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 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) here 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
