Forces of Nature

by Professor Brian Cox

  The regular crystalline structure leads to one of water’s most bizarre properties: ice floats ... 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 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 1h (the structure of which is shown in the lower illustration opposite). 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.

  Because solid H2O – ice – is less dense than its liquid form, even in the most compressed forms of ice like glacial ice, where most of the air bubbles have been squeezed out, this huge solid will still float in its own liquid form.

  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.

  In Antarctica, Emperor penguins exploit the fact that ice is less dense than liquid water, diving and swimming underneath icebergs.

  Quantum theory is simple in the sense that it consists of a concise set 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.

  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?

  HERA (Hadron-Electron Ring Accelerator) under construction in 1983. I worked with HERA in the 1990s to uncover the behaviour of the Pomeron as part of my thesis.

  The fundamental building blocks and the forces of Nature

  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 1028, 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 10-15 m – a thousand million millionths of a metre.4

  The neutral current DIS process via photon exchange.

  F2 (x, Q2) as measured at HERA, and in fixed target experiments, as a function of Q2 (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). 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’.5 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 F2 (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) opposite 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) on here 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.

  The 6.7km-long tunnel of the HERA collider in Hamburg. The machine is a giant electron microscope that is designed to allow us to look inside Pomerons and measure their size.

  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.