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and branching rules and it is remarkable for being the only way to build a quantum theory of tiny particles that also respects the Theory of Special Relativity. Armed with the apparatus of QFT, the hopping and branching rules are fixed and we lose the freedom to choose. This is a very important result for those in pursuit of fundamental laws because using ‘symmetry’ to remove choice creates the impression that the Universe simply has to be ‘like this’ and that feels like progress in understanding. We used the word ‘symmetry’ here and it is appropriate, because Einstein’s theories can be viewed as imposing symmetry restrictions on the structure of space and time. Other ‘symmetries’ further constrain the hopping and branching rules, and we shall briefly encounter those in the next chapter.

Before leaving QED, we have a final loose end to tie up. If you recall, the opening talk of the Shelter Island meeting concerned the Lamb shift, an anomaly in the hydrogen spectrum that could not be explained by the quantum theory of Heisenberg and Schrödinger. Within a week of the meeting, Hans Bethe produced a first, approximate, calculation of the answer. Figure 10.5 illustrates the QED way to picture a hydrogen atom. The electromagnetic interaction that keeps the proton and the electron bound together can be represented by a series of Feynman diagrams of increasing complexity, just as we saw for the case of two electrons interacting together in Figure 10.1. We’ve sketched two of the simplest possible diagrams in Figure 10.5. Pre-QED, the calculations of the electron energy levels included only the top diagram in the figure, which captures the physics of an electron that is trapped within the potential well generated by the proton. But, as we’ve discovered, there are many other things that can happen during the interaction. The second diagram in Figure 10.5 shows the photon briefly fluctuating into an electron–positron pair, and this process must also be included in a calculation of the possible energy levels of the electron. This, and many other diagrams, enter the calculation as small corrections to the main result.6 Bethe correctly included the important effects from ‘one-loop’ diagrams, like that in the figure, and found that they slightly shift the energy levels and therefore the detail in the observed spectrum of light. His result was in accord with Lamb’s measurement. QED, in other words, forces us to imagine a hydrogen atom as a fizzing cacophony of subatomic particles popping in and out of existence. The Lamb shift was humankind’s first direct encounter with these ethereal quantum fluctuations.

Figure 10.5. The hydrogen atom.

It did not take long for two other Shelter Island attendees, Richard Feynman and Julian Schwinger, to pick up the baton and, within a couple of years, QED had been developed into the theory we know today – the prototypical quantum field theory and exemplar for the soon-to-be-discovered theories describing the weak and strong interactions. For their efforts, Feynman, Schwinger and the Japanese physicist Sin-Itiro Tomonaga received the 1965 Nobel Prize ‘for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles’. It is to those deep-ploughing consequences that we now turn.

11. Empty Space Isn’t Empty

Not everything in the world stems from the interactions between electrically charged particles. QED does not explain the ‘strong nuclear’ processes that bind quarks together inside protons and neutrons or the ‘weak nuclear’ processes that keep our Sun burning. We can’t write a book about the quantum theory of Nature and leave out half of the fundamental forces, so this chapter will make right our omission before delving into empty space itself. As we’ll discover, the vacuum is an interesting place, filled with possibilities and obstacles for particles to navigate.

The first thing to emphasize is that the weak and strong nuclear forces are described by exactly the same quantum field theoretic approach that we have described for