What We Cannot Know: Explorations at the Edge of Knowledge. Marcus Sautoy du

      Alpha particles being deflected by the nuclei of atoms of gold.

      Geiger found that, on the contrary, some of the alpha particles were deflected wildly, to the extent that some bounced back off the gold foil in the direction they’d been fired from. Rutherford was staggered: ‘It was as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.’

      Again it was mathematical calculations that gave rise to a new model. By counting how many alpha particles were deflected, and by how much, they discovered that the data was consistent with the charge and mass being concentrated in a tiny centre of the atom, which became known as the nucleus. It still wasn’t clear whether this nucleus was indivisible or not.

      When Rutherford bombarded lighter atoms with alpha particles evidence emerged that the nucleus wasn’t a single entity but made up of constituent particles. Tracing the paths of the alpha particles in a cloud chamber, he detected paths that were four times longer than they should be. It was as if another particle four times as light was being kicked out of the nucleus by the impact of the alpha particles. Different gases produced the same result. Indeed, Rutherford found that pure nitrogen was being converted into oxygen by the impact. Knock out one of these particles and the element changed.

      Here was evidence for a building block from which all nuclei of atoms were built. It behaved just like the hydrogen atom with its electron stripped off. Rutherford had discovered the proton. The nuclei of atoms were built by taking multiples of this proton. The only trouble was that the charge on the atom didn’t make sense. Helium had a nucleus that was four times as heavy as the hydrogen atom, yet the charge was only twice as big. Perhaps there were electrons in the nuclei attached to protons, cancelling out the charge. But the physics being developed to explain the behaviour of these particles precluded electrons and protons in such close proximity, so that couldn’t be the answer.

      This led Rutherford in the 1920s to guess that there might be a third constituent, which he called a neutron, with the same ball-park mass as the proton but no charge. Producing evidence for this particle proved very tricky. He used to discuss with his colleague James Chadwick crazy ways by which they might reveal the neutron. Experiments conducted in the 1930s in Germany and France eventually picked up particles being emitted when various nuclei were bombarded with alpha particles, and, unlike the proton, these particles did not seem to possess any charge. But the experimenters mistakenly believed it was some sort of electromagnetic radiation, like the high-frequency gamma rays that had been discovered by French physicist Paul Villard at the beginning of the century.

      Chadwick, though, was convinced that these particles must be the neutrons he’d discussed with Rutherford. Further experiments revealed that they had mass just slightly bigger than the proton, and without charge this new particle was the missing ingredient that made sense of the numbers. With Chadwick’s discovery it seemed as if the building blocks of matter had been revealed.

      It was a very attractive model. Fire, earth, air and water, the four elements of Aristotle, had been reduced to three particles: the electron, proton and neutron. With these three building blocks scientists believed they could build all matter. Oxygen: 8 protons, 8 neutrons and 8 electrons. Sodium: 11 protons, 12 neutrons and 11 electrons. It was as if the music of the spheres was singing out and the foundations of matter were these notes: protons, electrons and neutrons. All matter seemed to be made up of whole-number combinations of these three particles. Why would you expect these particles to be made up of smaller entities? If they were, you might expect to see fractional pieces between the elements in the periodic table.

      Except the dividing didn’t stop there. It turned out that there were experimentally and mathematically very robust reasons to think that protons and neutrons were not indivisible. But the building blocks of the proton and neutron have a strange property: they don’t like to be seen in isolation. They only come in groups, making up something like a proton or a neutron. Safety in numbers. So if they have never been seen on their own, why do scientists think there are even smaller bits into which we can divide protons and neutrons?

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      Everything we call real is made of things that cannot be regarded as real.

      Niels Bohr

      At the end of the 1920s it seemed as if the basic building blocks of matter had been tracked down. The atoms of the periodic table could all be built by taking combinations of electrons, protons and neutrons. The electron has withstood any attempts to divide it further. But revelations over the next decades would lead scientists to believe that there was another layer of reality hiding below the other two building blocks.

      The principal reason for the realization that protons and neutrons might not be as indivisible as the electron came not from more sophisticated technology but from the mathematics of symmetry. It is striking that time and again mathematics appears to be the best microscope we have to look inside my casino dice. A mathematical model began to emerge to explain the proton and the neutron, and it was built on a mathematical concept that could be divided. If the mathematics came apart into smaller pieces, the feeling was that the same should apply to the proton and the neutron.

      The mathematical model responsible for this belief in the divisibility of the proton and neutron arose because physicists discovered that there were a lot more particles out there than just the three believed to be the constituents of stable atoms.

      The discovery of these new particles was a result of collider experiments. Not human-constructed colliders like the LHC, but naturally occurring collisions that happen in the upper atmosphere when cosmic rays strike the atmosphere.

       THE PARTICLE MENAGERIE

      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