Back in the Cavendish Laboratory in Cambridge, Wilson set out to reproduce the atmospheric effects that had created the illusion. The culmination of this research was the cloud chamber, an instrument that would show the tracks of charge particles passing through it. This device would play a vital role in the discovery of the electron by Wilson’s boss, the director of the Cavendish Laboratory J. J. Thomson.
The cloud chamber also had an important part to play in the career of another Cambridge physicist Paul Dirac, one of the great theoretical physicists of the 20^{th} century. Dirac had an intuitive feeling that the correct description of fundamental physics must be simple and elegant. Symmetry lay at the heart of his mathematics, which always had a beautiful austerity. When Dirac was asked to summarise his philosophy of physics, he wrote a single sentence on the blackboard:
PHYSICAL LAWS SHOULD HAVE MATHEMATICAL BEAUTY
One night in 1928 Dirac sat in his room in St John’s College staring into the fire. As he let his mind drift amidst the flames, he was struck by the idea that would enable him to construct an equation of a completely novel kind. He could see at once that his new approach was going to work. The equation describes the evolution of matter waves, such as electron waves, even when their speed approaches the speed of light. Dirac’s analysis of his equation persuaded him that there was a previously unsuspected symmetry at the heart of matter. The equation only made sense if the electron had a mirror image particle. A particle whose mass was the same as the mass of the electron, but whose electric charge was positive instead of negative. Just four year’s later the particle was found by an American physicist Carl Anderson who had constructed a cloud chamber in which he could study the tracks left by cosmic rays. We know this particle, the antiparticle of the electron, as the positron.
But Dirac’s equation describes the behaviour of all the different types of particles from which matter is formed. So it follows that there must also be a mirror image particle for other particles, such as the proton and the neutron. This is indeed the case. The antiproton was found in 1955 and the antineutron in 1956. These antiparticles will combine to form antimatter in the same way that ordinary particles combine to form matter. For example, a positron will bind to an antiproton to form an atom of antihydrogen. These antiatoms are now being actively studied in the laboratory at CERN.
Dirac’s interpretation of his equation offered a deep insight into electromagnetic interactions at the level of fundamental particles. According to Dirac, when an electron and a positron meet they can mutually annihilate and disappear in a burst of high energy gamma ray photons. Conversely, it is possible for a gamma ray photon to convert into an electron and a positron. This was a completely new idea. Matter was not eternal, it could be created or destroyed. Dirac had been led to formulate his equation by the desire to make quantum mechanics compatible with Einstein’s relativity. And now the interconvertibility of matter and radiation that Dirac had deduced from his equation gave a new significance to the most famous equation that Einstein had derived from his theory:
E = mc˛ .
This equation sums up the equivalence of mass and energy in a statement that is simple enough to be used as a slogan on a teeshirt. Dirac had now shown how the conversion of mass into energy and energy into mass worked at the level of particle interactions.
Dirac had taken the first step towards a quantum theory of electromagnetism. In the pictures drawn by Michael Faraday a charged particle such as an electron is surrounded by an electric field that permeates the whole of space. This is just a map of the electric force around the electron. In the new quantum picture of Faraday’s electric and magnetic fields, the fields are not continuous throughout space, they are composed of photons. The electron is bathed in a fluctuating cloud of photons that it is continually emitting and reabsorbing. This cloud of photons, which corresponds to Faraday’s electromagnetic field, is responsible for producing the electromagnetic force between charged particles. The way this works is that a photon that has been emitted by one electron might be absorbed by a second nearby electron. The photon has no way of recognizing its parent electron from any other electron so this process will inevitably happen to some of the photons in the cloud. The emission of the photon gives a kick to the first electron and its absorption gives an oppositely directed kick to the second electron. In this way the exchanged photon has transferred some of the energy and momentum of the first electron to the second electron. The trajectory of both electrons will be altered. This is the way that forces operate in quantum theory. They are due to the interaction of individual particles. The electromagnetic force is a consequence of the exchange of photons between charged particles.
This is a nice picture, but physicists need to be able to perform calculations in order to test a theory against experimental results. Unfortunately, there were serious technical difficulties in performing these calculations that would not be ironed out until after the Second World War. Several theorists contributed to the resolution of these difficulties, but the most elegant methods were found by a charismatic New Yorker called Richard Feynman. He was a great puzzle solver, who couldn’t sleep when introduced to a new puzzle until he had it cracked. Feynman liked to think visually and while playing with the equations of quantum electrodynamics (QED) he developed a pictorial shorthand to help him keep track of all the terms in the horrendously complicated equations. Each diagram was a kind of glyph that represented a mathematical expression, where each part of the diagram corresponded to a mathematical term that formed part of the expression. Feynman devised a recipe that allowed him to translate back and forth between the mathematical expressions that cropped up in QED calculations and his diagrams. This was very useful, because it is much easier to remember the structure of a simple diagram than the exact form of a complicated mathematical expression. But Feynman soon realised that his diagrams were much more than simply mnemonics. Not only did each picture represent a mathematical expression, it also appeared to depict a physical process – a type of particle interaction.
The first diagram that Feynman published in 1948 is shown below. It depicts an interaction between two electrons that is mediated by the exchange of a photon between them. The two electrons are represented by lines with arrows on them and the photon is represented by the wavy line. Time runs upwards in the diagram, which shows the two electrons approach each other, exchange a photon and then retreat from each other.
