Forces of Nature. Andrew Cohen

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

      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 here). 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