Forces of Nature

ANOTHER RULE GOVERNING THE BEHAVIOUR OF ELECTRONS IS THAT THEY DON’T MUCH LIKE EACH OTHER’S COMPANY. THIS IS KNOWN AS THE PAULI EXCLUSION PRINCIPLE.

One of the basic concepts in chemistry, which again goes all the way back to the fundamental laws of quantum theory, is that electrons can be shared between atoms. This results in the formation of a chemical bond. Two hydrogen atoms will share their single electrons with an oxygen atom if they can, pairing up to fill the two remaining outer slots around the oxygen nucleus; the result is a water molecule, which is shown in the top illustration. The reason for the 104.5-degree ‘kink’ is the presence of the other two pairs of electrons in the outer level of the oxygen atom. They take up residence on the opposite side of the oxygen atom to the hydrogen atoms, giving the water molecule its distinctive shape, and its many unusual properties.

The water molecule, like its constituent atoms, is electrically neutral, but the uneven distribution of electrons means that the hydrogen atom ‘legs’ have a very small net positive charge, whilst the oxygen end of things has a slight net negative charge. Water is known as a polar molecule for this reason – it has a negative end and a positive end. This opens up a world of complexity.

An important consequence of water’s polarity is that water molecules like to stick together. The negatively charged oxygen ends of water molecules attract the positively charged hydrogen ends of other water molecules and they attach together through what is known as a hydrogen bond. This happens to an extent in liquid water, resulting in quite large and complex structures.

The effects are even more dramatic when temperatures drop and water freezes to form ice. Water ice is very weird stuff. There are seventeen known forms of ice, the most common of which on Earth is called Ice 1

(the structure of which is shown in the lower illustration). The regular crystalline structure leads to one of water’s most bizarre properties: ice floats. This is very unusual behaviour. Every other commonly occurring solid is denser in the solid phase than in the liquid phase, and therefore does not float on its own liquid. The crystalline structure of ice, however, is so open that at atmospheric pressure and 0 degrees Celsius it is 8 per cent less dense than liquid water. This is why icebergs float on the oceans.

This is interesting, and it isn’t necessarily a trivial observation. It has been suggested that this unusual behaviour may have played a vital role in the evolution and persistence of life on Earth. If ice were denser than liquid water, sea ice would sink to the ocean floor. In such a scenario, particularly during Earth’s great glaciations, the lakes, seas and oceans of Earth could have frozen from the bottom up, perhaps becoming permanently solid. This would have had a dramatic impact on the ecosystems and food webs that rely on the bottom-dependent animal and plant life in fresh and seawater.

The complex structure of ice is a consequence of the laws of quantum theory, which are small in number and simple. By simple, we don’t mean to suggest that quantum theory is a simple thing to learn and apply; it isn’t. The mathematics can be technically difficult. Quantum theory is simple in the sense that it consists of a small number of mathematical rules that describe a wide range of natural phenomena of all sizes, from the structure of atoms and molecules to the nuclear reactions in the Sun. They also describe the action of real-world devices such as transistors and lasers and, more recently, exotic pieces of technology such as quantum computers.

A tremendous economy of description is one of the defining and most surprising features of modern science; it is not a priori obvious that a small collection of fundamental laws should be capable of describing the limitless complexity of objects that populate our Universe, and yet this is what we have discovered over the last few centuries. Perhaps a universe regular enough to permit the existence of natural objects as complex as the human brain must be governed by a simple set of laws, but since we do not yet understand the origin of the laws, we do not know. It is interesting that such complexity can emerge from underlying simplicity, however, and the humble water molecule is a good example. Its asymmetrical ‘kinked’ structure, which is ultimately responsible for the complex structure of ice, is a consequence of the laws of quantum theory, but these laws do not have ‘kinks’ built into them. Indeed, a physicist would say that the laws are possessed of a high degree of symmetry, as are the nuclei of hydrogen and oxygen; they form nicely spherical ‘nuclear boxes’ to trap the electrons. But bring them together and they form an asymmetrical structure.

The concept of symmetry is central to modern physics, and we’ll meet it throughout this book. For now, let us simply note that the asymmetric structure of the water molecule is a consequence of the way that electrons fit around the nucleus of an oxygen atom. It is because there are four available outer slots and six electrons to fill them that an asymmetric molecular structure results when two hydrogen atoms approach the oxygen, and that structure emerges spontaneously. Nobody had to design the water molecule and make an aesthetic choice about the 104.5-degree bond angle! It’s a consequence of, but not arbitrarily inserted into, the laws of quantum theory.

The properties of water are ultimately a result of the interactions between molecular building blocks. In turn, the properties of water molecules are a result of the interactions between their constituents – hydrogen and oxygen atoms. The properties of hydrogen and oxygen atoms are a result of the interactions between their constituents – protons, neutrons and electrons – and these interactions are governed by a simple set of rules. Is this infinite regression? How far can we go, digging deeper and deeper for more fundamental explanations for the properties of matter in general?

The fundamental building blocks and the forces of Nature (#ulink_44be4875-712c-593b-9cc6-85dd839d74dc)

It was twenty years ago today that I began my PhD. Today is 1 October 2015. Three years later I submitted my thesis ‘Double Diffraction Dissociation at Large Momentum Transfer’. I was interested in the behaviour of an object known as the Pomeron, named after the Russian physicist Isaak Pomeranchuk. I looked for it in the debris of high-energy collisions between electrons and protons, generated by a particle accelerator known as HERA. HERA is the wife of Zeus, and also the Hadron-Electron Ring Accelerator. The machine was 6.7 kilometres in circumference, located below the streets of northern Hamburg, which is a beautiful city in which to be a student. In the winter, the River Elbe freezes, but icebreakers clear a path to the port and the city feels proximate to the Baltic. In summer the small beaches that line the river beneath the old houses of Blankenese are busy and the city feels Mediterranean. In the early mornings at any time of year, a deracinated twenty-something from Oldham can be distracted on the Reeperbahn. It’s a remarkable thing that someone can spend three years looking at the fine detail of high-energy collisions between electrons and protons, hunting for a thing called a Pomeron.

Why was I interested in Pomerons? I was engaged in testing our best theory of one of the four fundamental forces of Nature. We’ve met one of these forces already – electromagnetism – which holds electrons in orbit around the atomic nucleus and water molecules together via hydrogen bonds. My investigations of the Pomeron were concerned with exploring another of the four – the strong nuclear force. The need for such a force is clear if you think about our description of the oxygen nucleus. It is a tightly knit ball of eight positively charged protons and eight uncharged neutrons. One of the fundamental properties of the electromagnetic force is that like-electrical charges repel each other; in which case, why doesn’t the atomic nucleus blow itself apart? The answer is that the strong nuclear force sticks the nucleus together, and it is far stronger than the electromagnetic repulsion between the protons.

Protons are small, but they make up just over half of you by mass. Most of the rest of you is made of neutrons. There are around twenty thousand million million million million protons in the average human being. In scientific notation, that’s 2 x 10

, which means 2 followed by 28 zeros. You are pretty simple at this level.

When you look deeper into the heart of the protons and neutrons themselves, things appear to get more complicated. Protons are small by everyday standards, but it is well within our current scientific and engineering capabilities to measure their size and look inside them. This is what HERA was designed to do. The machine was a giant electron microscope, peering deep into the heart of matter. You have to define what is meant by size carefully, because a proton doesn’t have a hard edge to it, but recent measurements put its radius at just over 0.8 femtometres, which is just under 10

m – a thousand million millionths of a metre.

The neutral current DIS process via photon exchange.

F

(x, Q

) as measured at HERA, and in fixed target experiments, as a function of Q

(a) and x (b). The curves are a phenomenological fit performed by H1 [26]. c (x) is an arbitrary vertical displacement added to each point in (a) for visual clarity, where c(x) = 0.6(n – 0.4), n is the x bin number such that n = 1 for x = 0.13.

Because I’m getting old and sentimental, but also in service of the narrative, I’ve indulged myself and included two plots from the thesis I wrote in Hamburg twenty years ago. After all, this was my snowflake. The first one shows a drawing I made using a 1990s UNIX computer program called xfig (see illustration here (#ulink_92465fda-cb3f-5320-b879-aead8e3d43b0)). Happy days. It shows an electron colliding with a proton. The language of modern physics is superficially opaque, as evidenced by the caption of my thesis figure, but the language isn’t designed to make physicists appear clever. To be honest, I never thought a non-physicist would read it. Every word is necessary and means something. George Orwell would approve. ‘A man may take to drink because he feels himself to be a failure, and then fail all the more completely because he drinks. It is rather the same thing that is happening to the English language. It becomes ugly and inaccurate because our thoughts are foolish, but the slovenliness of our language makes it easier for us to have foolish thoughts.’

Physics is about precision of thought, which is aided and evidenced by precision of language.

Here is the meaning of the caption. Neutral current means that the electron bounces off the proton by exchanging an electrically neutral object with it – in this case, a photon; a particle of light. The photon is shown in the diagram as the wavy line, labelled by the Greek letter γ. DIS stands for ‘Deep Inelastic Scattering’, which means that the photon is hitting something deep inside the proton, resulting in the proton being broken into pieces. This is how a modern particle physicist would describe the interaction between any two particles; interactions involve the ‘exchange’ of some other particle that carries the force. In this case, the force is electromagnetism and the force-carrying particle is a photon. The most fundamental description of the mechanism by which water molecules stick together to form ice is that photons are being emitted and absorbed by electrons in the water molecules, with the net result that water molecules stick together.

There is another way of thinking about this electron–proton collision. You can imagine the photon emitted from the electron smashing into the proton and revealing its inner structure. That structure is shown in the second figure from my thesis, shown opposite.

Allow me a single paragraph of postgraduate-level physics. I want to take this liberty for two reasons. The first is that there is great joy to be had in understanding a complex idea, and in doing so glimpsing the underlying simplicity and beauty of Nature. The biologist Edward O. Wilson coined the term ‘Ionian Enchantment’ for this feeling, named after Thales of Miletus, credited by Aristotle as laying the foundations for the physical sciences in 600 BC on the Greek island of Ionia. The feeling is one of elation when something about Nature is understood, and seen to be elegant. The second reason is to revisit and enhance an idea we’ve been developing. Science is all about making careful observations and trying to explain what you see. That might be the hexagonal structure of a beehive, the jagged symmetry of a snowflake, or the details of how electrons bounce off protons. Careful observations lead to Ionian Enchantment.

At HERA, we measured the angle and energy of the electrons after they hit the protons. This is a simple thing to do, and it allowed us to build up a picture of what the electron ‘bounced off’ – the fizzing heart of matter. Two different ways of visualising the inside of a proton are shown in the figure. The thing called F

(x,Q²) is known as the proton structure function. Now for the precise bit of observation that requires thought. Have a look at illustration (a) here (#ulink_a1755b70-6b80-5802-b9b5-e57032137dd7) and focus on the bottom line of the graph labelled x = 0.13. The points along this line tell you the probability that an electron will bounce off something inside the proton that is carrying 13 per cent of the proton’s momentum – this is what x = 0.13 means. The quantity Q² is known as the virtuality of the photon that smashes into the proton. One way to think about this quantity is as the resolving power of the photon. High Q² corresponds to short wavelength, which means that high Q² photons can see smaller details. The x = 0.13 line is pretty flat, which means that whatever the photon is bouncing off, it behaves as if it has no discernable size. This is because what we see does not change as we crank up the resolving power of the microscope (which corresponds to going to higher Q²), and this is what would happen if the photon were scattering off tiny dots of matter inside the proton. The dot is known as a quark, and as far as we can tell, it is one of the fundamental building blocks of the Universe. Together, these two plots describe in detail the innards of the proton as revealed by years of experimental study by many hundreds of scientists at the HERA accelerator.

The proton is a seething, shifting mass of dot-like constituents, continually evolving around scaffolding. The scaffolding consists of three quarks; two ‘up’ quarks and one ‘down’ quark. The quarks are bound together by the strong nuclear force, which is carried by particles called gluons in much the same way that the electromagnetic force is carried by photons. Unlike photons, however, the gluons can interact with each other through the exchange of more gluons, and that results in the proton having an increasingly complex structure as we dial up the resolving power. Illustration (b) shows this behaviour; the rising curves towards smaller x are telling us that there is a proliferation of gluons, each carrying very small fractions of the proton’s momentum. Illustration (a) also shows this. The lines are not flat at smaller x. In the jargon, this behaviour is known as ‘scaling violation’, which means that as we dial up the resolving power the dot-like constituents appear to be increasingly numerous. In other words, at low resolving power we tend to resolve only the scaffolding, i.e. the three quarks, while at high resolving power the full glory of the proton’s gluonic structure is revealed to us. Roughly speaking, gluons carry around half of the momentum of a proton, because there are so many of them buzzing around between the quarks. The lines on these graphs, which go pretty much through the data points, are calculated using our best theory of the strong nuclear force: Quantum Chromodynamics, or QCD. QCD is a set of rules that specifies the probability that a quark will emit a gluon, and also how gluons interact with other quarks and gluons. It’s a quantum theory – the same basic framework we referred to when we discussed the structure of the water molecule. When we are dealing with electric charges – for example, the interactions between electrons and the atomic nucleus – we use our quantum theory of electromagnetism called Quantum Electrodynamics, or QED.

I remember writing computer programs to skim through vast amounts of data about individual electron-proton collisions and make figures like the one above. On the computers we had in the 1990s these programs took days to run. Even now, looking at these plots, I find it exhilarating to consider that I’m looking at the structure of an object a thousand million millionths of a metre in size, measured using a machine 6.7 kilometres in circumference beneath the city of Hamburg, and that we have a theory that allows us to understand and describe what we see. Industrial engineering and subatomic beauty in concert. The Ionian Enchantment.

On the next page you will find a snapshot of the deep structure of ordinary matter. You are this, at the level of accuracy we can measure today. Two sorts of quarks, stuck together by gluons, to make protons and neutrons that are stuck together by more gluons to make atomic nuclei. Electrons are stuck in orbit around the nuclei by photons to make atoms and atoms stick together by exchanging photons between their electrons to make molecules. And so it goes! This simple picture is the result of a hundred years of experimental and theoretical investigation. The structure of everything can be explained using a set of building blocks and some rules. We’ve met three of the building blocks; up quarks, down quarks and electrons. We’ve also met two forces; the strong nuclear force and the electromagnetic force. There is another force called the weak nuclear force that can convert up quarks into down quarks, with the simultaneous emission of another sort of particle called the electron-neutrino. In total that makes four matter particles. The weak force is carried by particles known as the W and Z bosons. There is also the Higgs boson, discovered in 2012 at the Large Hadron Collider (LHC) at CERN, in Geneva, which gives the building blocks their mass.

The fourth and final fundamental force is the most familiar – gravity. It is so weak that its effects on the subatomic world are invisible even in our most high-precision experiments, like those at HERA. If this statement seems a little mystifying, particularly if you’ve ever fallen off a ladder, then park it in your memory for a while; we’ll get back to gravity later when we discuss the shape of planets and galaxies.

These four particles, four forces and the Higgs boson appear to be all that is needed to make a water molecule, a honeybee, a human being, or planet Earth. This is a dazzlingly elegant and simple structure. For some reason, Nature didn’t adopt this economical scheme but instead made two further copies of the family of up quarks, down quarks, electrons and electron neutrinos. These two extra families are identical to the first family in every way except that they are more massive, possibly because they interact with Higgs particles in a different way. The existence of the three families of particle is another of the great mysteries, and discovering why Nature appears to have been unduly profligate is one of the most important goals of twenty-first-century particle physics. She won’t have been unduly profligate, of course! We know that three families is the minimum number to accommodate a process known as CP violation, which is needed to explain why, if the Universe started out with equal amounts of matter and anti-matter, there is matter left over in the Universe today to make stars and people. But that’s not an answer to the ‘Why?’ question, and it would be nice to know if the existence of planets, stars and galaxies is down to more than blind luck.

With these extra families, there are twelve fundamental particles of matter, four different sorts of force-carrying particle and the Higgs particle. That’s it, as far as we know – although I wouldn’t be surprised if some more pop up at the Large Hadron Collider over the next few years. This is fuelled by the fact that we already have good evidence from many independent astronomical observations that there is another form of matter in the Universe known as dark matter. There is five times more dark matter than ‘normal’ matter in the Universe by mass, and the dark matter cannot be made up out of the twelve particles that we’ve seen in experiments at particle accelerators such as HERA or the LHC. The collection of fundamental building blocks, circa 2015, is shown in the illustration below.

The fundamental building blocks of the natural world, and three of the four fundamental forces of Nature: the strong nuclear force, carried by gluons; the weak nuclear force, carried by W and Z bosons; and the electromagnetic force, carried by photons.

This isn’t intended to be a complete course on particle physics, much as I’d like to deliver that; rather, it is a chapter about shapes and patterns in Nature and what they reveal about the way in which the Universe works. Having said that, if you’ll allow me one last foray into particle physics, the story of the discovery of the quarks inside the proton and neutron is a very beautiful example of the way physicists notice patterns and attempt to explain them. The remarkable thing is that quarks were predicted before they were discovered experimentally.

The theoretical prediction that building blocks exist beneath the level of protons and neutrons was made by Murray Gell-Mann and George Zweig in 1964. It was based on a pattern in the subatomic particles known at the time. By the early 1960s, an inelegant, profligate and seemingly ever-expanding list of subatomic building blocks had been discovered. The proton and neutron are part of a whole family of particles known as baryons; there are Lambdas, Sigmas, Deltas, Cascades and a host of others. There is also a family of particles known as mesons: Pions, Kaons, Rho and so on. There are thirteen different types of Lambda particle alone, nine Sigmas and eight Kaons. Particle physics was looking increasingly like a subatomic branch of botany. Then Gell-Mann and Zweig noticed a beautiful pattern. The particles could be arranged according to their observed properties in geometrical patterns. One such pattern is shown in the illustration here (#ulink_5cbad056-b7d5-5a4f-86cb-835cff7fc494). Today, these are known as ‘super-multiplets’.

As Kepler suspected when he considered the six-fold symmetry of snowflakes, patterns in Nature are often a clue that there is a deeper underlying structure. The patterns may or may not be easy to recognise – Gell-Mann received the Nobel Prize in Physics in 1969 for noticing the pattern amongst the particles – but they are the Rosetta Stone that allows Nature’s language to be deciphered. In this case, the pattern in the particles suggested to Gell-Mann and Zweig that the baryons are all constructed out of three smaller building blocks, that Gell-Mann called quarks. When they first recognised the pattern, they included three quarks in their scheme: up, down and strange. The different baryons on the lower planes of the super-multiplets are the possible three-fold combinations of the three building blocks. Adding a fourth quark – charm – constructs the higher layers. The quark constituents of the particles are shown in the illustration opposite: for example the ∆

contains three up quarks.

A baryon ‘super-multiplet’ showing the quark content of each baryon.

The particle on the base of the pyramid in the illustration, known as the Omega-minus, is of particular historical interest because its existence was predicted by Gell-Mann at a meeting at CERN in 1962, based solely on the pattern of the base of the pyramid. It was subsequently discovered at the Brookhaven National Laboratory in the United States in 1964. When a theory predicts the existence of something new that is subsequently discovered, we can have particular confidence that we are on the right track.

We’ve met three of the four fundamental forces of Nature; the strong and weak nuclear forces and electromagnetism, and the twelve building blocks of Nature. We will now turn to the final, weakest and most familiar force – gravity – and investigate it by thinking about the size and shape of the objects it sculpts. These are not tiny things like subatomic particles, or small things like snowflakes, but very much larger structures: planets, stars and galaxies.

Why is the Earth a sphere? (#ulink_391163dd-a029-5190-a66d-2064ac7fbb0d)

There is a photograph of our planet known as the Blue Marble. It was taken on 7 December 1972 by the crew of Apollo 17 during their journey to the Moon. Close to the winter solstice, Antarctica is a continent of permanent light, and Madagascar, the island of lemurs, takes centre stage. Ochre deserts set against blue oceans, green hues hinting at life.

On 5 December 2012, NASA released the Black Marble, an image of the Americas at night. Now we see a civilisation on the planet; the lights herald the dawn of the Anthropocene – the age of human dominance. What do we see in these images? What is the most basic property of Earth? Alexei Leonov, on completing the first human spacewalk on 18 March 1965, had an answer.

‘I never knew what the word round meant until I saw Earth from space.’

Alexei Leonov, Voskhod 2, Soyuz 19/ASTP

Seen from space, the Earth is a near-perfect sphere. All the planets in the Solar System, all the large moons and the Sun itself share this property, as does every star in the Universe. Why? If lots of different objects share a common feature, there must be an explanation. To make progress, let’s think about what could affect the shape of a planet, moon or star. It can’t be much to do with their composition because planets are made of different stuff to stars. The Earth is made up of heavy chemical elements such as iron, oxygen, silicon and carbon. The Sun, on the other hand, is primarily hydrogen and helium; it’s a giant ball of plasma with no solid surface. Giant planets such as Jupiter have more in common with stars than with Earth, at least in terms of their composition. They too are primarily composed of hydrogen and helium. Stars and planets are united, however, by the force that formed them and holds them together – gravity. So to understand why they are all spherical, we should explore the nature of the gravitational force further.