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The modern approach to fundamental physics, known as quantum field theory, does just this by supplementing the rules for how particles hop around with a new set of rules that explain how those particles interact with each other. These rules turn out to be no more complicated than the rules we’ve met so far, and it is one of the wonders of modern science that, despite the intricate complexity of the natural world, there are not many of them. ‘The eternal mystery of the world is its comprehensibility,’ Albert Einstein wrote, and ‘the fact that it is comprehensible is a miracle.’

Let’s start by articulating the rules of the first quantum field theory to be discovered – quantum electrodynamics, or QED. The origins of the theory can be traced all the way back to the 1920s, when Dirac in particular had an initial burst of success in quantizing Maxwell’s electromagnetic field. We’ve already met the quantum of the electromagnetic field many times in this book – it is the photon – but there were many problems associated with the new theory that were apparent but remained unsolved throughout the 1920s and 1930s. How exactly does an electron emit a photon when it moves between the energy levels in an atom, for example? And, for that matter, what happens to a photon when it is absorbed by an electron, allowing the electron to jump to a higher energy level in the first place? Photons can obviously be created and destroyed in atomic processes, and the means by which this happens is not addressed in the ‘old-fashioned’ quantum theory that we have met so far in this book.

In the history of science, there are a handful of legendary gatherings of scientists – meetings that certainly appear to have changed the course of science. They probably didn’t, in the sense that the participants had usually been working on problems for years, but the Shelter Island Conference of June 1947, held at the tip of Long Island, New York, has a better claim than most for catalysing something special. The participant list alone is worth reciting, because it is short and yet a role-call of the greats of twentieth-century American physics. In alphabetical order: Hans Bethe, David Bohm, Gregory Breit, Karl Darrow, Herman Feshbach, Richard Feynman, Hendrik Kramers, Willis Lamb, Duncan MacInnes, Robert Marshak, John von Neumann, Arnold Nordsieck, J. Robert Oppenheimer, Abraham Pais, Linus Pauling, Isidor Rabi, Bruno Rossi, Julian Schwinger, Robert Serber, Edward Teller, George Uhlenbeck, John Hasbrouck van Vleck, Victor Weisskopf and John Archibald Wheeler. The reader has met several of these names in this book already, and any student of physics probably has heard of most of them. The American writer Dave Barry once wrote: ‘If you had to identify, in one word, the reason why the human race has not achieved, and never will achieve, its full potential, that word would be meetings.’ This is doubtless true, but Shelter Island was an exception. The meeting began with a presentation of what has become known as the Lamb shift. Willis Lamb, using high-precision microwave techniques developed during the Second World War, found that the hydrogen spectrum was not, in fact, perfectly described by old-fashioned quantum theory. There was a minute shift in the observed energy levels that could not be accounted for using the theory we have developed so far in this book. It is a tiny effect, but it was a wonderful challenge to the assembled theorists.

We shall leave Shelter Island there, poised after Lamb’s talk, and turn to the theory that emerged in the months and years that followed. In doing so we will uncover the origin of the Lamb shift, but, to whet your appetite, here is a cryptic statement of the answer: the proton and electron are not alone inside the hydrogen atom.

QED is the theory that explains how electrically charged particles, like electrons, interact with each other and with particles of light (photons). It is single-handedly capable of explaining all natural phenomena with the exception of gravity and nuclear phenomena. We’ll turn our attention to nuclear phenomena