Baggott J. The Quantum Story: A History in 40 Moments

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the quantum story

220

known particles turned up ﬁ ve 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 ﬁ xed on SU(3).

He published his own version of the Eightfold Way in July 1961.

Both Ne’eman and Gell-Mann attended the ‘Rochester’ conference

in June 1962, held not in Rochester that year but at the Organisation

Européenne pour la Recherche Nucléaire (CERN) in Geneva. Both listened

intently to reports of new particles that had been discovered, a triplet of

spin-

³⁄

sigma-star particles (S

, and S

*−

)

with strangeness values

of −1, and a doublet of spin-

³⁄

xi-star particles (X

and X

*−

) with strange-

ness values of −2, which mirrored the spin-½ sigma and xi baryons.

Ne’eman immediately saw that these particles belonged to the deci-

met, to be added to the four delta particles already known. It took just a

moment to realize that with nine particles, the decimet lacked just one

more, yet to be discovered particle. This was a negatively charged particle

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, W

−

. After the discussion, Nicholas Samios, a particle

physicist from Brookhaven National Laboratory, asked Gell-Mann how

he thought the W

−

would decay. Gell-Mann sketched a prediction of its

decay modes on a napkin. Samios tucked the napkin in his pocket.

The pattern had been found. Now came the question of the underlying

explanation.

There remained the issue of the fundamental representation, the funda-

mental triplet at the heart of SU(3), which Gell-Mann had politely ignored.

Robert Serber at Columbia University began to play around with ways of

combining three fundamental ‘objects’ to create the two octets and the

decimet of the Eightfold Way. This was equivalent in many ways to con-

structing the periodic table from combinations of protons, neutrons, and

electrons. Serber, in effect, was asking if there might not be three fundamen-

tal particles, as yet undiscovered, underlying all the particles then known to

These were originally called Y

particles.

three quarks for muster mark!

221

0+1–1

Electric

Charge

Spin–

Baryons

–

∗–

–

∗0

∗+

Strangeness

–3

–2

–1

fig 13 Both Ne’eman and Gell-Mann saw that the newly-discovered triplet of R

particles and the doublet of spin-³⁄

X ≠

particles belonged to the decimet representa-

tion of SU(3). There was one further particle missing. Gell-Mann got there ﬁ rst. He

named the missing particle the X

−

physicists. When Gell-Mann arrived at Columbia in March 1963 to deliver a

series of lectures, Serber asked him what he thought about this.

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?” ’

Gell-Mann had considered it, and he had already dismissed it. He

asked Serber what the electric charges of this fundamental triplet of

objects would be. This was 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 parti-

cles would have to have fractional electric charges— −¹

⁄

, +²⁄

, like so—in

order to add up to a proton or neutron with a charge of plus or zero.’

the quantum story

222

Serber agreed that this was an appalling result. There was absolutely no

evidence for particles with fractional electric charges. In their discussion

Gell-Mann referred to Serber’s objects as ‘quorks’, deliberately chosen as

a nonsense word, and mentioned them in passing during his subsequent

lecture. 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 the discussion had set Gell-Mann thinking. The SU(3) symme-

try group demanded a fundamental representation and the fact that

the known particles could be ﬁ tted into the octet and decimet patterns

was very suggestive of a triplet of fundamental particles. The fractional

charges were problematic but, perhaps, if the ‘quorks’ were forever

trapped or conﬁ ned 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 mysterious 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 scientiﬁ c language.’

Gell-Mann published a short 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 +²⁄

, ‘down’ (d)

with a charge of −¹

⁄

, and ‘strange’ (s), also with a charge of −¹⁄

. Baryons

are formed from various permutations of these three quarks and mesons

from combinations of quarks and anti-quarks.

For example, 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. The ‘strange’ particles,

possessing strangeness quantum numbers other than zero, contain (not

surprisingly) strange quarks. The octet of spin-½ baryons was explained

three quarks for muster mark!

223

in terms of different possible combinations of up, down, and strange

quarks, the octet of spin-0 mesons in terms of combinations of quarks

and anti-quarks. Isospin was now explained in terms of the numbers of

up and down quarks in the composite nucleons. 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.

In his paper he thanked Serber for stimulating discussions.

–1

–1 +1

udd uud

uds

uus

dds

uds

ussdss

Electric

Charge

Spin-½ Baryons

Strangeness

–2

fig 14 The Eightfold Way could be neatly explained in terms of the various pos-

sible combinations of up, down and strange quarks, illustrated here for the octet of

spin-½ baryons . The K

and R

are both composed of up, down and strange quarks

but differ in their isospin.

An entirely equivalent scheme based on a fundamental triplet of particles was worked

out around the same time by Gell-Mann’s former Caltech student, George Zweig. By this time

a post-doctoral student working at CERN, Zweig called his fractionally charged fundamental

particles ‘aces’, and showed how it was possible to construct the baryons from ‘treys’ (triplets)

of aces and the mesons from ‘deuces’ (doublets) of aces and anti-aces. His work was issued as

a CERN preprint but he found that he could not get it published in a refereed journal. Zweig

joined the Caltech faculty in late 1964, and Gell-Mann took pains to ensure he was credited with

his role in the discovery of quarks.

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224

It was a beautifully simplifying scheme, but in truth it was not much

more than the result of playing with the patterns. There was simply no

experimental foundation for the scheme and it was consequently poorly

received. And there was another problem. As spin-½ fermions, the

quarks are subject to the Pauli exclusion principle, which forbids more

than one fermion from occupying a speciﬁ c quantum state. Yet the pro-

ton was meant to contain two up quarks, presumably in the same state;

the neutron two down quarks. How could this be squared with the exclu-

sion principle?

Gell-Mann didn’t help his cause by being rather cagey about the status

of his quarks. Wishing to avoid getting tangled in philosophical debates

about the reality or otherwise of particles that could in principle never be

seen, he referred to the quarks as ‘mathematical’. Some interpreted this

to mean that Gell-Mann didn’t think the quarks were made of real ‘stuff’,

entities that existed in reality and combined to give real effects.

Samios had returned to Brookhaven National Laboratory armed with

Gell-Mann’s suggestions for the decay modes of the W

−

. By mid-Decem-

ber 1963 the experiment to search for the W

−

was ready. On 31 January

1964 Samios and his team of thirty particle physicists found the tell-tale

tracks in a bubble chamber photograph. They ﬁ tted the predictions for

the W

−

almost exactly. Their paper was published in Physical Review on 11

February 1964. Gell-Mann’s paper on quarks had been published in the

CERN journal Physics Letters just ten days earlier.

The Eightfold Way was vindicated, but the quark theory was treated

with derision. From Caltech Gell-Mann called Weisskopf in Geneva, men-

tioning almost in passing that he had had an idea which accounted for all

the baryons and the mesons using particles with fractional charges. ‘Oh

nonsense, Murray,’ Weisskopf responded, ‘Don’t waste time on a trans-

atlantic call talking about stuff like that.’

It was hard to take the theoreticians seriously. Their toying with sym-

metries and gauge theories had turned up massless bosons that actually

had to be massive, weak neutral currents that didn’t exist, and now frac-

tionally charged particles that, by the way, would never reveal themselves.

Just who were these people trying to kid?

225

Some inklings of a possible solution to the problem of massless bosons in Yang–Mills ﬁ eld

theories began to emerge in the early 1960s. The solution was relatively long in gestation,

however, as its origin was in a different discipline, and physicists in different disciplines

rarely communicate with one another. And even when they do, it tends to be in rather

disparaging terms.

The quantum ﬁ eld theorists needed a ‘trick’ that would endow the massless bosons

with mass. Nature itself offered an important clue. Whilst many theoretical physical

descriptions depend on the identiﬁ cation of marvellous symmetries, related to conserved

physical quantities, it is a simple fact that the natural world we live in tends to be rather

more asymmetric in character, with clear preferences for this direction over that. A pencil

perfectly balanced on its tip is symmetrical. But when it topples over it does so in a speciﬁ c

direction. The symmetry is said to be spontaneously broken.

It might seem a little curious that after expending considerable energy searching for

the symmetries in nature, the physicists should now seek to ﬁ nd out how to break them.

Considerable progress had been made in solid-state physics, a branch of physics concerned

with the properties and behaviour of crystalline solids.

The archetypal example of spontaneous symmetry-breaking in a solid is afforded by a

simple ferromagnet. Heat a bar magnet to a high enough temperature and the alignment

of the iron atom magnetic moments becomes scrambled. The orientations of the atoms in

the bar become symmetric, favouring no particular direction, and the bar loses its mag-

netism. As the bar cools back to room temperature, the iron atoms start to crystallize and

The ‘God Particle’

Cambridge, Massachusetts, Autumn 1967

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226

a preferred orientation gradually emerges as their magnetic moments become aligned

once more.

The symmetry is spontaneously broken, and the bar becomes asymmetric as

‘north’ and ‘south’ poles are re-established.

Whilst spontaneous symmetry-breaking was familiar to solid-state physicists, it

was unfamiliar to quantum ﬁ eld theorists or particle physicists. The latter saw them-

selves as purists, dealing with theories of the physical world at its most fundamental.

They tended to perceive the physics of solids as horribly complex and riddled with

simplifying assumptions. Gell-Mann reﬂ ected something of this attitude when he

referred to the discipline as ‘squalid-state’ physics. In their turn, solid-state physicists

tended to be rather dismissive of what they perceived as particle physicists’ naïvety

about how the physical world really worked.

However, a sense of desperation can help to overcome any such social barriers, espe-

cially if the unfamiliar discipline offers the hope of a solution. In 1960, Japanese-born

American physicist Yoichiro Nambu drew analogies with the theory of superconductiv-

ity, an example of spontaneous symmetry-breaking in the gauge ﬁ eld of electromagnet-

ism, and suggested that this might be a mechanism that could give mass to the massless

Yang–Mills bosons. British-born physicist Jeffrey Goldstone went further. In 1961 he

studied the effects of symmetry-breaking and concluded that one consequence was the

production of yet more massless bosons.

This was not helping. In trying to ﬁ nd a way to give mass to the massless bosons of

quantum ﬁ eld theories, Goldstone had found that spontaneous symmetry-breaking cre-

ated even more massless particles.

It seemed like a dead end.

Abdus Salam had also identiﬁ ed spontaneous symmetry-breaking as a

potential solution. He and Steven Weinberg attended a conference at the

University of Wisconsin in Madison in the summer of 1961, where they

met Goldstone.

Goldstone told them about what he had discovered. He had found that

the only way to make the ﬁ eld theory of the symmetrical case equivalent

to the ﬁ eld theory with broken symmetry was to introduce an additional

In the absence of an externally applied magnetic ﬁ eld.

This does not mean that all symmetry is lost. The cold bar magnet retains some intrinsic

symmetries, but the symmetry group that contains these is a subset of the larger group that

characterizes the hot iron bar.

the ‘god particle’

227

massless boson, which came to be called a Nambu–Goldstone boson.

Although he had derived this result for some selected symmetries, he felt

instinctively that this would prove to be a general result, and elevated it to

the status of a principle. It became known as the Goldstone theorem.

Of course, these Nambu–Goldstone particles suffered from precisely

the same objections as the Yang–Mills bosons themselves. Massless par-

ticles, such as the photon, are associated with long-range forces, such

as electromagnetism. The short-range nuclear forces were expected to

be associated with massive particles. Any new massless particles pre-

dicted by theory could be expected to be as ubiquitous as photons. But,

of course, these additional particles had never been observed. They just

didn’t ﬁ t the bill.

Salam and Weinberg didn’t believe it. They called the new massless parti-

cle a ‘snake in the grass’ and worked together at Imperial College in London

that autumn to prove that it didn’t exist. They ended up proving precisely

the opposite. Nambu–Goldstone bosons appeared whenever isospin or

strangeness symmetries were broken. They published a paper jointly with

Goldstone to this effect in August 1962. Weinberg was dismayed:

I remember being so discouraged by these zero masses that when we

wrote our joint paper on the subject . . . I added an epigraph to the paper

to underscore the futility of supposing that anything could be explained

in terms of a non-invariant vacuum state: it was Lear’s retort to Cordelia,

‘Nothing will come of nothing: speak again.’

Goldstone had assumed that empty space—the vacuum—is ﬁ lled with

a hypothetical ﬁ eld which breaks the symmetry. It was a kind of elabo-

rate ‘ether’. Weinberg’s quote from King Lear was a sorry reﬂ ection on

the futility of trying to conjure mass from the vacuum. The editors of

Physical Review, not much given to ﬂ ights of dramatic fancy, duly excised

the quotation from the paper.

If any progress was to be made, some way of avoiding or beating the

Goldstone theorem had to be found.

For their part, the solid-state physicists were rather nonplussed. They

had been working with broken symmetries in crystalline solids for many

the quantum story

228

years and had uncovered no new massless particles in systems with a

local gauge symmetry. In the theory of superconductivity developed in

1957 by John Bardeen, Leon Cooper, and John Schrieffer, no new particles

had to be invoked to explain why certain materials, when cooled below a

critical temperature, lose all their electrical resistance.

We learn early on in our science education that like charges repel

each other. However, electrons in a superconductor experience a mutual

attraction, albeit weak. What happens is that an 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. This

vibration produces a region of 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 lat-

tice vibrations. Electrons are fermions and, as such, they are forbidden

from occupying the same quantum state by the Pauli exclusion principle.

In contrast, Cooper pairs behave like bosons: there is no restriction on

the number of pairs that can occupy a quantum state and at low tem-

peratures they can experience Bose condensation, gathering in a single

macroscopic quantum state.

The Cooper pairs in this state experience

no resistance as they pass through the lattice and the result is supercon-

ductivity.

The Bardeen–Cooper–Schrieffer theory of superconductivity is not

only elegant, it explains an otherwise puzzling set of phenomena entirely

within the framework of quantum electrodynamics. Other than symme-

try-breaking of the electromagnetic ﬁ eld, no new features and no new

particles are required.

This kind of logic led sold-state physicist Philip Anderson to reject the

Goldstone theorem. It was transparently obvious from many practical

examples in solid-state physics that Nambu–Goldstone bosons are not

always produced when gauge symmetries are spontaneously broken.

What are produced are quantized collective excitations, vibrations of the

Laser light is an example of Bose condensation involving photons.

the ‘god particle’

229

lattice, which can be thought of as the quantum particle equivalent of

wave patterns established in the solid. There was nothing particularly

mysterious about these.

In 1963, Anderson suggested that the problems the quantum ﬁ eld the-

orists were wrestling with may in some way resolve themselves:

It is likely, then, considering the superconducting analogue, that the way is

now open without any difﬁ culties involving either zero-mass Yang–Mills

gauge bosons or zero-mass [Nambu–]Goldstone bosons. These two types

of bosons seem capable of ‘canceling each other out’ and leaving ﬁ nite

mass bosons only.

It was to prove a prescient proposal. It was also roundly ignored.

Anderson was a solid-state physicist and it was therefore assumed that

he had little to say that might be of interest to quantum ﬁ eld theorists

or particle physicists. And, as Anderson had provided no formal proof

that the Goldstone theorem was invalid, those few theorists who did note

what he had to say tended to disbelieve him.

Anderson’s paper did provoke a minor controversy over the domain of

applicability of quantum ﬁ eld theory. In 1964 this led, in turn, to a number

of papers detailing mechanisms for spontaneous symmetry-breaking

in which the various massless bosons did indeed ‘cancel each other out’,

leaving only massive particles. These were published independently by

Belgian physicists Robert Brout and François Englert working at Cornell

University in New York State, English physicist Peter Higgs at Edinburgh,

and Gerald Guralnik, Carl Hagen, and Tom Kibble at Imperial College in

London.

The mechanism is commonly referred to as the Higgs mechanism.

In a paper published earlier in 1964, Higgs established that Anderson’s

instincts concerning the boson problem were essentially correct,

although this happens to be the case just for Yang–Mills gauge theo-

ries. The Nambu–Goldstone bosons produced by symmetry-breaking

These three papers were all published in the same volume (13) of the journal Physical Review

Letters in 1964, on pp. 321–323, 508–509 and 585–587, respectively.