____________
Gell-Mann was working alone but he was not the only theorist searching for a pattern. Yuval Ne’eman was a late entrant to the firmament of theoretical physics. Where Gell-Mann had gone to Yale at the tender age of fifteen, Ne’eman, a native of Tel Aviv, had joined the Haganah, the Jewish underground, in what was then the British Mandate for Palestine. He had commanded an infantry battalion in the 1948 Arab–Israeli war and served as acting head of the Israeli Secret Service.
He had achieved the rank of Colonel in the Israeli Defense Force when he decided to seek an opportunity to study for a doctorate in physics. Moshe Dayan, defense chief of staff, agreed to appoint him as a defence attaché at the Israeli Embassy in London. Dayan figured that Ne’eman could study for his PhD in his spare time.
Ne’eman had originally intended to study relativity at King’s College in London, but he quickly discovered that the city traffic made it impossible for him to get there from the Embassy in Kensington in time to attend lectures and seminars. He switched to Imperial College and particle physics. At Imperial College he was pointed in the direction of Pakistan-born theorist Abdus Salam.
Ne’eman worked in the evenings and at weekends. He began a search for symmetry groups that might accommodate the known particles and turned up five candidates, including SU(3). Initially excited by the very resonant possibilities afforded by a symmetry group that produced a Star of David pattern, Ne’eman eventually fixed on SU(3). He published his own version of the Eightfold Way in July 1961.
Salam was initially sceptical, but when a draft of Gell-Mann’s paper arrived on his desk he quickly set aside his reservations. Despite having a slight head start, Ne’eman was beaten into print by Gell-Mann (although Ne’eman’s paper was actually the first to be published in a physics journal). But he was not disappointed. On the contrary, he was thrilled to find himself in such good company.
Both Ne’eman and Gell-Mann attended a particle physics conference in June 1962, held at the Organisation Européenne pour la Recherche Nucléaire (CERN) in Geneva. Both listened intently to reports of further new particles that had been discovered, a triplet of what later came to be called sigma-star particles with strangeness values of –1, and a doublet of xi-star particles with strangeness values of –2.
Ne’eman saw immediately that these particles belonged to another representation of SU(3) consisting of ten dimensions. It took him just a moment to realize that of the ten particles implied by this representation, nine had now been found. The particle needed to complete the pattern was negatively charged with a strangeness value of –3.
He raised his hand to speak, but Gell-Mann had made precisely the same connection and was sitting closer to the front of the auditorium. It was therefore Gell-Mann who stood to predict the existence of a particle he called the omega. It was discovered in January 1964.
The pattern had now been found, but what of the underlying explanation?
4
Applying the Right Ideas to the Wrong Problem
____________
In which Murray Gell-Mann and George Zweig invent quarks and Steven Weinberg and Abdus Salam use the Higgs mechanism to give mass to the W and Z particles (finally!)
Japanese-born American physicist Yoichiro Nambu was deeply worried.
Nambu had studied physics at Tokyo Imperial University, graduating in 1942. He was drawn to particle physics by the reputations of Yoshio Nishina, Sin-Itiro Tomonaga, and Hideki Yukawa, the founders of particle physics in Japan. But there was no great particle physicist in Tokyo, so he studied the physics of solids instead.
From Tokyo, Nambu moved in 1949 to take up a professorship at Osaka City University. Three years later he was invited to the Institute for Advanced Study in Princeton. He moved to the University of Chicago in 1954 and was appointed to a professorship there four years later.
In 1956 he attended a seminar given by John Schrieffer on the new theory of superconductivity he had developed together with John Bardeen and Leon Cooper. This was an elegant application of quantum theory to explain why certain crystalline materials, when cooled below a critical temperature, lose all their electrical resistance. They become superconductors.
Like charges repel each other. However, electrons in a superconductor experience a weak mutual attraction. What happens is that a free electron passing close to a positively charged ion in the crystal lattice exerts an attractive force which pulls the ion out of position slightly, distorting the lattice. The electron moves on, but the distorted lattice continues to vibrate back and forth. This vibration produces a slight excess positive charge, which attracts a second electron.
The upshot of this interaction is that a pair of electrons (called a ‘Cooper pair’), each with opposite spin and momentum, move through the lattice cooperatively, their motion mediated or facilitated by the lattice vibrations. Recall that electrons are fermions and, as such, they are forbidden from occupying the same quantum state by Pauli’s exclusion principle. In contrast, Cooper pairs behave like bosons, which are not so constrained. There is no restriction on the number of pairs that can occupy a quantum state and at low temperatures they can ‘condense’, gathering in a single state which can build to macroscopic dimensions.* The Cooper pairs in this state experience no resistance as they pass through the lattice and the result is superconductivity.
What worried Nambu was that the theory did not seem to respect the gauge invariance of the electromagnetic field. In other words, it did not seem to respect the conservation of electric charge.
Nambu nagged away at this problem and was able to draw on his background in solid-state physics. He realized that the Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity is an example of spontaneous symmetry-breaking applied to the gauge field of electromagnetism.
Examples of symmetry-breaking are common. A pencil balanced on its tip is perfectly symmetrical, but very unstable. When it topples over it does so in a specific (though apparently random) direction, and the symmetry is said to be spontaneously broken. Likewise, a marble balanced atop a sombrero is perfectly symmetrical, but unstable. The marble rolls down a specific (though apparently random) direction and comes to rest in the shallow brim of the hat. In truth, tiny fluctuations of the background environment are responsible for the pencil toppling over or the marble rolling down the hat. These tiny fluctuations form part of the background ‘noise’.
Spontaneous symmetry-breaking affects the lowest-energy, so-called ‘vacuum’ state of a system. Like any material, a superconductor could be expected to have a vacuum state in which all particles retain fixed positions in the lattice structure and its electrons remain motionless. However, the possibility of cooperative motions of Cooper pairs mediated by lattice vibrations results in a vacuum state that is lower in energy. In this case, the U(1) gauge symmetry of electromagnetism is broken by the presence of another quantum field, whose quanta are the Cooper pairs. The laws describing the dynamics of electrons in the material remain invariant under the local U(1) gauge symmetry, but the vacuum state does not.
Nambu realized that because the Cooper pairs exist in a state of lower energy, it is now necessary to input energy to break them apart. Free electrons created in this way would possess an additional energy equal to half the energy required to break the pairs apart. This additional energy would appear as extra mass. He was struck by the possibilities, and summarized these some years later as follows:1
What would happen if a kind of superconducting material occupied all of the universe, and we were living in it? Since we cannot observe the true vacuum, the [lowest-energy] ground state of this medium would become the vacuum, in fact. Then even particles which were massless…in the true vacuum would acquire mass in the real world.
Break the symmetry, Nambu reasoned, and you get particles with mass.
In 1961, Nambu and Italian physicist Giovanni Jona-Lasinio published a paper which outlined just such a mechanism. To get it to work, they had to invoke a background quantum fi
eld which creates a ‘false’ vacuum. In the above example, the pencil topples over when it interacts with the background ‘noise’, breaking the symmetry. Similarly, to break the symmetry in a quantum field theory requires a background with which to interact. What this implies is that empty space is not actually empty. It contains energy in the form of an all-pervasive quantum field.
In their model, this false vacuum provided the background required to break the symmetry in a theory of strong-force interactions involving hypothetical massless protons and neutrons. The result was indeed protons and neutrons with mass. Breaking the symmetry had ‘switched on’ the particle masses.
But this was not plain-sailing. British-born physicist Jeffrey Goldstone also studied symmetry-breaking and concluded that one consequence is the creation of yet another massless particle.
In fact, Nambu and Jona-Lasinio had actually stumbled across the same problem in their model. In addition to giving mass to protons and neutrons, their model also predicted massless particles formed from nucleons and anti-nucleons. In their paper they had tried to argue that these may actually acquire a small mass and so could be identified as pions.
These new massless particles came to be called Nambu–Goldstone bosons. Goldstone felt instinctively that the creation of these particles would prove to be a general result, applicable for all symmetries, and in 1961 elevated it to the status of a principle. It became known as the Goldstone theorem.
Of course, these Nambu–Goldstone bosons suffered from precisely the same objections as the massless particles of the quantum field theories. Any new massless particles predicted by theory could be expected to be as ubiquitous as photons. But, of course, these additional particles had never been observed.
Spontaneous symmetry-breaking promised a solution to the problem of massless particles in Yang–Mills field theories. Yet symmetry-breaking had to be accompanied by yet more massless particles that had never been seen. As one problem was fixed, another was created. If any progress was to be made, some way of avoiding or beating the Goldstone theorem had to be found.
____________
Both Gell-Mann and Ne’eman had skipped over the fundamental representation of the global SU(3) symmetry group. They had found that they could accommodate the proton and neutron in the next, eight-dimensional representation, applied to baryons. The implications were fairly obvious. The eight members of the baryon octet – including the proton and neutron – must be composites formed from three even more fundamental particles unknown to experimental science. Obvious, perhaps, but this was a conjecture with some very uncomfortable consequences.
In 1963 Robert Serber at Columbia University began to toy with combinations of three (unspecified) fundamental particles to create the two octets of the Eightfold Way. In this model, each member of the baryon octet would be formed from combinations of the three new particles, and the meson octet from combinations of the fundamental particles and their anti-particles. When in March that year Gell-Mann arrived at Columbia University to deliver a series of lectures, Serber asked him what he thought about this idea.
The conversation took place over lunch at the Columbia Faculty Club.
‘I pointed out that you could take three pieces and make protons and neutrons,’ Serber explained. ‘Pieces and anti-pieces could make mesons. So I said “Why don’t you consider that?”’2
Gell-Mann was dismissive. He asked Serber what the electric charges of this new triplet of fundamental particles would need to be, something Serber hadn’t considered.
‘It was a crazy idea,’ Gell-Mann said. ‘I grabbed the back of a napkin and did the necessary calculations to show that to do this would mean that the particles would have to have fractional electric charges like so – in order to add up to a proton or neutron with a charge of plus one or zero.’3
Serber agreed that this was an appalling result. Just twelve years after the discovery of the electron, American physicists Robert Millikan and Harvey Fletcher had performed their famous ‘oil drop’ experiment, measuring the fundamental unit of electric charge carried by a single electron. When reported in standard units, the charge on the electron is a complicated number with many decimal places,* but it was quickly recognized that all charged particles carry charges that are integral multiples of this fundamental unit. At no time in the 54 years that had elapsed since the notion of a fundamental unit of charge had been established had there been even the merest hint that there might exist particles with charge less than this.
In their subsequent discussion Gell-Mann called Serber’s new particles ‘quorks’, a nonsense word deliberately chosen to highlight the absurdity of the suggestion. Serber took the word as a derivative of ‘quirk’, as Gell-Mann had said that such particles would indeed be a strange quirk of nature.
But despite the appalling consequences, the logic was inescapable. The SU(3) symmetry group demanded a fundamental representation and the fact that the known particles could be fitted into the two octet patterns was very suggestive of a triplet of fundamental particles. The fractional charges were problematic but perhaps, Gell-Mann now reasoned, if the ‘quorks’ were forever trapped or confined inside the larger hadrons then this might explain why fractionally charged particles had never been seen in experiments.
As Gell-Mann’s ideas took shape, he happened on a passage from James Joyce’s Finnegan’s Wake which gave him a basis for the name of these ridiculous new particles:
Three quarks for Muster Mark!
Sure he hasn’t got much of a bark.
And sure any he has it’s all beside the mark.
‘That’s it!’ he declared, ‘Three quarks make a neutron and a proton!’ The word didn’t quite rhyme with his original ‘quork’ but it was close enough. ‘So that was the name I chose. The whole thing is just a gag. It’s a reaction against pretentious scientific language.’4
Gell-Mann published a two-page article explaining this idea in February 1964. He referred to the three quarks as u, d, and s. Although he didn’t say so in his paper, these stood for ‘up’ (u), with a charge of , ‘down’ (d) with a charge of , and ‘strange’ (s), also with a charge of . Baryons are formed from various permutations of these three quarks, and mesons from combinations of quarks and anti-quarks.
In this scheme the proton consists of two up-quarks and a down-quark (uud), with a total charge of +1. The neutron consists of an up-quark and two down-quarks (udd), with a total charge of zero. As the model was elaborated, it transpired that isospin is related to the content of up- and down-quarks in the composite particle. The neutron and proton possess isospins that can be calculated as half the number of up-quarks minus the number of down-quarks.* For the neutron this gives an isospin of ½×(1 – 2), or –½. ‘Rotating’ the isospin of the neutron is then equivalent to changing a down-quark into an up-quark, giving a proton with an isospin of ½×(2 – 1), or +½. The conservation of isospin now becomes the conservation of quark number. Beta-radioactivity now involves the conversion of a down-quark in a neutron into an up-quark, turning the neutron into a proton, with the emission of a W− particle, as shown in Figure 11.
The ‘strange’ particles have strangeness values given simply as minus the number of strange-quarks present.† It was now apparent that a graph of charge or isospin versus strangeness simply maps out the quark content of the particles, with different combinations of quarks appearing at different locations on the map (see Figure 12).
Once again, Gell-Mann was working alone but was not the only theorist on the trail of an underlying explanation. Having returned from Britain to Israel a couple of years before, Ne’eman and Israeli mathematician Haim Goldberg had worked on a very speculative proposal concerning a fundamental triplet, but they had stepped back from declaring that these could be ‘real’ particles with fractional electric charges.
FIGURE 11 The mechanism of nuclear beta-decay is now explained in terms of the weak-force decay of a down-quark inside a neutron (d) into an up-quark (u), turning the neutron into a proton
, with the emission of a virtual W− particle.
FIGURE 12 The Eightfold Way could be neatly explained in terms of the various possible combinations of up-, down-and strange-quarks, illustrated here for the baryon octet. The Λo and Σ0 are both composed of up-, down-, and strange-quarks but differ in their isospin. The Λo has isospin zero and Σ0 has isospin 1. This difference can be traced to the different possible combinations of the up-down quark wavefunctions. The Λo has an anti-symmetric (ud – du) combination, the Σ0 has a symmetric (ud + du) combination.
At around the same time that Gell-Mann’s speculations appeared in print, former Caltech student George Zweig had developed an entirely equivalent scheme based on a fundamental triplet of particles that he called ‘aces’. He figured that baryons could be constructed from ‘treys’ (triplets) of aces and the mesons from ‘deuces’ (doublets) of aces and anti-aces. Zweig was working as a postdoctoral associate at CERN, and published his ideas as a CERN preprint in January 1964. Having subsequently seen Gell-Mann’s paper, he moved quickly to elaborate the model, produced a second, 80-page CERN preprint, and submitted this to the prestigious journal Physical Review.
He was shouted down by his peer reviewers. The paper was never published.
Gell-Mann was already an established physicist, with many notable discoveries to his credit, and could be forgiven his ‘lapse’ of judgement over the quarks. As a young postdoctoral associate, Zweig was not in such a fortunate position. When shortly afterwards he sought an appointment at a leading university, one of the faculty members, a respected senior theorist, declared the ace model to be the work of a charlatan. Zweig was denied the appointment, and re-joined the Caltech faculty in late 1964. Gell-Mann later took pains to ensure Zweig was credited with his role in the discovery of quarks.
Higgs:The invention and discovery of the 'God Particle' Page 7
