Understanding the Higgs 8: Physics is worth a mass

People remember 1967 for different reasons.

It was the year of the Six-Day War in the Middle East and the military coup in Greece. It was the year when North Sea gas came ashore in Britain, when the Beatles issued Sergeant Pepper, and when Celtic won the European Cup. Nicole Kidman was born, Elvis Presley got married, and Woody Guthrie died.

Dr Christiaan Barnard carried out the first heart transplant and Jocelyn Bell discovered pulsars.

And two physicists, working independently, applied the Higgs mechanism to unite electromagnetism and the weak interaction into a single overall structure. Twelve years later, they would share the Nobel Prize.

The two men were very different in background. Steven Weinberg, born in New York City, is an atheist and a strong supporter of the state of Israel. He takes a view of nature which can sometimes seem quite bleak.

Abdus Salam, born in Jhang, Punjab, was a Muslim who quoted the Quran in support of the scientific quest for knowledge. He had a particular interest in symmetry.

‘That may come from my Islamic heritage for that is the way we consider the universe created by Allah with ideas of beauty and symmetry and harmony, with regularity and without chaos.’

But the two also had much in common, including a deep concern to act on global issues. Weinberg has written, spoken and campaigned strongly on the dangers of nuclear weapons, and continues to do so. For a time in the early 1970s he was a consultant to the U.S. Arms Control and Disarmament Agency, ACDA, providing them with technical background for the SALT arms reduction talks with the Soviet Union. Salam established the International Centre for Theoretical Physics in Trieste as a place where physicists in developing countries could go for periods of creative stimulation, enabling them to keep at the forefront of their subject without joining a brain-drain to America and Europe.

And in physics, both were clear about the need to pursue the task of seeking structure and using the techniques of symmetry and of quantum field theory – and if necessary to opt out of the tide of fashion and choose their own direction.

Salam had studied mathematics at the University of the Punjab and then won a scholarship to Cambridge, where he was a research student of Nicholas Kemmer. When Kemmer moved to Edinburgh, Salam was appointed in his stead, and then in 1957 became professor at Imperial College London where he built up a brilliantly talented team, among them Tom Kibble who told him about the Higgs mechanism.

Weinberg had been in the same class at high school as Sheldon Glashow, and had gone on to study at Cornell and Princeton, and to become professor of physics at the University of California in Berkeley. in 1966 he took leave from his post at Berkeley to go to Massachusetts, so that his wife could study at Harvard Law School; today she is Professor of Law at the University of Texas at Austin. In Massachusetts Weinberg spent time at Harvard with Schwinger, who he would later succeed there, and at MIT. In 1967 he was working on the strong interaction, trying to apply the Higgs mechanism to it and getting conflicting results – and then realised that his model was in fact telling him about the weak interaction instead.

Turning the key

‘When I started doing research in early 1950s,’ Weinberg observed recently, ‘physics seemed to be in a dismal state.’ The problem was the proliferation of all kinds of particles and forces.

‘Nature, like an enemy, seemed intent on concealing from us its master plan.

‘At the same time, we did have a valuable key to nature’s secrets. The laws of nature evidently obeyed certain principles of symmetry, whose consequences we could work out and compare with observation, even without a detailed theory of particles and forces… It was like having a spy in the enemy’s high command.’

Both Weinberg and Salam realised that the Higgs mechanism provided a means of keeping the symmetry of the electroweak interaction and at the same time breaking it sufficiently for the pulses of the weak force to be concentrated in particles with a non-zero mass.

Their papers predicted three such particles – and in 1983 all three were found by the Super Proton Synchrotron at CERN. The team leaders, Carlo Rubbia and Simon van der Meer, were awarded the Nobel prize the following year for the discovery.

The new particles were the W+ and the W, and the neutral Z0. They are very massive, with the W about 80 times the mass of a proton, and the Z just over 90 times. By comparison, the mass of an iron atom is around 55 times the proton’s mass.

With such a large mass, their lifetime is very short indeed, and they only travel an incredible short distance before vanishing.

The Weinberg and Salam papers also predicted a fourth particle – one that was a kind of leftover after all the necessary weak particles had been put in place. This additional particle was the Higgs, and so its discovery puts one large additional piece of support for Weinberg and Salam’s work.

In addition to the experimental support, a strong theoretical underpinning came from two Dutch physicists, Martinus Veltman and his student Gerardus t’Hooft. They showed that mathematically the theory held together so well that it had none of the infinities that had plagued so much of field theory for so long. That work earned them the Nobel Prize for Physics in 1999.

The Standard Model

The momentum from the success with the electroweak interaction carried forward to the strong interaction, using the idea of SU(3) symmetry and quarks, with various physicists playing a part in developing what is now called the Standard Model.

But the aim of science is always to press on to get closer to the truth, and it is clear that the Standard Model is not the final stage. The big unresolved challenge is to reconcile it, the theory of the very small, with general relativity, the theory of the very large, and that seems a long way from completion. The Standard Model encompasses the strong, weak and electromagnetic forces, but not gravitation.

And indeed although the Higgs particle consolidates the Standard Model, it also provides deep and perhaps unsettling philosophical challenges.

First of all, it finally removes any hope of a material base to physics. That hope was really lost in 1926 when Schrodinger produced his wave theory of matter, picturing an unknown substance in motion – its unknown nature was why he gave it the mathematical symbol psi – out of which matter somehow formed as the waves on the ocean. In the Schrodinger picture we see the wave and can model it and calculate its shape, but we know nothing of the deep sea beneath.

The Schrodinger picture was countered by Heisenberg, who insisted that we could still have particles, while not needing to look at their deeper nature. We could not zoom too closely in on their direct moments of contact, he said, but instead we much stand back at a distance and simply correlate the measurements of what went in and what comes out.

Heisenberg’s approach meant that physicists could avoid the issue of what matter is and simply talk about how it behaves. So they could continue to talk about particles in fairly familiar – and fairly material – language.

The concept of the Higgs field means that this approach is no longer good enough. It tells us that what makes matter the way it is – is something quite specific but also quite non-material, a field. We start with something fundamental, whose essence we do not know, namely light. We add in something even more non-material, the concept of symmetry. And we add in something else non-material, the Higgs field. And the outcome of these various insubstantial and non-material entities is – the stuff that builds up through atoms and molecules into lumps of iron and concrete.

2500 years of argument

The old debate amongst the Greeks was between Aristotle and Plato, who argued about what was the primary factor of existence. Plato said that it was form and Aristotle said that it was substance. Plato said that the fundamental essence was a set of patterns – universal templates or archetypes – which created the real world when they were somehow stamped onto a formless kind of clay.

Aristotle said that the clay was the essence, and that forms were secondary, being the patterns which we notice. He gave the example of the concept of a snub nose. Could we say that snubness somehow existence as a form and was imposed on the various noses of the world? He asked. No, was his reply, snubness is a concept that we create to enable us to better catalogue the noses around us.

The debate was one by Aristotle and he and the Greeks set us off down a trail of substance. This was why they developed the concept of an atom as something fundamental – it was part of a picture in which substance was primary.

But now we have a theory in which substance is not primary, but created out of light, mathematics and a field. A field is simply a form – a kind of abstract structure in space – indeed if an atom is an example of pure substance, then a field might be seen as a case of pure form.

That in turn leads to the question of whether or not we should be talking about particles, or whether we should use the language of waves.

And deep under the surface is the question of order. Symmetry is now invoked to impose order on nature – but where does symmetry come from? And how does it ‘impose’ itself?

So in one way the Higgs discovery reinforces a remarkable theory that took its present shape in the early 1970s. In another way it undermines a worldview that formed 2,500 years ago – and thus points the way forward to the next development in physics, whatever it might be, with as many questions as answers. These are good reasons for physicists to be cheerful – and to burst into song.

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Understanding the Higgs 7: Three roads converge

By 1964 the challenge was clear. The familiar phenomena of electricity and magnetism looked as if they could be part of something more comprehensive, an electroweak interaction, with the electromagnetic field one of its aspects and the weak interaction another.

The reasoning came from symmetry. When the electroweak field was looked at from one perspective it appeared as electromagnetism. When viewed from another perspective, it appeared as the weak interaction which causes radioactivity.

But because the weak interaction in the world is very different from the electromagnetic one, the symmetry could not be complete. So somehow the symmetry had to be broken.

Can we somehow keep symmetry and yet break it? The answer at first might seem to be no, if we think of symmetry as something like a vase which we break when we drop it. But we don’t have to go that far in the concept of breaking things. We could think of the symmetry of a circle or a five-pointed star and allow it to break a little – and get a rose. The original symmetry is still there, but with edges that are somehow ‘softer’.

The problem was that Goldstone’s theorem seemed to force the choice to be between a perfect vase or a smashed one, ie no vase at all. But Philip Anderson’s 1963 paper had suggested that in superconductivity a similar problem was in fact resolved by a process of condensation. Particles in a crystal had their behaviour shaped by the lattice of the crystal.

That suggestion from Anderson was enough to encourage physicists at three centres to take up the challenge anew – and each independently to come up with a solution.

Breaking it gently

The way to resolve the problem is to invoke a new field which fills all of space – today called the Higgs field. This field obeys the rules of symmetry, just as does the existing field of the electroweak theory. But it somehow condenses into a single state – in the same way as the theory of a bar magnet tells us that the jumbled-up magnetic domains drop down into place in a single direction which locks in. Or in the way in which the electrons in a superconductor lock in to a single coordinated structure.

So the field itself is symmetric – but the fact that it condenses into a single fixed state breaks the symmetry.

And it is this field that provides the mass. It links with the Yang-Mills field (the field which has to exist to maintain gauge symmetry) and the particles of the Yang-Mills field acquire mass as a result. The outcome is not only the photon for electromagnetism but no less than four other particles. Three of these are concentrations of the weak interaction, now given mass by the condensing of the Higgs field. And there is a fourth, a kind of by-product of the process, something new – the particle which has become known as the Higgs.

In Brussels

The first to publish were at the Free University of Brussels – Francois Englert and Robert Brout.

Englert’s first degree had been in engineering, but he switched to physics and went to work at Cornell as Brout’s research assistant. They found that their approaches to physics were so similar that when the time came for Englert to go back to Belgium, Brout decided to move there with his family, and went on to acquire Belgian citizenship and to play a big part in the further development of physics in the country, up till his death last year.

One of the features that Englert and Brout shared was a readiness to look afresh at any problem, and that, says Englert today, is how they made their breakthrough with what has come to be known as the Higgs particle.

‘The generality of our results is largely attributable to the use of quantum field theory, which at the time was largely ignored in elementary-particle physics. Its use in deriving the mechanism was no accident. Driven by his unusual faculty to translate abstract concepts into tangible intuitive images, Robert always conspicuously disregarded academic knowledge and favored entering any subject from scratch. For him, the fact that he was no expert on particle physics was an advantage: He could easily free himself from fashionable trends in the quest for a consistent theory of short-range fundamental forces.’

At Imperial

Imperial College London was the base of Tom Kibble, who had taken his physics degree and doctorate at Edinburgh. He was of Scots descent and born in Madras in India, where his grandfather had been a medical officer and his grandmother, Helen Bannerman, had become a well-known writer of children’s books. Working with him at Imperial were two visiting Americans, Gerry Guralnik and Dick Hagen, who had both attended lecture courses by Julian Schwinger during their earlier studies.

The paper written by the three was just being put in the post for publication when the papers by Englert and Brout and by Peter Higgs arrived.

In Edinburgh

Meanwhile at Edinburgh Peter Higgs had been following the arguments about Anderson’s work on superconductivity. In particularly, he noted a criticism made by Wally Gilbert, a remarkable man who started out as a physicist but switched to biology after meeting the James Watson (of double helix fame) and went on to win the Nobel Prize for his work in sequencing DNA. Today in retirement, he is an artist-photographer whose work is exhibited in galleries across the US, with the images including an Orkney series.

In 1964 Gilbert had argued that there was a fault in the argument that symmetry-breaking could lead to mass. Peter Higgs thought at first that this was indeed the end of any hope of a way forward, but then realised that a method developed by Julian Schwinger could be applied to show Gilbert was wrong. He sent a letter accordingly to the journal Physics Letters which is published at CERN, the particle accelerator centre near Geneva.

He then worked on a second paper, to put together the actual way in which the symmetry-breaking occurs, using the Higgs field. He sent off this paper to Physics Letters as well – only to have it returned as not suitable for publication. It turned out afterwards that the editor of the journal had thought the paper ‘not to have any relevance to particle physics’.

‘I was rather shocked,’ he says. ‘I did not see why they would accept a paper that said this is a possible way to evade the Goldstone theorem, and then reject a paper that showed how you actually do it.’

So during August he revised the paper and with the encouragement of one of his colleagues, Euan Squires, added on a paragraph that drew attention to the fact that the theory had practical experimental consequences – that it predicted a new particle which could be looked for. This emphasis was one of the factors that associated Peter Higgs’s name with the search for the particle.

He sent the paper to the editor of another journal, Physical Review Letters, who confirmed that he would accept it and mentioned the paper by Englert and Brout which he was also about to publish.

The Edinburgh connection

Peter Higgs had come to Edinburgh four years before to take up a lecturing post in the Tait Institute of Mathematical Physics. Its graduates include Sir David Wallace (seen above on the left with Peter Higgs) who subsequently became President of the Institute of Physics and Master of Churchill College, Cambridge, and Dennis Canavan, who went on to become first a teacher and then one of Scotland’s most highly regarded political figures.

The Institute took its name from James Clerk Maxwell’s friend and colleague, Peter Guthrie Tait, and was housed in Roxburgh Street, just across the road from the Physics Department.

The Tait Chair in Natural Philosophy had been established in 1922, with the aim of developing the study of mathematical physics, and its first incumbent was Sir Charles G. Darwin, the physicist grandson of the great naturalist. After him came Max Born, one of the founding fathers of quantum theory, who won the Nobel Prize for the probabilistic interpretation.

Born had begun his career at Göttingen as assistant to the mathematician David Hilbert and his own assistants included Werner Heisenberg, Wolfgang Pauli and Enrico Fermi.

In 1953 Born was succeeded by one of his former students, Nicholas Kemmer, who established the Tait Institute itself. Kemmer, born in St Petersburg, had been educated in Germany when his family moved there after the Russian Revolution. He had worked in Zurich as Pauli’s assistant, then on wartime atomic energy research, and after the war at Cambridge. His own research had developed the use of symmetry for protons, neutrons and mesons, and was a first stage in the developments that would grow into a core concept in particle physics today. At Cambridge, he gave priority to his teaching work, for which he was in much demand, with his students including Ron Shaw and Freeman Dyson, who speaks of the high quality of Kemmer’s teaching of quantum field theory.

And indeed it was another one of Kemmer’s Cambridge research students – Abdus Salam – who along with Steven Weinberg took the step of using the Higgs approach to solve the problem of electroweak theory.

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Understanding the Higgs 6: Can the circle be unbroken?

In the 1960s the tide in physics flowed towards tackling the strong interactions, as those grappling with the weak interactions had come up against an apparently unshiftable block.

The technique that seemed to be the most powerful one was the use of symmetry, and the use of Lie groups enabled a classification to be made that brought the weak interaction into a possible unification with the electromagnetic one. That was truly amazing. The long-distance electromagnetic field that gives us light and radio waves was somehow linked at a deep level with the weak interaction which we only know through its by-products in processes at the quantum level like radioactive decay.

A second application of the treatment involved another type of symmetry, gauge symmetry, which required the existence of a new type of field, the Yang-Mills-Shaw field, which brought the weak interactions even closer, by giving them a new particle of their own to complement the electromagnetic one (the photon).

But – damn and blast – the predicted ‘weak photon’ was massless, which could not be the case in reality. And – damn and blast three times over – Goldstone’s theorem showed that there was no way in which you could generate a mass-possessing weak particle without destroying the symmetry completely.

For those few people who refused to abandon the problem, if they had any request from Father Christmas it would be for a symmetry-breaking kit – something that would break the symmetry while preserving it.

The situation required the kind of ingenuity of an Orcadian student from Birsay who had happily stuck photos of his native islands on the wall of his Edinburgh digs with Copydex, which at the time was regarded as proof against just about anything – a problem which his landlady encountered when she decided that the pictures infringed the rules of the house. She tried to haul them off the wall and took off a quantity of wallpaper with them, and irately confronted him for his misdeeds. Without the slightest appearance of a pause for thought, he said with a kind of calm authority: ‘Oh, what a pity that you didn’t ask me for the Copydex remover.’

Something this was needed with the electroweak interaction – to remove some of the picture-equivalents off the wall without at the same time taking the wallpaper with them.

The equivalent of the Copydex remover came indeed not from looking at a wall but from things that are much bigger and solider than the world of very small particles. There were three situations in solid state physics that produced the clues.

Situation number 1

When atoms join up to form a crystal, their outer electrons loosen and begin to drift. Having lost these outer electrons, the previously electrically-neutral atoms have a net positive charge. The electrons stay in the crystal, not attached to any particular atom, and an electric field can start them moving in a particular direction – this is what forms an electric current. However, the effect of the positive lattice with the little pulls of the various atoms in the structure can be to slow down the electrons – and make them appear to be more sluggish and massive than they would otherwise have been.

So one way for a particle to behave as if it has more mass is to put it in some kind of external lattice like this.

Situation number 2

A magnetic substance is formed out of many little units which are themselves magnetic – they are called domains. When the substance is very hot, the domains will move around and point in a random mix of ways and from the outside we would never know that there was the potential for magnetism there. But if we let the temperature drop, there comes a point where suddenly the domains click together into pointing in a single direction. Somehow each lines up with its neighbour, but not in a one-by-one fashion but all an overall ‘decision’. We have no way of knowing in advance which direction they will happen to lie along.

The reason why they line up in this way is because this is the most stable form they can take. It is as if they have dropped down to the lowest point they can reach. It is a bit analogous to us filling a jar with sugar and tapping it from time to time – to see the level sink as the sugar grains start to fit together better and better. In the case of the magnetic substance, there is no tapping process, and the alignment happens almost in an instant. But there is a parallel in that in each case the little units – whether domains or grains – ‘find’ that by aligning themselves closely a stable ground-state is reached.

The magnetic substance when it was hot was very symmetric in that we could turn it around in as many ways as we would like, and in terms of magnetism each direction looked the same. But after we cooled it, we had this sudden transition of the domains into an overall direction. So the individual units still retained their own internal symmetry while the collective result was to make a break.

Situation number 3

This is in a very strange world, the interior of a superconductor. Here electrons can travel through the crystal lattice so smoothly that nothing slows them down in any way and they can travel forever. Here something has happened which is a kind of parallel to the magnet in that there has been a process of internal ordering. The electrons have a kind of overall link between them that enables them to get through the lattice without bumping into any of the lattice atoms.

It is a bit like dancing the conga. If a group of people are in a crowded room and all try to make for the door on their own, their will be a lot of bumping into others and an ever-slowing rate of progress, but if they line up in conga formation they can negotiate their way round in a coordinated way and avoid touching anyone.

Where does this get us? Well, from situation 1 we see that some kind of background lattice can cause particles within it to slow down and behave as if they have become more massive. So maybe we need to find some kind of background lattice encompassing the whole of space, so that it can somehow interact with the particles we have been studying and cause them to behave ‘massively’. We need in fact a background lattice that consists purely of forces – and that is just a definition of something that we have already become familiar with, a field.

So we need an additional field to interact with the field that we already have, in particular the Yang-Mills field.

But how will this field get round the constraints of Goldstone’s theorem? – which the Yang-Mills field on its own could not get beyond.

Here is where situations 2 and 3 come in. This new background field has to have the various symmetries, otherwise we have broken them completely, but since it is a brand-new field with only one task, to help us out of our problem, we do not need to allow it to have all the myriad of options that the more familiar fields do. Indeed, it only requires to have one option, just like the magnetic bar does, and just like the electrons in the superconductor do. There is one single position that the choice of options locks in to – so to that extent it has broken the symmetry – but the break is not so bad that we have lost the symmetry completely.

Superconductor superstructure

In 1963 Philip Anderson looked closely at what happens inside a superconductor and said that there was something important for particle physicists to be aware of. Anderson was a specialist in the solid state, and went on to share the Nobel Prize in 1977 for his work on the electron interactions in phenomena like magnetism and superconductivity. His studies at Harvard had been interrupted by the war, in which he had been deployed in research on building radio antennas, and after going back to Harvard to complete his training (and where his fellow-students included Tom Lehrer) he went to work at Bell Laboratories, joining a glittering array of researchers there. He found that the sophisticated mathematical techniques of quantum field theory that he had learned from Schwinger at Harvard had practical applications in the advanced radio work. In his background there are professors on both sides of the family, together with a love of the outdoors, and from a sabbatical year in Japan there is a deep interest in Japanese culture and he is a first-degree master of the game of Go.

The paper that Philip Anderson wrote in 1963 showed that in a superconductor the ordered cloud of electrons acts like a single quantum system which can be energised, and that the bursts of energy look like particles. The presence of an electromagnetic field affects these excitations in a way that makes them behave as if they had acquired a mass. So, he noted, symmetry was being broken but yet mass was being generated, and so the blocking effect of Goldstone’s theorem had been overcome. The Goldstone difficulty was, he said – ‘not a serious one’. It was this paper that opened the way for the breakthrough of Peter Higgs.

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Understanding the Higgs 5: The strong dominate the field

By the mid-1960s, the situation in particle physics was not good. Its aim had been to uncover the basic building blocks of matter, and for a time it had seemed that the end was in sight. In 1917 Ernest Rutherford had split the atom and show that it consisted of a positive nucleus surrounded by negative electrons, and in 1932 John Cockcroft and Ernest Walton, working under his direction, had split the nucleus.

The work of the experimenters had stimulated the mathematical physicists to develop a series of powerful theories. First came quantum theory, then quantum field theory which extended the classical concept of a field to the new quantum world that was opening up. With Paul Dirac one of its main creators, it was elegant and beautiful, with various hints in it of something even deeper.

But then the progress started to decline. As the power of the particle accelerators was stepped up, more and more ‘elementary’ particles began to appear. By the 60s it was becoming like a zoo, with several hundred categorised. And worse than that, the refined landscape of quantum field theory started to show up some potholes. Certain calculations produced terms which went to infinity, the equivalent of the ground blowing up under the investigator’s feet. Stopgap methods were deployed, one being just to subtract out the infinities. It worked, but the feeling of mathematical beauty was being lost.

So particle physicists looked for territory that might yield more promising results, and homed in on the strong interaction. There it was possible to do calculations, as techniques had been developed for working out what would happen when one particle collided with another – a process known as scattering. The techniques involved gathering today much data and putting it in an array of numbers called a matrix, and the theory was known as S-matrix theory, the S representing scattering.

There was something of a tidal flow from quantum field theory to S-matrix theory, and the move involved not only a shift in content but a shift in style. S-matrix theory was very much about nuts and bolts and practicalities. Quantum field theory was about a search for abstract structure.

The work of Murray Gell-Mann and Yuval Ne’eman in applying Lie groups to the strong interactions did for a time start to turn the tide back towards the search for mathematical structure, but that wasn’t for long, as their theory also pointed to something for particle calculations.

They had found that the strongly interacting particles seemed to be grouped in templates of the Lie group SU(3). This group produces patterns of eights and tens. But at its deepest level it is formed – generated – out of just three basic units. In 1964 Gell-Mann suggested (as did another physicist, George Zweig, working independently), that as the upper level were fully associated with known particles, then the very lowest level would also have its counterpart in nature.

The counterpart of this lowest level would be three particles with charges that were in multiples of one-third.

At first, the idea seemed quite hypothetical, since the theory showed that these particles were so tightly bound together that it would be impossible to separate them and give any one of them a separate existence. But them in 1968 the Stanford Linear Accelerator showed that the proton did indeed seem to have much smaller, point-like objects within it. It was a bit like finding a layer of rock so hard that no geologist’s hammer could break a piece off and yet noticing that it had a finely-shaped pattern running over it.

So the new particles had to be taken seriously, and calculations could be made – and there was a whole new territory of work to do.

For a time there was caution about using the name Gell-Mann had given the new particles, and the particle-like signs within the proton were termed partons. But as the case for them strengthened, so too did the name – which was quark.

According to Gell-Mann, he came to the name from the sound first, which was ‘kwork’, but he didn’t have a spelling.

‘Then, in one of my occasional perusals of Finnegans Wake, by James Joyce, I came across the word “quark” in the phrase “Three quarks for Muster Mark”.’

This is the passage that reads:

Three quarks for Muster Mark!
Sure he has not got much of a bark
And sure any he has it’s all beside the mark.

So, explained Gell-Mann, ‘Since “quark” (meaning, for one thing, the cry of the gull) was clearly intended to rhyme with “Mark”, as well as “bark” and other such words, I had to find an excuse to pronounce it as “kwork”. But the book represents the dream of a publican named Humphrey Chimpden Earwicker. Words in the text are typically drawn from several sources at once, like the “portmanteau” words in “Through the Looking-Glass”. From time to time, phrases occur in the book that are partially determined by calls for drinks at the bar. I argued, therefore, that perhaps one of the multiple sources of the cry “Three quarks for Muster Mark” might be “Three quarts for Mister Mark”, in which case the pronunciation “kwork” would not be totally unjustified. In any case, the number three fitted perfectly the way quarks occur in nature.’

Zweig preferred the name ace for the particle, but given the nature of the apparent guess that turned out to be brilliantly correct, three quarks trumped three aces and the terminology of Gell-Mann (and James Joyce) is the one which has stuck.

So with Lie groups to steer them and quarks to crunch together, the strong interactions dominated the early 1960s.

Few people continued to work on the weak interactions, where progress had at one time seemed so promising.

The weak interaction and the electromagnetic interaction had been shown to have features in common, a kind of overall symmetry, which might be the hallmark of a more overarching unity, in which they each would become an aspect of a single electroweak interaction.

Some of the differences between them could be accounted for by taking account of a further symmetry, gauge symmetry. This could be applied to a model of an electroweak interaction to break it down into the two types. The approach was developed by Yang, Mills and Shaw, and applied by Sheldon Glashow – who found that it produced two particles. One of these was a familiar one, the photon, a particle-like burst of energy that is formed with the interaction of light with matter. The other one was something new, a kind of ‘weak interaction photon’.

And that is where the snag came in that stopped any further progress for several years. The photon has zero mass. This is because, as we noted some time back, mass increases with speed, so that a mass-possessing particle would go toward infinite mass as it approached the speed of light. So a particle can only travel at light-speed if it has a zero mass to start with.

The masslessness of the photon is also connected with the distance which it can travel – which is infinite. As we know, if nothing gets in its way, light can continue on its way for ever, which is how astronomers can observe the light from stars so far away that it takes billions of years for the light to cover the distance.

But the weak interaction is quite the opposite. It also takes place between particles that are exceptionally close together. Indeed, it is so incredibly localised that the distance over which it can act is no more than a fraction of the diameter of a proton.

So if the weak force is to somehow involve the appearance of some kind of particulate energy-burst, that particle has to be born and die within this incredible short distance. This means that on the one hand its lifetime has to be incredibly brief, and on the other that it must have a substantial mass, in order to carry sufficient energy with that ultra-short life.

So a theory that proposes a zero-mass photon-like weak particle is simply flying in the face of the facts.

It became even worse than that when the British-born physicist Jeffrey Goldstone showed mathematically that it was not possible to get mass into the weak particles out of this approach. The hope had been that you could start with the symmetry and break it a little to get particles with mass. But Goldstone showed that mass would only come if you broke it completely – and thereby defeated the purpose of starting with symmetry in the first place.

The challenge looked hopeless – which is why Glashow’s work was put on the shelf and sat there, while the flow of the tide was to the strong rather than the weak.

It was the solution of this challenge that was the genesis of the Higgs particle.

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Understanding the Higgs 4: Symmetry for the weak

The weak interactions are really weak compared to the strong ones. Indeed they are really weak compared to electromagnetism – about 100 billion times weaker. Yet there are also some similarities with electromagnetism. As far back as 1941 Julian Schwinger had felt that these similarities were significant, and took a step forward in a paper of 1957.

Schwinger is regarded as one of the giants of fundamental physics, both from the quality of his work and the way in which he inspired and assisted others. He shared the Nobel Prize in Physics in 1965 for his work in unifying the quantum theory of the electron with classical electricity and magnetism. This is the territory known as quantum electrodynamics – the deep interaction between light and matter. Some of his techniques were developed during wartime work on the theory of radar; he started then to look at nuclear physics as an electronics engineer might do. He loved music to such an extent that at one time he wondered if he would become a composer by the age of 30, but a year before that he was a professor of physics at Harvard.

To students and colleagues he would sometimes give the appearance of being austere and withdrawn, and would not allow questions in his lectures, but this was part of the high level of concentration he focused on whatever he was doing. His wife recalled after his death that when a little niece was asked why she loved Uncle Julian she said: ‘Because he listens.’ At Harvard he took on a greater number of research students than most, inspiring them to such an extent that four followed as Nobel laureates.

One of these, Sheldon Glashow, took the work of linking the weak and electromagnetic interactions a step further. He noted that the weak interactions and electromagnetism can both be categorised by Lie groups, and suggested that that each of these Lie groups would fit together very neatly into a bigger overall Lie group, called U(2).

Any hope of confirmation of this meant having to overcome two big challenges. The first of these involved the production of a particle.

Electricity and magnetism are the forces which together create light waves and many other forms of electromagnetic radiation, such as radio waves and X-rays. We are used to a very smooth action of electricity and magnetism in daily life, but when these forces act on a very small subatomic particle, it is more of a jerky kind of encounter, that looks like a strike from a very small pulse of electromagnetic energy. This pulse of energy behaves like a particle and is called a photon.

So if the weak interactions were to be brought into the same framework as electromagnetism, there would have to be some kind of ‘weak interaction photon’ involved in them as well.

Somehow some additional factor had to be found that could be applied to the proposed ‘electroweak’ force, and enable the weak interactions to express themselves in a very tight burst of energy forming a particle.

Schwinger knew a method that might do it – an additional type of symmetry whose origin went back forty years.

When we speak of forces, the best language to use is that of a field. Instead of looking at forces as something tangible being carried by particles, we have to go to a deeper level and see the forces as being somehow ‘carried’ by empty space – or having some deeper level of existence. When we travel through space, we feel the influences of these forces, through such phenomena as electricity, magnetism, gravitation, which are somehow ‘there’ like the plough-marks on a field. We have to imagine that the earth is removed – while the plough-marks remain. (Perhaps this is what Lewis Carroll meant in Alice in Wonderland when the Cheshire cat’s face gradually vanished from view, leaving only the grin behind.)

When Michael Faraday introduced the concept of a field, he met almost total disbelief, as no one could see how empty space could carry any kind of imprint. the majority of pysicists of the time saw electricity and magnetism as forces that leaped across a gap, from object to object, indeed like electric sparks. Faraday looked instead at the empty space between objects as the matrix from which the forces emerged. Out in a boat on a lake in Switzerland, he saw a rainbow at the base of a waterfall, with the wind blowing spray across it so that the rainbow disappeared. Then another gust would come and blow the spray in another direction and rainbow would reappear. Faraday felt that in the same way, when all the clutter of matter was removed to leave apparently empty space, deep down there would be a structure – and this is what is expressed by the concept of the field.

Now when we map a field, we start to put numbers in, with so many units of field strength at any particular point, and it is reasonable to assume that the overall picture of the field should not depend on the particular location-numbers which we have used on the chart. This is a kind of deep symmetry, whereby we can make many kinds of variations in the mapping system and still retain the exact same description of the field.

This turns out to be a much tighter requirement than we might have expected. In fact, if we start with an electric field on its own, we find that the requirement leads us to the appearance of an additional field – which is just the familiar magnetic one. So the reason why electricity and magnetism are linked closely is that this is in accordance with a deep underlying symmetry.

This deep symmetry is called gauge symmetry, and it was first developed in 1918 by the German physicist Herman Weyl, one of the very few at the time who realised the potential power of Lie groups for physics.

In 1954 Chen-Ning Yang and his student Robert Mills at the Institute for Advanced Study at Princeton applied gauge symmetry to a model of the strong interactions. They found that the outcome was a particle that looked like the photon but in addition one or more other particles that had an electric charge and so had more of the properties of the familiar particles such as the proton and neutron.

Meanwhile at Cambridge University, a postgraduate research student came independently to the same conclusions as Yang and Mills. His name was Ron Shaw, and he wrote up the idea in his PhD thesis. When taking his first degree there, he used to enjoy discussions with a fellow mathematician, a Scottish student called James Mackay. Thirty years later, when he was writing a textbook, he recalled a particularly incisive comment by the Scot and expanded on it in one section. By that time he was on his way to becoming professor of mathematical physics at Hull University, and James Mackay, who had switched to law after his graduation, was on his way to becoming Lord Chancellor as Lord Mackay of Clashfern.

It was the work of Yang and Mills that Sheldon Glashow built on. They found that their ideas could only go so far with the strong interactions and did not continue. Glashow, on Schwinger’s advice applied their ideas to the proposed electroweak structure. The outcome of the mathematics was something that looked like a photon – and also something that looked like a ‘weak interaction photon’.

If his thinking was right, there had to be some kind of particle-like behaviour for the weak interaction, some way in which it involved a short burst of energy.

Confirmation of his work would depend on someone getting to work to identify the predicted ‘weak interaction photon’. But there was a snag, so big that it took seven years before the next step was taken, that led to Glashow receiving the Nobel Prize along with two others, Steven Weinberg and Abdus Salam. The breakthrough was to come when they heard about the work of Peter Higgs and others and realised that there was a solution.

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Understanding the Higgs 3: Symmetry for the strong

When the Norwegian mathematician Sophus Lie died in 1899 he was a bitter and disappointed man. True, his mathematical ability had been recognised by some of the greatest people in the field, including the great German mathematician Felix Klein, and Lie had succeeded Klein in the chair of mathematics at Leipzig. But those who understood the true significance of his work and its potential for physics were very few; and indeed after only two years in the post he resigned and went back to Norway and suffered a mental breakdown. His physical health declined as well, and his last years were dark brooding ones, frustrated by his inability to find people who could recognise the significance of his work.

But sixty years after his death the theory he created was established at the very heart of physics.

Sophus Lie developed a theory of symmetry which today is one of the most powerful tools of physics – the theory of a structure called a continuous group.

A group is a collection of operations. If there are a fixed number of them, it is called a finite group, and if there are so many that they run together like the distances on a line, they are called a continuous group – or nowadays a Lie group.

Anyone who has been in the Boys Brigade will be familiar with a finite group of operations – four operations, in fact. The commands Left Turn/Right Turn/About Turn form a group, provided that you also invent a further command Stay as You Are. What gives these four operations the structure of the group is the fact that if we combine any two of them, one after the other, the effect is the same as some other member of the group. This property of closure is one of the features that characterise a group.

That is a finite group – with just four members. We can go on to a much bigger continuous group by extending the possible turns to any number of degrees. This group will contain not only the 90-degree or 180-degree turns that we had originally, but turns through 31.62587 degrees, or 0.0000001 degrees – of whatever number we care to think of.

This new group is built up out of one basic operation – an infinitesimally small turn, since by putting together the appropriate number of copies of this very small term, we can build up to any amount of turning that we please. What we now have is a continuous group, a Lie group, with every member in it generated by the infinitesimal turn.

One of the most powerful uses of the group concept is in the study of symmetry. One way to express the symmetry of a geometrical figure like a square is to observe it remains the same under those four parade-ground turns that we spoke of just now. The study of the symmetry of the square involves identifying the group of operations that keep it unaltered.

We say that the square has a very simple type of rotational symmetry. There are four rotations which leaves the layout unaltered. These are through 90 degrees, 180 degrees, 270 degrees, or 360 degrees.

A circle has a much higher form of rotational symmetry. We can express it in terms of the Lie group of rotations that we have now encountered – with the whole lot of them leaving the shape unaltered. And we can go on to look at the symmetry of shapes like a sphere or a cylinder and in each case find the appropriate Lie group.

Thus the language of the mathematical group applies to geometrical shapes – and it also can be applied to any form of data that looks to have a pattern. The concept of a group involves the categorising of the form of symmetry found in data.

And this leads to the power of this thinking when applied to the world of elementary particles. When people first looked for elementary particles, they found just a very few – ones familiar to us today, such as the proton, the neutron, which between them form the core of an atom, its nucleus, and the electron, which swirls in a cloud around the nucleus to form an atom. But as time went on and particle-detectors became more sophisticated, the number grew of particles, and now there are several hundred.

Quite a lot of them might hardly seem to deserve the name ‘particle’, since they twinkle in and out of existence in a micro-fraction of a second. But to the researchers they still count, and they have been carefully analysed and recorded.

The particles are categorised by numbers, specifying aspects such as their electric charge and various other features. And when the particles are all set out in array, according to the various numbers, patterns start to emerge.

The situation is rather like what happened in chemistry in the 19th century, when the Russian chemist Dmitri Mendeleev studied the properties of the various chemical elements.

It was clear that there were patterns, with some being metals, some being very reactive gases, some being very unreactive gases, and so on. And within each group there were gradations of verious properties. Eventually he set them out in a table. In the form we use it today, eaxch column stands for a different type of element, with the lightest ones at the top and the heaviest at the bottom.

The only snag was that there were gaps in the table. Could they be weakness in the theory? No, said Mendeleev, the gaps stood for elements that have not yet been discovered. The challenge for the experimenters was to find them, and Mendeleev used the table to predict the properties of the missing elements.

In the diagram above, the column on the far right contains very reactive gases – F fluorine at the top, then Cl chlorine, Br bromine, and I iodine (actually solid crystals but only just, vapourising with the heat of your hand). All four were known in Mendeleev’s time, so he could list them, the lightest at the top.

But if we look three columns to the left of this, there is a gap. In the column headed by C carbon, with Si silicon below it, the next space down is empty. Nothing was known in Mendeleev’s time that could fit. But based on the pattern going from carbon and silicon above to indium and tellurium below, he could predict the properties of the missing element.

Look, he said, for something with similarities to silicon. Some thing with a mass of 70 units, a density of 5.5 units, a high melting point – and grey in colour. That was in 1869. Seventeen years later the German chemist Clemens Winkler studied a new mineral from a silver mine and found that when he removed the silver and sulphur from it there was a substance left, which he purified – and discovered germanium, element number 32. Its mass is 72.6, its density 5.35, its melting point 947 degrees – its colour is grey.

In all, Mendeleev had eight predictions for new elements, every one on target.

The particle zoo

Almost a century on from Mendeleev, particle physicists faced a similar type of problem. They had a proliferation of ‘elementary’ particles, as diverse as the animals in a zoo, and the challenge was to find a way to classify them. And that is when they started to discover the work of Sophus Lie.

There are four different types of forces at the particle level. The strong interaction is a powerful attraction operating only at very short range, holding the protons and neutrons in a nucleus of an atom together (otherwise the mutual positive charge of the protons would force themselves apart).

The weak interaction, again very short-range, is involved when particles decay, as in radioactivity.

Thirdly, there is a force more familiar to us – electromagnetism.

Fourthly, another familiar force, gravitation, is at the particle level incredibly weak, 100 million billion billion times weaker than the weak interaction.

For the strongly-interacting particles (they are called hadrons), the breakthrough was made by Murray Gell-Mann and Yuval Ne’eman. They found the hadrons fell into patterns of eights and tens in the pattern of one of Lie’s groups, known as SU(3). Gell-Mann called the approach which led to the octet the Eightfold Way, echoing the Noble Eightfold Path of Buddhism.

In one of the patterns of ten, Gell-Mann and Ne’eman could fit nine known particles into place in a diagram. Based on the details of the nine, they predicted the properties of the missing particle that should sit at the pattern’s apex. They knew what its mass should be, along with its charge, and several other key features, and Gell-Mann christened it the omega-minus – with the Greek symbol Ω.

 

The experimenters took up the challenge, and in 1964 a team at the Brookhaven National Laboratory found the predicted particle.

Both Gell-Mann and Ne’eman made a series of other contributions to physics, and each of them had other interests. Gell-Mann, now in his 80s, is an avid birdwatcher, a collector of antiquities, and a keen linguist, who has established a big research project on the evolution of human languages.

 

Ne’eman, who died some years ago, was a soldier from the age of 15, becoming a brigade commander in the Israeli army. He was a founder of a right-wing breakaway party opposed to peace with Egypt, and for a short time a minister in a coalition government.

Gell-Mann and Ne’eman’s use of Lie groups to predict the omega-minus was the vindication of the life’s work of Sophus Lie, who believed that the principles of physics have their origin in group theory. The power of the tools he gave physics was also applied to the weak interactions.

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Understanding the Higgs 2: What makes light matter?

The big question is: what is the process that somehow freezes or condenses energy into particles of matter? In this process, the energy somehow acquires the characteristic of mass – for which we can go again to David Bohm: ‘Mass is a phenomenon of connecting light rays which go back and forth, sort of freezing them into a pattern.’

It is as if the light ray that flows through space and time has been somehow trapped, its forward motion locked into a extremely tiny circle.

And when the opposite process takes place, in which a particle and antiparticle meet and mutually annihilate, this involves a kind of freeing of the light trapped in each, enabling it to return to its original form and go on its way.

How these processes can happen is the big question in which the search for the Higgs particle has been playing a key part.

One approach to the question has been taken by Roger Penrose. It is a mathematical one, looking at the meaning of some of the existing mathematics in one of the building blocks of modern physics, the Dirac equation.

Paul Dirac himself, brought up by an authoritarian father, was a man of very few words. Graham Farmelo’s biography, The Strangest Man, tells how in childhood Dirac’s father, who had moved to Bristol from Geneva, insisted that his son speak only French to him at mealtimes, which caused great stress. ‘Since I found that I couldn’t express myself in French, it was better for me to stay silent,’ said Dirac in later life.

His deeper feelings came out instead in his mathematics, and in his belief in mathematical beauty. If a piece of scientific theory has mathematical beauty, he said, then it has to be true.

‘In fact,’ he said at the age of seventy, ‘one can feel so strongly about these things, that when an experimental result turns up which is not in agreement with one’s beliefs, one may perhaps make the prediction that the experimental result is wrong and that the experimenters will correct it after a while. Of course one must not be too obstinate over these matters, but still one must sometimes be bold.’

Dirac’s equation, elegant and today inscribed on the wall of Westminster Abbey, is a miracle of compression. A very few symbols between them bring together quantum theory and relativity for the electron.

It looks so compact that it is difficult to believe that so few symbols could contain so much, but indeed its situation is a bit like that of some modern device such as a mobile phone. It may look simple from the outside, but when we open up the case we see all kinds of complex material within.

The Dirac equation can in fact be unpacked in a variety of ways. Roger Penrose’s approach is to note that although the equation represents a single electron, it can also be seen as carrying two separate mathematical components, bundled up so well together that you might never notice their individual existence.

Each of these two hidden components in the Dirac equation represents a motion of the electron and there are two unusual features about them. First, the motion represented by each is a movement at the speed of light, made by something that is massless. And second, there is difference in direction between them, so that together they make a kind of zig-zag motion. In fact, he nicknames them ‘zig’ and ‘zag’. Very small and very fast zigs and zags, every one of them at the speed of light, aggregate to give a slower motion forward for the electron. It is like a ship heading into the wind and tacking to left and to right to make progress. Some of the motion cancels out some of the motion build up as a slower forward progress.

Somehow the two underlying massless components that are concealed in the Dirac equation aggregate together and produce an effect that from a distance we see as the forward motion of a mass-possessing electron.

And what is the nature of the interaction between the massless zig and the massless zag? Penrose notes that the mathematics of the Dirac equation show that this is none other than the Higgs field, the source that has been postulated as the origin of mass and which as a kind of by-product can give us the Higgs particle.

In other words, there is a mechanism which somehow binds massless light-energy into mass-possessing matter, and this process – called the Higgs mechanism – is what has now been validated by the discovery of one of its products, the Higgs particle.

The approach that Peter Higgs and others took did not begin with the Dirac equation, but with an even older concept, going back to a little-understood Norwegian who died over a century ago.

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