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Dealing with particles ‘of no size’ sounds problematic, and perhaps impossible. But nothing we said in the previous chapters presupposed or required that particles have any physical extent. The notion of truly point-like objects need not be wrong, even if it flies in the face of common sense – if indeed the reader has any common sense left at this stage of a book on quantum theory. It is, of course, entirely possible that a future experiment, perhaps even the Large Hadron Collider, will reveal that electrons and quarks are not infinitesimal points, but for now this is not mandated by experiment and there is no place for ‘size’ in the fundamental equations of particle physics. That’s not to say that point particles don’t have their problems – the idea of a finite charge compressed into an infinitely small volume is a thorny one – but so far the theoretical pitfalls have been circumvented. Perhaps the outstanding problem in fundamental physics, the development of a quantum theory of gravity, hints at finite extent, but the evidence is just not there to force physicists to abandon the idea of elementary particles. To be emphatic: point-like particles are really of no size and to ask ‘What happens if I split an electron in half?’ makes no sense at all – there is no meaning to the idea of ‘half an electron’.

A pleasing bonus of working with elementary fragments of matter that have no size at all is that we don’t have any trouble with the idea that the entire visible Universe was once compressed into a volume the size of a grapefruit, or even a pin-head. Mind-boggling though that may seem – it’s hard enough to imagine compressing a mountain to the size of a pea, never mind a star, a galaxy, or the 350 billion large galaxies in the observable Universe – there is absolutely no reason why this shouldn’t be possible. Indeed, present-day theories of the origins of structure in the Universe deal directly with its properties when it was in such an astronomically dense state. Such theories, whilst outlandish, have a good deal of observational evidence in their favour. In the final chapter we will meet objects with densities, if not at the ‘Universe in a pin-head’ scale, then certainly in ‘mountain in a pea’ territory: white dwarves are objects with the mass of a star squashed to the size of the Earth, and neutron stars have similar masses condensed into perfect, city-sized spheres. These objects are not science fiction; astronomers have observed them and made high-precision measurements of them, and quantum theory will allow us to calculate their properties and compare them with the observational data. As a first step on the road to understanding white dwarves and neutron stars, we will need to address the more prosaic question with which we began this chapter: if the floor is largely empty space, why do we not fall through it?

This question has a long and venerable history, and the answer was not established until surprisingly recently, in 1967, in a paper by Freeman Dyson and Andrew Lenard. They embarked on the quest because a colleague had offered a bottle of vintage champagne to anyone who could prove that matter shouldn’t simply collapse in on itself. Dyson referred to the proof as extraordinarily complicated, difficult and opaque, but what they showed was that matter can only be stable if electrons obey something called the Pauli Exclusion Principle, one of the most fascinating facets of our quantum universe.

We shall begin with some numerology. We saw in the last chapter that the structure of the simplest atom, hydrogen, can be understood by searching for the allowed quantum waves that fit inside the proton’s potential well. This allowed us to understand, at least qualitatively, the distinctive spectrum of the light emitted from hydrogen atoms. If we had had the time, we could have calculated the energy levels in a hydrogen atom. Every undergraduate physics student performs this calculation at some stage in their studies and it works beautifully, agreeing