by Marcus Chown
ATLAS had about three thousand physicists from thirty-eight countries working on it, and CMS had some 4,300 from forty-one nations. CMS was so massive that it weighed as much as the Eiffel Tower. Together, the ATLAS and CMS teams were looking for two distinctly different collision events, and each was the ‘smoking gun’ for the existence of a hypothetical subatomic particle. One like nothing ever seen before. One that was the key to understanding why the universe looks the way it does. And one whose existence had been predicted in a single sentence almost four decades before …
Edinburgh, August 1964
Peter Higgs was annoyed. His second paper in three weeks – on how nature’s force-carrying particles might have acquired their masses – had been rejected by the editor of Physics Letters. The only thing that tempered his annoyance, as he looked out from his office at the city sparkling in the August sunshine, was his enormous relief that he was back here in his beloved Edinburgh, and no longer enduring the abject misery of the Western Highlands.
The camping trip had been a week ago but it still loomed large in his mind, like a nightmare that persists into the daylight hours. A friend had mentioned a place which, she had read in an article, had the lowest rainfall in Scotland, and Higgs had duly headed there with his American wife of one year Jody, whom he had met through their involvement with the Campaign for Nuclear Disarmament. Unfortunately, when they arrived, it was pouring with rain and they broke their borrowed tent while attempting to put it up. Sopping wet and bedraggled, they had holed up in a nearby bed and breakfast. To make matters worse, on their premature return to Edinburgh, their friend admitted that she had misread the article; far from having the lowest rainfall in Scotland, the spot she had recommended had the highest.3
The camping trip had assumed mythic status in the minds of Higgs and his wife as one of those ‘worst holiday ever’ anecdotes, guaranteed to elicit laughter when trotted out over drinks with friends. But for Higgs, the appalling weather was only part of the reason why the trip was so awful. Leaving his work half finished was the last thing he needed when he was on the verge of cracking the problem that had been his waking obsession for several years.
In his first paper, a mere one thousand words long, which he had completed on 24 July and submitted to the journal Physics Letters, he had shown how a promising theory of nature’s fundamental forces that everyone believed was fatally flawed was not in fact flawed at all.4 He had written it on a Monday after a light-bulb moment over the weekend and he considered it his very first real idea; in fact, the only idea he had ever had (he was a modest man).5
The paper finished on a cliff-hanger, with a tantalising promise of a second instalment to follow, but then had come the trip to the Highlands. The fact that his mind had so clearly been elsewhere had not helped his relationship with his wife. However, back in Edinburgh, warm, dry and free from distraction, he was able to apply total concentration to his work. He had quickly written, and on 31 July, submitted the second paper to Physics Letters.
When it had come back rejected, it had stung. There was no point pretending it had not. In his covering letter, Jacques Prentki, the journal’s editor, suggested that Higgs do some more work on his theory. But the question was, what?
*
Higgs’ two papers had had a long gestation. He was fascinated by quantum field theory, which melded into a coherent whole the two towering achievements of twentieth-century physics – Einstein’s special theory of relativity, which describes what happens to space and time for bodies travelling close to the speed of light, and quantum theory, which describes the submicroscopic world of atoms and their constituents. The physicist who had taken the first step towards such a unification was Paul Dirac, whose illustrious name appeared repeatedly on the board of honoured former pupils at Cotham School. Higgs, a pupil at the same Bristol institution, often wondered who Dirac was during morning assembly. It was his curiosity to discover what the great man had done that had led him to quantum field theory.
The quantum fields are ultimately what the world is made of.6 Matter is composed of atoms. Atoms are composed of nuclei and electrons. Nuclei are made of protons and neutrons. Protons and neutrons are made of quarks (although, in 1964, this was still a very new idea). The quarks and electrons are made of fields. And as far as we know, the quantum fields are the bottom rung of nature’s ladder.
A field is simply something that has a value at each point in space–time. It could be a number such as a temperature, or it could be a number with an associated direction such as a wind speed. Or it could be something altogether more complicated. Each fundamental particle has an associated field. There is an electron field, a photon field, an up-quark field, and so on. Such fields jitter because it is the nature of quantum things that they are inherently restless. And if a particular field is jiggled enough – in other words, if sufficient energy is injected into it – a ripple propagates through it, and this is a particle. A good visual image is of a wind disturbance propagating through a field of wheat. A ripple in the electron field is an electron, a ripple in the electromagnetic field a photon, and so on. The twist is that a quantum field cannot be rippled at any arbitrary rate but only at certain discrete frequencies, or energies. Its oscillations are said to be ‘quantised’.
In this way, quantum field theory unifies the two puzzling and seemingly mutually exclusive properties of the subatomic world that were discovered in the early twentieth century: the ability of atoms and their constituents to behave both as particles and as waves.
One of the most remarkable features of the quantum field theory of the electron, which left a big impression on Higgs and many others, is that it is possible to deduce from it, almost trivially, the existence of the electromagnetic force, as described by James Clerk Maxwell in 1862. The key is ‘symmetry’, a property of any entity that remains unchanged when something is done to it. For instance, a circle has rotational symmetry because, when it is rotated about its centre, it remains the same. A square remains unchanged only if it is rotated by a quarter of a turn or by several quarter turns in succession.
In 1918, the German mathematician Emmy Noether, who was described by Einstein as the most important woman in the history of mathematics, proved a powerful theorem which relates to this. Whenever there is a symmetry, there exists a corresponding conservation law, which dictates that a certain physical quantity can neither be created nor destroyed. For instance, the fact that it makes no difference to the result of an experiment whether it is done today or next week – so-called ‘time-translational symmetry’ – corresponds to the ‘law of conservation of energy’, which maintains that energy can neither be created nor destroyed. And Noether’s theorem has profound consequences for the quantum field theory of the electron, too, because transformations of its equations that do not change any of its observable consequences are also possible.
An electron is described by a ‘wave function’. This spreads through space according to the Dirac equation, and the probability of finding the electron at any location is given by the square of the height of the wave (or, strictly speaking, the square of its ‘amplitude’, its maximum excursion from the zero level). The wave function has a ‘phase’, which describes where it happens to be in its undulating pattern. It turns out that changing the phase by the same amount everywhere – or, in the jargon, multiplying the wave function by a ‘phase factor’ – simply moves the peaks and troughs of the wave along and does not change anything observable, such as the probability of finding the electron at any particular location. The existence of this symmetry, according to Noether’s theorem, must necessarily correspond to a conservation law. And it does: the law of the conservation of electric charge, which states that charge cannot be created or destroyed.
Noether’s theorem applies to a change made everywhere at once that has no observable consequence, but such a ‘global’ symmetry is only one type of possible symmetry. There is another, far more restrictive type, in which the phase of the wave function is no
t changed by the same amount everywhere but by a different amount at every location of space and time. It might seem ridiculous to expect such changes to have no observable consequences and for the electron wave function to exhibit such a ‘local symmetry’, but it is not.
Imagine a billiard ball travelling across a billiard table in a straight line.7 Raising the table vertically, whether by one metre or ten metres, does not change the trajectory of the billiard ball, which is dictated by Newton’s laws of motion. But there is a hidden assumption here: that all parts of the billiard table can be raised simultaneously. While this is certainly true for a common-or-garden table, imagine a cosmic-scale billiard table, ten light years across. In this case, it would be impossible to make a change to all parts of the table simultaneously because, according to Einstein, nothing can travel faster than the speed of light. Distant locations will react to a change in the table’s height later than nearby ones. In fact, it would be impossible for a change to the near side of the table to be ‘noticed’ by the far side before ten years have elapsed. In general, if an attempt is made to change the height of the billiard table, a step in height travels across its surface, causing the table to have a different height at different locations and times. This is the best that is possible in an Einsteinian universe.
Here is the point. We can still hope for the laws of physics to be the same everywhere, so that a billiard ball continues to follow the straight-line trajectory required by Newton’s laws of motion. However, since the surface of the billiard table is no longer flat, this can happen only if at every location and at every time the billiard ball experiences a ‘force’ that precisely compensates for the uneven terrain.
The height of the table is a simple example of what physicists call a ‘gauge’, a term coined by the German physicist Hermann Weyl in 1929. The insistence that the laws of physics remain the same when the gauge is changed continuously from place to place and from time to time is known as ‘local gauge invariance’. As the example of the billiard table shows, maintaining gauge invariance locally requires the existence of a compensating force. This is the key thing.
In the case of the electron, maintaining gauge invariance means insisting that there should be no observable consequences from continuously changing the phase of the electron wave function from location to location and from time to time. The phase of the electron wave function is obviously a more abstract mathematical thing than the height of a billiard table, but just as in that example, maintaining gauge invariance requires the existence of a compensating force. Remarkably, the force turns out to be the electromagnetic force described by Maxwell in the nineteenth century.
So the electromagnetic force – with its bewildering array of phenomena – is nothing more than an unavoidable consequence of local gauge invariance. Basically, the electromagnetic field exists so that when electric charges rearrange themselves at one location in space and time, news of this is communicated to other locations so local gauge invariance can be maintained. That news is carried by the electromagnetic field, which is composed of photons – ripples in the electromagnetic field.
Remarkably, even if we knew nothing about electricity, magnetism and photons but we knew about the gauge principle, we would be able to deduce that all these things exist simply to enforce local gauge invariance of the electron wave function. This extraordinary discovery was made in the 1950s by Julian Schwinger, one of the pioneers of quantum electrodynamics, the quantum theory of the electromagnetic force. It is so striking that it is natural to wonder whether it might be a universal principle. Could the necessity to enforce local gauge invariance be the reason for the existence of not just the electromagnetic force but all of nature’s fundamental forces?
Besides the electromagnetic force, nature’s fundamental particles are glued together by three other basic forces. The most familiar, gravity, was described by Einstein’s general theory of relativity. Like electromagnetism, it is underpinned by a symmetry principle: the equations which reveal how gravity – that is, the curvature of space–time – depends on the distribution of energy have the same mathematical form for everyone, no matter what their motion or ‘co-ordinate’ system. Even Einstein’s earlier ‘special’ theory of relativity arises from the insistence that the speed of light must appear the same to all observers moving at constant velocity relative to each other. In fact, Einstein was the first person to realise the importance of symmetry in underpinning the fundamental laws of nature. ‘Nature seems to take pleasure in exploiting all possible symmetries for her fundamental laws, like a painter eager to use all the most splendid colours on her palette,’ says Italian physicist Gian Francesco Giudice.8
But leaving aside the force of gravity, which for various reasons nobody has any idea how to express as a quantum field theory, there are two other fundamental forces, the strong and weak nuclear forces, which operate only within the ultra-tiny realm of the atomic nucleus.
The first person to seriously think that the gauge principle was the key to understanding not just the electromagnetic force but the strong and weak forces was the Chinese physicist Chen Ning Yang. ‘The only true voyage of discovery’, wrote Marcel Proust, ‘consists not in seeing new landscapes but in having new eyes.’ In the 1950s, Yang and his collaborator, the American physicist Robert Mills, opened new eyes on the world and wrote down an equation that a quantum field would have to obey to enforce a more generic local gauge symmetry on a wave function.
The Yang–Mills equation revealed that the electromagnetic field is the simplest possible ‘gauge field’; not only is it transmitted by a single ‘gauge particle’, but that particle – the photon – carries no electric charge. Since electric charge is essential for a particle to interact with the electromagnetic field, the photon is immune to the electromagnetic force.
However, in the more complex gauge fields permitted to exist by the Yang–Mills equation, the force carriers do carry ‘charges’. These analogues of electric charge, which can similarly be neither created nor destroyed, cause the force carriers to feel the gauge field. In the case of the strong force, for instance, such particles interact not only with the field but with each other, in complex ways that are difficult to predict. This hampered early attempts of physicists to show that the strong force is a consequence of local gauge invariance, as did their mistaken belief that the force principally operates between protons and neutrons. As became clear only in the late 1960s, protons and neutrons are composite particles, and it is their constituent quarks that are glued together by the strong force.
But those pursuing the idea that the fundamental forces are a consequence of local gauge invariance faced an even bigger obstacle. The quantum field theory of the electron, which originated with Paul Dirac in the 1930s, had been plagued by the equations ‘blowing up’ and making nonsensical predictions. It had been possible to remove such ‘infinities’ with a mathematical trick, but the problem was that this ‘renormalisation’ worked only if the force carriers were massless. Although this was the case for the electromagnetic field, whose gauge particle is the photon, it did not appear to be true for the strong and weak forces. The hint was their short range.
In the quantum picture, a force is viewed as arising from a kind of submicroscopic game of tennis. Force carriers are batted back and forth between particles, causing the particles to recoil from each other. Although this picture conveys the general idea, like many scientific analogies it is not perfect, since it explains the origin of a repulsive force but not an attractive one.
Because the laws that orchestrate the submicroscopic world are very different from those that govern the large-scale everyday world, the force-carrying particles such as the photon have a very special character. As mentioned before, one of the cornerstones of physics is that energy can be neither created nor destroyed, but is merely transformed from one form into another. In the quantum world, however, there is a twist. Energy can be conjured from nothing – strictly speaking, the vacuum – and nature will turn a bli
nd eye as long as it is paid back quickly.
In 1905, Einstein discovered that mass is a form of energy – the most concentrated form possible – so the energy that is conjured from the vacuum can become the mass-energy of subatomic particles. Such particles, because of their fleeting existence, are known as ‘virtual’ particles, to distinguish them from ‘real’ ones. It turns out that the greater the energy borrowed from the vacuum, the faster it must be paid back. Consequently, the more massive a virtual particle, the more fleeting its existence and the shorter the distance it is able to travel before disappearing back into the vacuum.
Because the photon has no ‘rest mass’, it takes very little energy to create one, so there is very little energy to be paid back. This means it can exist for a very long time and reach the farthest corners of the universe, which is why the electromagnetic force has an infinite range. However – and this is the key point – the intimate connection between the range of a force and the mass of its force carriers suggests that the strong and weak forces, because of their ultra-short range, are transmitted by massive force carriers. (This logic turns out to be wrong for the strong force; nature, as will later become clear, has found another way of making it short-range.)
The problem is that the only quantum field theories that are devoid of catastrophic infinities are local gauge theories – something proved by the Dutch physicist Gerard’t Hooft in 1971 – but this essential feature exists only if the gauge particles are massless. It is lost the instant massive force carriers are introduced. This was one of the reasons why quantum field theory was not in favour in the early 1960s.
By July 1964, the problem of keeping all the desirable properties of a local gauge theory while also having massive force-carrying particles was something that had been occupying Higgs’ mind for several years. What if the force carriers were intrinsically massless, he wondered, but were given masses by some external process? Might that square the circle of having massive particles but retaining a renormalisable local gauge theory? Higgs imagined space being filled with a previously unsuspected invisible field, which, like the water in a swimming pool, resists motion through it.
