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The first evidence of new particles was found in the cloud chambers that experimenters had built in their labs to record the paths of charged particles. Cloud chambers consist of a sealed tank full of a supersaturated vapour of water and alcohol. The supersaturation is such that any charged particle passing through leaves a trail of condensation behind it.

Carl Anderson, a physicist working at Caltech, had used these cloud chambers in 1933 to confirm the existence of a strange new sort of matter called antimatter that had been predicted some years earlier by British physicist Paul Dirac. Dirac’s attempt to unify quantum physics and the theory of electromagnetism had successfully explained many things about electrons, but the equations seemed to have a complete mirror solution that didn’t correspond to anything anyone had seen in the lab.

Dirac’s equations were a bit like the equation x² = 4. There is the solution x = 2, but there is another mirror solution, namely x = –2, because –2 × –2 is also equal to 4. The mirror solution in Dirac’s equations implied that there was a mirror version of the electron with positive charge. Most thought this was a mathematical curiosity that emerged from the equations, but when, four years later, Anderson spotted in his cloud chamber traces of a particle behaving like an electron in a mirror, antimatter went from theory to reality. Anderson’s positrons, as they came to be known, had been created in the particle interactions happening in the upper atmosphere. And they weren’t the only new things to appear.

Even stranger particles that had not been predicted at all were soon leaving trails in Anderson’s cloud chamber. Anderson started to analyse these new paths with his PhD student Seth Neddermeyer in 1936. The new particles corresponded to negatively charged particles passing through the cloud chamber. But they weren’t electrons. The paths these new particles were leaving indicated a mass much larger than that of the electron. Just as Thomson had done, mass can be measured by how much the particle is deflected under the influence of a magnetic field. The particle seemed to have the same charge as the electron but was much harder to deflect.

Now called the muon, it was one of the first new particles to be discovered in the interactions of cosmic rays with the atmosphere. The muon is unstable. It quickly falls apart into other particles, most often an electron and a couple of neutrinos. Neutrinos were another new particle that had been predicted to explain how neutrons decayed into protons. With almost no mass and no charge, it took until the 1950s before anyone actually detected these tiny particles, but they theoretically made sense of both neutron decay and the decay of this new muon. The decay rate of the muon was on average 2.2 microseconds, which is sufficiently slow that enough particles won’t have decayed by the time they reach the surface of the Earth.

The muon helped to confirm Einstein’s prediction from special relativity that time slows down as you approach the speed of light. Given its half-life, far fewer muons should be reaching the surface of the Earth than were being detected. The fact that time slows down close to the speed of light helps explain this discrepancy. If a clock was attached to the muon, it would show that a smaller interval of time had elapsed before it hit the Earth. Thus more muons would therefore survive, as revealed by experiment. I will return to this in the Fifth Edge when I consider pushing time to the limits of knowledge.

The muon appeared to behave remarkably like the electron but had greater mass and was more unstable. When the American physicist Isidor Rabi was told of the discovery, he quipped: ‘Who ordered that?’ It seemed strangely unnecessary for nature to reproduce a heavier, more unstable version of the electron. Little did Rabi realize how much more there was on the menu of particles.

Having realized that cosmic ray interactions with the upper atmosphere were creating new forms of matter, physicists decided that they better not wait for the particles to reach the cloud chambers in the labs, by which time the particles might have decayed into traditional forms of matter. So the cloud chambers were moved to high-altitude locations in the hope of picking up other particles.

The Caltech team chose the top of Mount Wilson near their home base in Pasadena. Sure enough, new tracks indicated that new particles were being picked up. Other teams placed photographic plates in observatories in the Pyrenees and the Andes to see if they could record different interactions. Teams in Bristol and Manchester also saw traces of new particles in their own photographic plates. It turned out that the muon was the least of Rabi’s worries. A whole menagerie of new particles started showing up.

Some had masses about one-eighth that of a proton or neutron. They came in positively or negatively charged varieties and were dubbed pions. An electrically neutral version that was harder to detect was later discovered. In Manchester two photographs from their cloud chamber showed what appeared to be a neutral particle decaying into pions. The mass of these new particles was roughly half that of a proton. The cloud chamber at the top of Mount Wilson recorded more evidence to support the discovery of what would become known as kaons, four in number.

As time went on, more and more particles were uncovered, so much so that the whole thing became totally unwieldy. As Nobel Prize winner Willis Lamb quipped in his acceptance speech of 1955: ‘The finder of a new elementary particle used to be rewarded by a Nobel Prize, but such a discovery now ought to be punished by a $10,000 fine.’ The hope was that the periodic table would be simplified once scientists had discovered how it was put together using electrons, protons and neutrons. But these three particles turned out to be just the tip of the iceberg. Now there were over a hundred particles that seemed to make up the building blocks of matter. As Enrico Fermi admitted to a student at the time: ‘Young man, if I could remember the name of these particles, I would have been a botanist.’

Just as Mendeleev had managed to find some sort of order with which to classify and make sense of the atoms in the periodic table, the search was on for a unifying principle that would explain these new muons, pions, kaons and other particles.

The underlying structure that finally seemed to make sense of this menagerie of particles – the map, as it were, to find your way around the zoo – ultimately came down to a piece of mathematics.