Our greatest endeavour in basic science over the past century has, undoubtedly, been the study of the electromagnetic, strong and weak forces. Although the general theory of relativity was formulated more than 80 years ago, gravitational forces are only now entering the arena of basic scientific research. This is happening because the greatest synthesis of all time, which describes the basic interactions of all the known elementary particles, has finally been achieved in the form of the Standard Model of particle physics. This synthesis is the result of the work of physicists the world over, who have dedicated themselves to the study of what happens when the stable building-blocks of matter (protons, electrons and nuclei) are made to interact at higher and higher energies.

The laboratories where physicists have experimentally tested the Standard Model are found around the world, and include famous European names such as CERN in Geneva, the DESY lab near Hamburg, and the Gran Sasso and Frascati labs in Italy. Physicists at Fermilab, Brookhaven and Stanford in the US have also made huge contributions, as have scientists at labs in China, the former Soviet Union and Japan.

However, I believe that none of these laboratories would exist today if, in the 1920s, modern science had followed the priorities dictated by Albert Einstein when he was at the pinnacle of his scientific power and glory. Einstein’s achievements represent the end point of classical physics, which began with the work of Galileo Galilei and Isaac Newton. Indeed, the mainstream of physics in the 20th century turned out to be quantum physics.

Nevertheless, I was delighted to find that Einstein was selected as “person of the 20th century” by Time magazine, thanks to the role that he played as an ambassador of science across the world. What surprised me, however, was that Einstein came top of Physics World‘s poll of more than 100 of the world’s leading physicists, who selected him as the greatest physicist of all time (December 1999 pp7-13).

Relative reputations

So why is Einstein held in such high regard? As far as the public is concerned, Einstein’s fame is based on two fascinating achievements: the principle of relativity and his deduction that light can be deflected by gravitational fields. Physicists, of course, are well aware of Einstein’s many other huge contributions to physics, but even they may not be fully aware of the role played by other scientists before him.

In fact, the first person to formulate the principle of relativity was Galilei (or Galileo, as he is known to English speakers). His formulation is so well written – “No matter which experiment you perform, it will be impossible to detect effects that depend on the velocity of a reference system provided that the velocity is constant” – that it does not exclude any force of nature, even those, such as electromagnetism, that Galilei knew nothing about. (Incidentally, the equations describing relativity were discovered before Einstein’s time by Hendrik Lorentz in his studies of electromagnetism.) Galilei was also probably convinced that the speed of light was finite. In fact, he tried to measure it, but failed because it is so fast.

However, Galilei succeeded in measuring the acceleration due to gravity – despite its high value – thanks to the invention of the pendulum and the discovery of the force of gravity using the inclined plane. Galilei’s measurements in turn enabled Newton to discover the law of gravitational interaction, which predicted, among other things, that a beam of light can be deflected by the force of gravity. (Indeed, Newton’s laws made predictions that were wrong by only a factor of two compared with Einstein’s calculations more than 200 years later.)

But how many people are aware of the contributions of Newton (in second place in the Physics World poll), Galilei (sixth) and Lorentz to these culturally fascinating discoveries of relativity and of the effects that mass has on space-time? I find it unfortunate that both of these discoveries tend to be fully attributed to Einstein. Here, however, I would like to praise the man who came eighth in the Physics World poll – Paul Dirac.

To do this I need to make a further point relating to CERN and the other particle-physics labs, and to the Standard Model. Suppose Einstein had been appointed “supreme advisor” by some enlightened “world prime minister” and had been asked to suggest the way forward for physics. Einstein’s top priority would, I believe, have been the study of gravitational forces. He would no doubt have recommended other avenues, but they would not have been his priorities. Indeed, I believe he would have ignored many other research activities and discoveries from his time, such as Rutherford’s discovery of the nucleus, Enrico Fermi’s rigorous mathematical formalism of the weak forces, and Hideki Yukawa’s description of the strong nuclear forces.

Making sense out of nonsense

In the 1920s the young English physicist Paul Dirac began trying to understand and describe the space-time evolution of the electron – the first elementary particle to have been discovered. Dirac was puzzled by an unprecedented property of space-time discovered by Lorentz in his studies of electromagnetic forces, whereby if space was real, time had to be imaginary, and vice versa. In other words, space and time had to be a “complex” mixture – the sum of a real and an imaginary quantity.

Furthermore, the “elementary particle” was the source of another disturbing puzzle. The study of hydrogen spectra in the 1920s revealed that an electron not only has an orbital angular momentum related to its motion about a nucleus, but also an intrinsic angular momentum or “spin”. But where did this spin come from? Why was the spin of the electron only half of the minimum value measured from atomic spectra? And why was the “gyromagnetic ratio” of the electron – the magnetic moment divided by its angular momentum – twice as large as the ratio measured from atomic spectra?

Dirac deemed that this tricky matter had to be understood, and decided to study the electron in complex space-time. In 1928 he published his now famous equation (see “Paul Dirac: the purest soul in physics” by Michael Berry Physics World February 1998 pp36-40).

The great novelty of the Dirac formalism was the introduction of the spinor, which is a mathematical function having four components. Imagine you want to move in space-time with a bicycle: you need two wheels. However, you could also move using a unicycle, as an acrobat would do. Similarly, before Dirac came along, mathematics used only one “function” to describe a particle: a scalar function. Dirac’s claim was that to describe an electron, you need a mathematical object having four components. In our daily life this would be like saying that to evolve in space-time we need a car with four wheels, not a unicycle with just one.

Dirac’s equation also came up with the seemingly nonsensical prediction of “negative energies”. Only a real genius could transform this catastrophic prediction into a formidable new frontier for science: the existence of the antielectron and of the “Dirac sea”. Dirac also realized that every particle in our world must have an antiparticle with an opposite charge. This discovery was the seed for the “radiative effects”, the “running” of the gauge couplings, and the correlation between the fundamental forces and their unification: in other words, it led physics to the triumph of the Standard Model.

The impact of the Dirac equation

I once had the privilege of speaking to the great Soviet physicist Piotr Kapitza, who was at Cambridge with Dirac, where they were both pupils of Rutherford. Every week the pair would attend a lecture. “No matter what the topic of the seminar,” Kapitza told me, “at the end of the lecture I would always address the same question to Dirac: ‘Paul, where is the antielectron?’.” Kapitza was a great friend of Dirac, but remained convinced that his equation was only creating trouble. His comments are a reminder that no-one at the time took Dirac’s equation seriously. No one suspected what a gold mine the equation would turn out to be.

The most spectacular consequence of the equation is the existence of “radiative effects”. In fact, the existence of the antielectron (or “positron” as it has become known) implied that when a particle (of any type) collided with its antiparticle they would annihilate each other, releasing their rest-mass energy as high-energy photons (or other gauge bosons). For example, in the case of a process described purely by quantum electrodynamics, a gamma-ray photon can create an electron-positron pair, which can transform itself back into a photon. This process, which is called “vacuum polarization”, was the first radiative effect to have been theoretically predicted.

The first physicist to compute the vacuum-polarization effects in the hydrogen atom was Victor Weisskopf. He predicted that the 2p_1/2 level in a hydrogen atom should be very slightly higher in energy than the 2s_1/2 level, by some 17 MHz. However, in 1947 Willis Lamb and Robert Retherford discovered that the 2p_1/2 level was in fact lower than the 2s_1/2 level by some 1000 ± 100 MHz.

It was this experimental discovery of the Lamb shift that prompted all theorists, including Weisskopf, Hans Bethe, Julian Schwinger and Richard Feynman, to compute the very simple radiative process in which an electron emits and then absorbs a photon. But had it not been for the discovery of the positron – and therefore the existence of electron-positron pairs – no one would have imagined that such radiative effects could exist in nature. And without “radiative effects”, there would have been no “running” of the gauge couplings, no correlation between the different forces and, ultimately, no grand unification of all the fundamental forces.

Think of a photon, which is governed by quantum electrodynamics, that can transform into a quark-antiquark pair (governed by quantum chromodynamics – the theory of the strong force) or into a W⁺W^– pair (governed by quantum-flavour dynamics – the theory of the electroweak force), before both pairs annihilate and form a photon again. The annihilation allows these three theories to be present in radiative effects. Without these results, the problem of the renormalization of the gauge forces (with or without spontaneous symmetry breaking) would never have been conceived. And if that problem had not been solved – as it was in the early 1970s by the 1999 Nobel prize winners Gerard ‘t Hooft and Martinus Veltman – we would not have the Standard Model, with its many precise quantitative predictions that have been experimentally validated in labs all over the world.

The roots of the Standard Model are in the Dirac equation. We are all children of this equation. Without it there would be no particle-physics labs and no Standard Model. Of course – and fortunately for us – there are sound reasons to believe that there is a lot of new physics beyond the Standard Model. The recent results on neutrino oscillations (see Neutrino mass discovered) and the new values for direct “CP-violation” in K-meson physics (CP and T violations: new results leave open questions) are opening new avenues beyond the Standard Model. However, none of these discoveries are affected in any way by the gravitational force, which was Einstein’s main interest.

At the roots of everything

Early in the 1970s Weisskopf, Eugene Wigner, Bob Wilson and other eminent scientists attended a seminar held in Erice, Sicily, entitled “The Roots of Modern Physics”. At this seminar, they all concluded that the effective origin – the real seed of modern physics – was the Dirac equation.

Three decades later their conclusion has been further corroborated. Imagine modern physics without the possibility of particle-antiparticle symmetry and, consequently, no possibility of annihilation. There would be no “running” of the gauge couplings and no coupling among different gauge forces. Suppose that no one had ever tried to describe the evolution of an electron in space-time or thought through the extreme consequences of this work. We would be nowhere.

It is for these reasons that I believe that Paul Dirac had a much bigger impact on modern science in the 20th century than Albert Einstein.