley. But the weak nuclear force can change strangeness. So since the strong nuclear force decays a Delta baryon into a proton, they have the same measure of strangeness equal to 0; while the Sigma baryon has a different value of strangeness because it needs the weak nuclear force to decay it to a proton, and its strangeness is given value –1. (It was a quirk of how all the different particles were numbered that these ones got given –1 rather than 1. It wouldn’t really have changed anything had they been given value 1 and others –1.)
Then even more exotic particles were detected, created by higher-energy collisions that seemed to decay in two steps. They were called cascade particles. The proposal was that these were doubly strange, so were given strangeness number –2. The first step in the decay had strangeness –1 and then they ended up with protons and neutrons, which had strangeness 0. It may seem a bit like pulling a rabbit out of a hat, but that’s part of the process of doing science. You keep pulling things out of the hat. Most of them you chuck away because they get you nowhere. But pull enough things out of the hat and every so often you’ll get a rabbit. As Gell-Mann admitted: ‘The strangeness theory came to me when I was explaining a wrong idea to someone, but then I made a slip of the tongue and I had the strangeness theory.’ Strangeness turned out to be a pretty amazing rabbit.
Originally the idea of strangeness was meant just as a bookkeeping device, something that conveniently kept track of the decay patterns between particles. There wasn’t meant to be any physical meaning to the idea of strangeness. It was just another set of cages to help classify the animals in the particle zoo. But it transpired that this new feature was actually the first hint of a much deeper physical reality at work underneath all these particles. The exciting moment came when they took particles of a similar sort of mass and began to plot them on a graph measuring their strangeness and charge together. What they got were pictures full of symmetry.
The pattern of particles created a hexagonal grid with two particles occupying the centre point of the grid. If one took the pions and kaons and arranged them on a grid of strangeness against charge, a similar picture emerged. When you get a pattern like this you know you are on to something. The key to the deeper reality underneath these particles was spotting that the hexagonal patterns these particle pictures were making were not new – they’d been seen before. Not in physics, but in the mathematics of symmetry.
To someone trained in the mathematics of symmetry, these arrangements of cages in a hexagonal pattern with a double point at the centre look very familiar. They are the signature of a very particular symmetrical object called SU(3).
For me this is brilliant. Symmetry is something I know about. This gives me a chance to get a handle on what is going on in the depths of my dice. In fact, my dice is a perfect vehicle to explain the ideas that are at the heart of the mathematics of symmetry. The symmetries of my cube (disregarding the spots) are all the ways I can pick my dice up, spin it, and place it back down again so that it looks like it did before I started spinning it. There are actually 24 different moves I can make. For example, I could just rotate the cube by a quarter of a turn round one of the faces or I could spin the dice by a third round one of the axis running through opposite corners of the cube.
In total there are 24 different moves I can make (including a strange one where I just leave the cube where it is and do nothing). This collection of symmetrical moves is given the name S4, or the symmetric group of degree 4. If I include mirror symmetry, which means I also view the dice in a mirror, there are in total 48 different symmetries of my cube.
The cube should be thought of as the geometrical shape in three dimensions on which the group of symmetries S4 act. But there are other geometric shapes whose symmetries will be the same. For example, the octahedron is another three-dimensional geometric shape whose group of symmetries is the same as that of the cube. But there are higher-dimensional objects whose symmetries are also S4. So there are lots of different geometries that have the same underlying group of symmetries.
It was not the symmetries of my dice behind the hexagonal pictures made up of particles, but a symmetrical object called SU(3). SU(3) stands for ‘the special unitary group in dimension 3’, but it can describe the symmetries of a range of different geometric objects in different dimensions. The hexagonal grids created by the particles are the same as the picture mathematicians use to describe the way SU(3) acts on an object in eight-dimensional space. The eight particles of the hexagonal grid correspond to the number of dimensions you need to create this symmetrical object.
This hexagonal picture was the Rosetta Stone that opened up a whole new culture at play in particle physics, though it was a different cultural analogy that took hold to highlight the breakthrough. The guiding light of this figure with eight particles corresponding to this eight-dimensional representation led to the phenomenon being called the eightfold way, invoking the Buddhist idea of the eightfold way to spiritual enlightenment.
There were other pictures which corresponded to objects in different dimensions that SU(3) could act on. The exciting revelation was that these different pictures could be used to collect together other members of the particle menagerie. The different geometric representations of the symmetries of SU(3) seemed to be responsible for the different physical particles that make up matter in the universe.
It is amazing to me how time and again the physical world seems to turn into a piece of mathematics. We have to ask to what extent this is just a good story that helps tie the physical universe together, or is the physical universe actually a piece of physicalized mathematics? With this new link, fundamental particles became pieces of geometry that are stabilized by this group of symmetries acting on the geometric space.
Heisenberg was right when he wrote: ‘Modern physics has definitely decided in favour of Plato. In fact, the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.’ Plato’s watery icosahedron and fiery tetrahedron have been replaced by this strange new symmetrical shape SU(3).
When the physical world turns into a piece of mathematics, I immediately feel that this is something I can comprehend. The mathematics of symmetry is my language. For most, turning fundamental particles into maths means a move away from things that they know. Comparing particles to billiard balls or waves lends the particles a more tangible reality. How can we know anything unless it grows out of how we physically interact with the world around us? Even the abstract language of eight-dimensional symmetrical objects is possible only because we are abstracting the ideas of things we have physically encountered, like the symmetry of my Las Vegas cube.
The essential point here is that you can have several different geometric objects whose underlying group of symmetries is the same. Conversely, if I have a group of symmetries, there can be many different physical objects whose symmetries are described by that group. Mathematicians say that the object is a representation of the abstract group of symmetries, in the same way three apples or three dice are both physical manifestations of the abstract concept of the number 3. For example, if I take my casino cube, there are 24 different rotations that I can make. If I consider the four diagonal lines running between the opposite corners of the cube, these rotations permute these lines around.
In fact, if I put four playing cards (Ace, King, Queen and Jack) on the corners then each rotation is like shuffling these four cards: there are 24 different ways to shuffle four cards. But I can get yet another physical representation of this group of symmetries. If I take a tetrahedron and consider the rotations and reflections of this shape, there are again 24 different symmetries. If I stick the playing cards on the faces of the four-faced triangular pyramid, the symmetries of the tetrahedron give us the 24 different ways the cards can be shuffled. The group of symmetries now has two distinct three-dimensional realizations as the symmetry of some geometric object: one as the rotations of a cube, the other as the rotations and reflections of a tetrahedron. It turns out that if you look at all the physical geometric representations of this object called SU(3) in all dimensions, the symmetrical objects give you a way of generating all the different fundamental particles that were appearing.
It was physicists Gell-Mann and Yuval Ne’eman who in 1961 independently recognized the patterns in these particles. Ne’eman was in fact combining his physics with a career in the IDF, the Israeli Defence Force, and had been posted to London as their military attaché. He’d meant to study general relativity at King’s College, but when he realized that it was miles from the Israeli Embassy in Kensington he decided instead to check out what was happening five minutes down the road at Imperial College. They were doing particle physics. Ne’eman turned his attention from the very big to the very small.
Although the pattern for the Lambda, Sigma and Xi particles, together with the proton and neutron, matched the eight-dimensional symmetry of SU(3), the corresponding pattern of kaons and pions was missing a particle at its centre. It was either wrong or there was a new particle to be discovered. Gell-Mann published his prediction of this missing particle in a Caltech preprint in early 1961. Sure enough, the Eta particle was discovered a few months later by physicists in Berkeley.
This is the perfect scenario for a new theory. If it makes a physical prediction that is subsequently confirmed, you know you’re on to a winner. The same thing happened again when both Gell-Mann and Ne’eman attended a conference in June 1962 at CERN. At the conference a whole host of new particles was announced: three Sigma-star baryons with strangeness –1, and two Xi-star baryons of strangeness –2. The guess was that these particles would correspond to one of the other pictures that show how the group of symmetries SU(3) acts on a symmetrical object in higher dimension.
As Gell-Mann and Ne’eman independently sat there in the lecture filling in their pictures of how to arrange these new particles, a different picture began to emerge corresponding to another of the symmetrical objects that SU(3) acts on, an object in ten dimensions. But one of the corners of the picture was missing. There were only nine particles. Both Gell-Mann and Ne’eman simultaneously realized that one place had been left empty, leading to the prediction of a new particle. It was Gell-Mann who stuck his hand up first and predicted the Omega particle with strangeness –3, a prediction that would be confirmed in January 1964.
It was the twentieth-century version of the story of Mendeleev’s periodic table: a recognition of an underlying pattern but with missing jigsaw pieces. Just as the discovery of the missing atoms gave credence to Mendeleev’s model, so too the discovery of these missing particles helped convince scientists that these mathematical patterns were powerful ways to navigate the particle zoo.
It transpired that the patterns Mendeleev discovered in the periodic table were actually the result of these atoms being made from the more fundamental ingredients of the proton, electron and neutron. There was a feeling that the patterns in all the newly discovered particles hinted at a similar story: the existence of more fundamental building blocks at the heart of the hundreds of particles that were being detected.
A number of physicists had spotted that if you place the patterns corresponding to the different multidimensional representations of SU(3) in layers, you get a pyramid shape – with the top layer missing. There should be something akin to a simple triangle sitting on top of all this. This corresponded to the simplest physical representation of SU(3) acting on a three-dimensional geometry. If you looked at these layers from the perspective of symmetry, this missing layer was really the one from which you could grow all the other layers. But no one had spotted any particles that corresponded to this missing layer.
Triangle hinting at three new particles: the up quark u, the down quark d, and the strange quark s.
Robert Serber, who had been Oppenheimer’s right-hand man during the Manhattan Project, was one of those who conjectured that maybe this extra layer suggested three fundamental particles that could be used to build all the particles corresponding to the other layers. At a lunch with Gell-Mann in 1963, Serber explained his idea, but when Gell-Mann challenged him to explain what electrical charge these hypothetical particles would have, Serber wasn’t sure. Gell-Mann started scribbling on a napkin and soon had the answer. The charges would be ⅔ or –⅓ of the charge on a proton. The answer seemed ridiculous. ‘That would be a funny quirk,’ Gell-Mann commented. Nowhere in physics had anything been observed that wasn’t a whole-number multiple of the charge on the electron or proton.
It was reminiscent of the days of Pythagoras. Everything was meant to be made up of whole-number multiples, but here was something that seemed to cut this basic unit into pieces. They were still whole-number ratios, but no one had ever seen such fractional charges. Although Gell-Mann was initially sceptical about these hypothetical particles with fractional charge, by the evening they were beginning to work their magic on him. In the subsequent weeks he began teasing out the implications of these ideas, calling the particles ‘kworks’ whenever he talked about them, a word he had used previously to denote ‘funny little things’. Serber believed the word was a play on the idea of the quirkiness Gell-Mann had mentioned at lunch.
It was while perusing James Joyce’s experimental novel Finnegans Wake that Gell-Mann came across a passage that determined how he would spell the word he was using to describe these hypothetical particles. It was the opening line of a poem ridiculing King Mark, the cuckolded husband in the Tristan myth, that caught his attention: ‘Three quarks for Muster Mark!’
Given that there were three of these hypothetical new particles that could be used to build the other layers, the reference seemed perfect. The only trouble was that Joyce clearly intended the new word ‘quark’ to rhyme with ‘Mark’ not ‘kwork’. But the spelling and pronunciation Gell-Mann wanted won out.
These quarks would eventually become what we now believe to be the last layer in the construction of matter. But it would take some time for the idea to catch on. During a conversation on the telephone to his former PhD supervisor about these quarks, Gell-Mann was stopped in his tracks: ‘Murray, let’s be serious … this is an international call.’
For Gell-Mann the patterns seemed too beautiful not to have at least some underlying truth to them. The idea was that sitting below these layers of particles was a new layer of three fundamental particles: the up quark, the down quark and the strange quark, with charge ⅔, –⅓ and –⅓ respectively. The other particles were made up of combinations of these quarks (and their antiparticles in the case of kaons and pions). The number of strange quarks in the make-up determined the strangeness of the particle. So I can redraw the picture of the eightfold way made of the proton, neutron, Sigma, Xi and Lambda particles in terms of these quark ingredients.
As I sweep up the picture, the number of strange quarks drops by one at each step. If I head off in the direction of increasing charge I see at each step an increase in the up quark, the quark with charge ⅔. There is a third direction which controls the increase of down quarks. The other layers of particles had similar stories.
Gell-Mann wasn’t the only one to play with the idea of pulling matter apart into these smaller particles. American physicist George Zweig also believed these patterns hinted at a more fundamental layer of particles. He called them aces, but, probably more than Serber or Gell-Mann, he believed that these particles had a physical reality. His preprints explaining his ideas were dismissed as ‘complete rubbish’ by the head of the theory group at CERN. Even Gell-Mann, who had come up with similar ideas, didn’t regard them as more than a mathematical model that created some coherent order in the pictures they were drawing. They were a mnemonic, not concrete reality. Gell-Mann dismissed Zweig’s belief in the physical reality of these particles: ‘The concrete quark model – that’s for blockheads.’
That would all change when evidence emerged from experiments conducted at the end of the 1960s by physicists working at the Stanford Linear Accelerator Center in which protons were bombarded with electrons. Analysis of a proton’s charge reveals that it can be thought to have a size which spreads over a region of 10–15 metres. The belief was that the proton would be uniformly distributed across this small region. But when electrons were fired at the proton blob, the researchers got a shock from the resulting scatter patterns. Rather like the surprise Rutherford got when atoms of gold were bombarded with alpha particles, the proton, like the atom, turned out to be mostly empty space.
The scattering was consistent with a proton that was made up of three smaller particles. Just as in Rutherford’s experiments, every now and again one of these electrons would score a direct hit with one of these three points and come shooting back towards the source of the electrons. The experiment seemed to confirm the idea that the proton was made up of three quarks. Although a quark has never been seen in the open, the scattering of the electrons indicated that, sure enough, there were three smaller particles that made up the proton.
It turns out that the blockheads were right. The up, down and strange quarks were not just a mathematical mnemonic but seemed to be a physical reality. It was discovered that these three quarks weren’t enough to cover all the new particles, and eventually we’ve found ourselves with six quarks together with their antiparticles. In addition to the three Gell-Mann named, three more appeared on the scene: the charm quark, the top quark and the bottom quark.
The discovery of this way of ordering the menagerie of particles in physics using the mathematics of symmetry is one of the most exciting discoveries of the twentieth century. Seeing these fundamental particles lining up in patterns that were already sitting there in the mathematics of symmetry must have been so thrilling. If I could choose a discovery in physics that I would have loved to have made, this one would rank pretty high. It must have been like an archaeologist coming across patterns that had previously been seen only in some other distant part of the world. Seeing such distinctive patterns, you knew there had to be a connection between the two cultures.
The weird thing is that this pyramid of triangles and hexagons giving rise to different representations of SU(3) goes on to infinity, implying that you could keep on gluing together more and more of these quarks to make more and more exotic particles. The physical model seemed to run out at the layer that pieces together three quarks. But announcements from the LHC in 2015 revealed exciting evidence for a five-quark particle. The researchers at CERN almost missed the particle, called a pentaquark, thinking it was just background noise. But when they tried to remove the noise they discovered a strong signal pointing towards this next layer in the symmetry tower. As one of the researchers working at CERN admitted: ‘We didn’t go out looking for a pentaquark. It’s a particle that found us.’
How much further can we push the mathematics to make predictions of what else we might see in the LHC? There is an even bigger symmetrical object called SU(6) that would unite all six quarks – up, down, strange, charm, top and bottom – into a fusion of fascinating particles. Instead of the two-dimensional pictures I’ve drawn combining particles together in families, you’d need five-dimensional pictures. Although it is possible to cook up some of these more exotic combinations of quarks, because the mass differences between the basic quarks get larger and larger, the beautiful mathematical symmetry gets broken and the reality of such particles becomes less and less plausible. Indeed, the top quark is so unstable that it decays before it ever has time to bind to another quark. Why the quarks have these different masses seems to be a question that the physicists don’t know the answer to – yet. The mathematics seems to suggest a much richer cocktail of particles than physical reality can actually sustain. Reality seems a pale shadow of what might be possible mathematically. However, understanding that reality still holds many challenges.
I must admit that, even with the mathematical toolkit that I’ve spent years putting together, I’m still not sure I know what these quarks really are. I’ve sat at my desk poring over books on particle physics for months – for example, Sudbury’s Quantum Mechanics and the Particles of Nature – and lecture notes downloaded for Oxford graduate courses on symmetry and particle physics. And as I sit here surrounded by these tales of the inner workings of my dice, I begin to despair a little. There is so much that I still don’t know: path integrals describing the futures of these particles, the inner workings of the Klein–Gordon equations, what exactly those Feynman diagrams that physicists so easily draw up on the board really mean. I look enviously at my son who has started his degree in physics. He will have the time to steep himself in this world, to get to know these things as intimately as I know the area I chose to specialize in.
It is the same with my cello. As an adult I hanker to play those Bach suites now, not in ten years’ time. But just as it took years to learn the trumpet, so it will be a slow, gradual, sustained period of learning that will bring me to the point where I can play the suites. I’ve at least managed to pass my grade 3 this month. I was shocked by how nervous I got. My bow was shaking all over the place. Although I was surrounded by a bunch of 11-year-olds waiting to do their grade 1 recorder, it still felt good to get that sense of achievement.
As with the cello, I know that if I spent enough time in this world of particle physics I would have some hope of knowing what my colleagues across the road in the physics department live and breathe daily. It frightens me to realize I don’t have time to know it all. But even those physicists whom I envy for the ease with which they play with our current state of knowledge recognize that ultimately they’ll never know for sure whether they know it all.
I arranged to meet one of the scientists responsible for discovering one of the last pieces in the quark jigsaw to see whether particle physicists think the current jigsaw might be made of even tinier pieces. Now a professor at Harvard, Melissa Franklin was part of the team responsible for detecting the top quark at Fermilab in America. Contrary to popular perception, discovering a particle is not a eureka moment but a slow burn. But Franklin preferred it that way: ‘If it’s just “boom”, it would be a drag. You spend 15 years building the thing and boom, in one minute it’s over? It would be terrible.’ It probably took a year of gathering data from 1994 till the team felt confident enough in 1995 to confirm the discovery of this particle predicted by the mathematics.
Franklin is definitely on the experimental rather than theoretical side of the physics divide. Happier with a power drill in her hand than a pencil, she helped to build the detector at Fermilab from the bottom up.
We were both talking at the Rome Science Festival on the theme of the unknowable, so we agreed to meet in the lobby of the rather strange hotel we were staying in, which seemed to be dedicated to the sport of polo. Given that Franklin strides round the department in cowboy boots, I thought that perhaps she might feel more at home in this hotel covered in images of horses than I did.
However, she ended up making an extremely dramatic entrance, crashing to the bottom of the stairs into the lobby. Having dusted herself down, she strode over and sat down as if nothing had happened.
I was very keen to know if she thought quarks were the last layer or whether there might be more structure hiding beneath the particles she’d helped to discover.
‘We’re down to 10–18 metres. The next seven or eight orders of magnitude are kind of hard to investigate. But certainly a lot more could happen in there. It’s kind of strange that I could die before – especially if I keep falling down the stairs – I could die before we get any further.’
I wondered whether there might be fundamental limits to what we could know?
‘There are definitely limits in my lifetime but I’m not sure there are any other limits. In experimental physics, saying there’s no way we can do something is the perfect way to get someone to figure out how to do it. In my lifetime I’m never going to be able to measure something that decays in 10–22 seconds. I don’t think there’s any way. That’s not to say it’s provably unknowable.
‘We couldn’t have imagined the laser or the atomic clock, right? I think all the limitations in physics are going to be atomic because all the things we do are with atoms. I know that sounds weird but you need the atoms in your detector.’
But it’s intriguing how Einstein inferred the existence of atoms from looking at how they impacted on things you could see, such as pollen grains or coal dust. And today we know about quarks because of the way particles bounce off protons. So perhaps there will be ways to dig deeper.
‘I’m sure those guys like Heisenberg and Bohr couldn’t have imagined what we can detect today. I guess the same must apply to our generation … although of course we’re much smarter,’ she laughed.
And I guess that is the problem each generation faces. How can we ever know what cunning new method might be developed to dig that bit deeper into the fabric of the universe? But Franklin wondered how much we were missing that’s already there in the data coming out of the current generation of detectors.
‘Many young people in my field don’t believe it’s possible to find anything new that wasn’t predicted by theorists. That’s sad. If you found something and it wasn’t predicted by theory, then you’ll probably think it’s wrong and you’ll dismiss it, thinking it’s a fluctuation. I worry that because of the way our experiments are constructed you have these triggers that trigger on certain things, but only things you’re looking for and not other things. I wonder what we’re missing.’
I guess that was almost the fate of the pentaquark that CERN recently announced. It nearly got dismissed as noise. Given that I was writing a book about what we cannot know, Franklin was intrigued to know whether, if I could press a button and know it all, would I do so? As I was putting out my hand to press her hypothetical button, selling my soul to Mephistopheles to know the proofs of all the theorems I’m working on, she stopped me.
‘I wouldn’t.’
‘Why not?’
‘Because it’s not fun that way. There are certain things, like if I could push a button and speak perfect Italian, I would do it. But not with science. I think it’s because you can’t really understand it that way. You have to struggle with it somehow. You have to actually try and measure things and struggle to understand things.’
I was intrigued. Wouldn’t she press the button if she could know there were more particles sitting underneath the quarks?
‘If they just told me the method, then that would be great. But a lot of the reason we like doing science is coming up with the ideas in the first place. The struggle is more interesting. This whole pushing the button is really complicated.’
I think in the end Franklin likes making things, driving forklift trucks and drilling concrete in the search for new particles, not sitting at a desk thinking.
‘Experimentalists are a bit like cowboys in a way. Lasso that old thing over there and bring it over here. Don’t mind that boy over there sitting in the corner thinking about stuff.
‘When I turn 60, I’m going to be less judgemental and more open-minded. I’m going to stop being a cowboy … No, I don’t want to stop being a cowboy … I don’t know … It’s hard. Cowboys can be deep. When you’re wearing cowboy boots to work it’s kind of making a statement.’
And with that she mounted her taxi and rode off into the Rome sunset, continuing the scientific quest to know what else there is out there to lasso.
Are the quarks that Franklin helped discover the final frontier or might they one day divide into even smaller pieces, just as the atom broke into electrons, protons and neutrons, which in turn broke into quarks?
Many physicists feel that current experimental evidence, combined with the mathematical theory that underpins these experiments, has given us the answer to the question of what the true indivisible units are that built my dice. Just as the periodic table of 118 chemical elements could be reduced to different ways of putting together the three basic building blocks of the electron, proton and neutron, the hundreds of new particles found in the cosmic-ray collisions could be reduced to a simple collection of ingredients. The wild menagerie of particles had been tamed. But how sure am I that the gates might not open again to unleash more new beasts? The truth is that physicists don’t know if this is the last chapter in the story.
If you look at the symmetrical model underlying these particles, then the triangle corresponding to the quarks is the last indivisible layer describing the different physical representation of this object SU(3). The mathematics of symmetry suggests that we’ve reached rock bottom. That triangle corresponding to the quarks is the indivisible layer that builds all the other layers. So the mathematics of symmetry is trying to tell me I’ve hit the indivisible. And yet maybe we are falling into the same trap that Gell-Mann did when he first dismissed quarks because they’d have to have fractional charge. But there is another feature of quarks and electrons that provides some justification for believing they might not come apart: they don’t seem to occupy any space but behave as if they are concentrated at a single point.
In mathematics, geometry is made up of three-dimensional solids, two-dimensional planes, one-dimensional lines and zero-dimensional points. The strange thing is that these were meant to be abstract objects that didn’t have a physical reality in our three-dimensional universe. After all, what is a line? If you draw a line on a piece of paper and look at it under a microscope, you’ll see that the line actually has width. It isn’t really a line. In fact, it even has height, because the atoms that are sitting on the page are piling up to create a little ridge of lead (or whatever pencils are made of today) across the page.
Similarly, a point in space might be identified by its GPS coordinates, but you wouldn’t expect to have an object which is located solely at this point and nowhere else. You could never see it. Its dimensions are zero. And yet an electron behaves in many ways as if it is concentrated in a single point in space, as do the quarks inside the proton and neutron. The manner in which electrons scatter off one another and off the quarks inside protons and neutrons makes sense only if you create a model in which these particles all have no volume. Give them volume and the scattering would look different. If they truly are point particles, you wouldn’t expect them to come apart.
But what about the fact that electrons have mass? What is the density of an electron? That’s mass divided by volume. But the volume is zero. Divide by zero and the answer is infinite. Infinite? So is every electron actually creating a tiny black hole? We are firmly in the territory of the quantum world, because where a particle is located turns out not to be as easy a question to answer as one might expect, as I shall find out in the next Edge.
Have the discrete notes of my trumpet won out over the continuous glissando of the cello? It will be very difficult to know whether this story has reached its end. Atoms were regarded as indivisible because of the indivisible nature of the whole numbers that showed how they combine. And yet they eventually fell apart into the tiny pieces that make up our current ideas about the universe. Why shouldn’t I expect history to repeat itself with more surprises as I dig deeper and deeper? Why should there be a beginning, a first layer that made it all? It’s a classic problem of infinite regress that we shall meet over and over again. As the little old lady once retorted to a scientist’s attempt to mock her theory that the universe was supported on the back of a turtle: ‘You’re very clever, young man, very clever, but it’s turtles all the way down!’
Even if electrons and quarks are particles concentrated at a single point in space, there is no reason why a point can’t actually be pulled apart to be made of two points. Or perhaps there are hidden dimensions we have yet to interact with. This is the suggestion of string theory. These point particles in string theory are actually believed to be one-dimensional strings vibrating at resonant frequencies, with different frequencies giving rise to different particles. I seem to have come full circle and be back with Pythagoras’ model of the universe. Perhaps my cello does win out over the trumpet and the fundamental particles are really just vibrating strings.
If I am on the search for things we can never know, the question of what my dice is made from could well qualify. The story of what we do know about my dice is full of warnings. Will we ever find ourselves at the point at which there are no new layers of reality to reveal? Can we ever know that the latest theory will be the last theory?
But there may be another problem. The current theory of the very small – quantum physics – proposes that there are limits to knowledge built into the theory. As I try to divide my dice more and more, at some point I run up against a barrier beyond which I cannot pass, as my next Edge reveals.
