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In theoretical physics we attempt to build abstract constructs which rationalize, explain and predict physical phenomena. To do this we need mathematics: mathematics is the language of physics. The success with which the underlying structure of the physical world can be understood using mathematics is a never ending source of amazement to the theoretical physicist.

A theory to be useful must make contact with experiment, and it must be mathematically consistent. The best theories are generally thought to be the simplest – in a sense the most ‘beautiful’. Simplicity can be quantified: a simple theory explains alot of experimental data with only a few assumptions and tunable parameters. It can thus make predictions – which may even turn out to be true. However no theory, however beautiful, is any good if it contradicts experiment. So a good theorist attempts to stay in contact with both mathematicians and experimentalists.

Many of the mathematical and computational techniques used by the theoretical physicist are common to a wide range of different areas – from cosmology and astrophysics to condensed matter and materials to atomic and particle physics. Moreover there are curious links: to describe the early universe requires an understanding both of particle physics and of nonequilibrium thermodynamics, for example. Indeed many breakthroughs have been made through the application of lessons learned in one area to another: the Higgs mechanism is a good example.

At the Higgs Centre we thus bring together theorists across a wide range of different areas of theoretical physics: together we talk a common language, and the breadth of activity is a stimulus to new ideas.

Some remarkable predictions of theoretical physics:

In 1687 Newton formulated a theory of gravity with an inverse square law. In 1845 two astronomers, Adams and Le Verrier, used observed irregularities in the orbit of Uranus and Newtonian gravity to predict the existence of a new planet, Neptune. It was observed the following year.

In 1865 Maxwell showed that electricity and magnetism could be unified, and in the process found that light is an electromagnetic phenomenon, thus also unifying electromagnetism with optics. Electromagnetic radiation was first produced and detected by Hertz in 1885. Radio, television, and satellite communications are an inevitable consequence.

In 1900 Planck solved the 'ultraviolet catastrophe' in the black body spectrum by postulating that the energy of electromagnetic radiation is quantized. In 1905 Einstein was able to explain the photoelectric effect in terms of the emission of these quanta, which he called photons. The reality of photons was demonstrated explicitly by Compton in 1923.

In 1905 Einstein used a symmetry of Maxwell’s equations to show that space and time are only relative concept. Generalising this idea, he had shown by 1915 that gravity could be understood as a curvature of space-time. General Relativity predicted a small shift in the perihelion precession of Mercury: this was observed by Eddington in 1919. In 1927 Lemaitre showed that General Relativity predicts that the Universe is expanding: this was confirmed by Hubble two years later.

In 1925 Heisenberg, Born and Jordan together constructed a mathematical self consistent theory, ‘quantum mechanics’, to explain atomic spectra in terms of photon emission and absorption. One inevitable consequence of quantum mechanics was that physics is not deterministic: theoretical physics can only predict probabilities. A precise test was devised by John Bell in 1964: it was confirmed by Alain Aspect in 1981. The essential principles of quantum mechanics underpin all of theoretical physics to this day.

In 1928 Dirac showed that a consistent theory of the electron which combines relativity and quantum mechanics necessarily implies the existence of an ‘anti-electron’. The positron was duly discovered by Carl Anderson in cosmic ray experiments in 1932. Anti-hydrogen was first made at CERN in 2010.

In 1930 Pauli postulated the existence of the neutrino to explain the apparent nonconservation of energy and momentum in weak decays. A true theory of weak decays was first written down by Fermi in 1934, but the neutrino was not actually detected until 1956. 

Between 1946 and 1949, Tomonaga, Schwinger, Feynman and Dyson showed how the quantum theory of electromagnetism, quantum electrodynamics, could be used to explain the Lamb shift in the levels of the hydrogen atom, and predict the anomalous magnetic moment of the electron. This prediction can be made so precise that it has now been confirmed to ten significant figures!

In 1964, Gell-Mann and Zweig postulated ‘quarks’ as a mathematical construct to explain the hadron spectrum emerging at that time. A gauge theory of quarks, interacting through ‘gluons’, was shown to be weakly interacting at high energy in 1970 by Gross, Wilczek and Politzer: the predictions of this theory, QCD, are now routinely confirmed in high energy colliders.

Also in 1964 Englert, Brout and Higgs showed that broken gauge symmetries could be used to construct a theory of the weak interaction. Higgs pointed out that such theories necessarily contained a massive scalar particle. In 1968 Glashow, Weinberg and Salam used broken gauge symmetry to construct a unified theory of the electromagnetic and weak interactions. It predicted the existence of a new type of interaction, ‘neutral currents’: these were discovered at CERN in 1973. It also predicted a new quark, charm: this was discovered the following year. The W and Z bosons responsible for the weak interactions were first seen in 1983, again at CERN. The Higgs boson, as it came to be known, was first observed in 2012.