Werner Heisenberg. Photograph by Friedrich Hund, AIP Emilio Segrè Visual Archives.
In 1932, Werner Heisenberg mused on an odd fact. The proton and the neutron (which had been discovered only earlier that same year by James Chadwick) had almost exactly the same mass. Despite their different charges, they also responded identically to the forces that dominate within the atomic nucleus.
To Heisenberg's nose, this had a whiff of an uncovered symmetry about it. Appropriating the mathematics that Wolfgang Pauli had used to describe spin (Milestone 3), he postulated that the proton and neutron were two states of the same particle, the nucleon. These states differed only in a quantity analogous to spin — the 'isotopic spin', or isospin as it came to be known. The nuclear force conserved isospin, which accounted for the similarities between protons and neutrons. Other forces, such as electromagnetism, broke isospin symmetry, which explained the nucleons' differences
As Eugene Wigner wrote of the isospin concept in a 1937 paper, "no such states are known to be of any importance [...] [but they] will turn out to be very useful". In that paper, he used isospin to predict correctly the energies of all nuclei up to atomic number 42; more recent work has extended that success to even heavier nuclei. Much like the quantum-relativistic prediction of a spinning electron by Paul Dirac (Milestone 4), isospin was an example of what Wigner would later, in a celebrated essay, describe as the "unreasonable effectiveness" of mathematics in predicting physical phenomena.
And how. In 1935, Hideki Yukawa modelled a nuclear force mediated by lighter particles exchanged between the nucleons. Isospin conservation demanded three such particles. Believers in unreasonable effectiveness could not have been surprised when, some 10 years later, three particles answering the description turned up in cosmic rays and in the first accelerator experiments: the two charged and one neutral pion.
In 1954, Chen Ning Yang and Robert Mills took the ideas of Yukawa further to establish their principle of 'gauge invariance'. This was the centrepiece of a generalized mathematical description of forces mediated by exchange particles of integer spin and isospin — the bedrock of current quantum field theories of the fundamental forces of nature.
Meanwhile, however, physics was entering the accelerator age, and the discovery of a seemingly unordered menagerie of particles similar to the pions was straining the foundation of isospin symmetry. It gradually became clear that isospin was not a fundamental symmetry, but just one corner of a larger edifice. In addition, the proton and neutron were not two states of the same particle. In fact, they were not elementary particles at all, but were made up of smaller entities — quarks.
Once deprived of its original legitimacy, one might have expected spin's nuclear sibling to disappear. In fact, the same mathematical description resurfaced within the new fundamental paradigm as 'weak isospin', a property of quarks that is conserved in weak interactions — a testament to how deeply embedded the language of spin seems to be in the workings of the world.
