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

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the quantum story

210

The tau and theta particles became one particle, the positive kaon.

There followed further skirmishes between theoreticians and experi-

mentalists over the precise nature of the weak force. Gell-Mann had in

the meantime moved to the California Institute of Technology (Caltech)

in 1955, where he worked with Feynman on a theory of the weak nuclear

force and became enamored of Yang–Mills ﬁ eld theory.

Feynman and Gell-Mann, and two other physicists, Indian-American

George Sudarshan and American Robert Marshak, argued that the weak

force had to possess certain so-called vector properties, in contradiction

to the experimentalists’ interpretation of the evidence. The theorists pre-

vailed. Further experiments performed in late 1957 by Maurice Goldhaber

and his colleagues at Brookhaven established that the neutrino is ‘left-

handed’ and the anti-neutrino ‘right-handed’, conﬁ rming the universal-

ity of the Universal Fermi Interaction and establishing the weak force as

a fundamental force of nature.

In his landmark paper on beta radioactivity, Fermi had drawn on the

analogy between the weak force and electromagnetism. He had made

his estimates of the relative strengths of the forces using the electron

mass as a yardstick. In 1941, Schwinger had pondered on the implica-

tions of assuming that the weak force is carried by a much larger particle.

He estimated that if this ﬁ eld particle was actually a couple of hundred

times the proton mass, then the coupling strengths of the weak and

electromagnetic forces might actually be the same.

It was the ﬁ rst hint that the weak and electromagnetic forces could be

uniﬁ ed.

In November 1957, Schwinger published an article in the journal Annals

of Physics in which he speculated that the weak force is mediated by three

ﬁ eld particles. Two of these particles, the W

and W

−

were necessary to

account for the transmission of electric charge in weak interactions. The

third was needed to account for instances in which no charge is trans-

ferred. This third, neutral, particle was, he believed, the photon.

Yang and Lee were awarded the 1957 Nobel Prize for physics for their suggestion.

Again, for the purposes of clarity I am using the currently accepted names for these particles.

some strangeness in the proportion

211

Beta radioactivity would now work like this. A neutron would

decay, emitting a massive W

−

particle and turning into a proton. The

short-lived W

−

would in turn decay into a high-speed electron and an

anti-neutrino.

Schwinger had manipulated his theory to be consistent with the

prevailing interpretation of the nature of the weak force. When that

interpretation was shown to be false, he abandoned work on weak inter-

actions completely. However, he had in the meantime assigned one of

his Harvard graduate students to work on the problem. His name was

Sheldon Glashow.

An American-born son of Russian Jewish immigrants, Glashow

graduated from the Bronx High School of Science in 1950 together with

classmates Steven Weinberg and Gerald Feinberg. He moved to Cornell

University with Weinberg, securing his bachelor’s degree in 1954. From

Cornell Glashow moved to Harvard, where he became one of Schwinger’s

graduate students.

As a doctoral project, Schwinger asked him to think about the W

and

−

as carriers of the weak nuclear force and for two years this is precisely

what he did. He thought about it.

What he realized was that the electric charges carried by the W parti-

cles meant that it was impossible to separate the theory of the weak force

from that of electromagnetism. ‘We should care to suggest,’ he wrote in

an appendix to his PhD thesis, ‘that a fully acceptable theory of these

interactions may only be achieved if they are treated together . . .’

Glashow reached for the SU(2) ﬁ eld theory that had been developed

by Yang and Mills, taking ‘on faith’ Schwinger’s argument that the three

ﬁ eld particles were the two W particles and the photon. He took care to

ensure that interactions involving the W particles would violate the con-

servation of both parity and strangeness, but that interactions involving

the photon would not. Although the result was rather ugly, by November

1958 Glashow thought he had arrived at a deﬁ nitive uniﬁ ed theory of the

weak and electromagnetic forces. What’s more, he believed his theory

was renormalizable.

But any euphoria he experienced was to be short-lived. He had com-

pleted a paper on the theory whilst working at Niels Bohr’s Institute

for Theoretical Physics in Copenhagen. In the spring of 1959 he visited

the quantum story

212

London and delivered a lecture on the subject. Sitting in the audience,

Pakistan-born theoretical physicist Abdus Salam and his collaborator

John Ward were stunned. Inspired by Schwinger’s paper they, too, had

been working on a Yang–Mills SU(2) ﬁ eld theory involving two charged

ﬁ eld particles and the photon. The problem was that, try as they might,

they could not make their theory renormalizable.

Glashow had made a series of errors. When these were exposed, he

retreated to Copenhagen to think about it some more.

It was easy to dismiss Glashow’s errors as the folly of youthful inexperi-

ence ( he was still only 26, Salam was 33). And yet the result of his further

reﬂ ection on the problem was nothing short of youthful bravado. As a

ﬁ eld particle in an SU(2) theory of both weak and electromagnetic interac-

tions, the photon had been forced to do too much. It was doubling as the

carrier of both the weak and electromagnetic forces, tasks that tortured

the theory in what Glashow now realized were unacceptable ways.

The solution was to enlarge the symmetry by combining the Yang–

Mills SU(2) gauge ﬁ eld with the U(1) gauge ﬁ eld of electromagnetism, in

a product written SU(2) × U(1). This came at the cost of full uniﬁ cation,

but had the advantage that it freed the photon from responsibility for

carrying the weak force. However, this also meant that it was necessary

to introduce yet another ﬁ eld particle to account for neutral weak-force

interactions, so-called ‘weak neutral currents’.

In effect, Glashow now

had three weak-force particles equivalent to the triplet of B particles ﬁ rst

introduced by Yang and Mills. These were the W

, W

−

, and Z

Glashow lectured in Paris in March 1960, where he encountered Gell-

Mann, on sabbatical leave from Caltech and working as a visiting pro-

fessor at the Collège de France. Over lunch, Glashow described his SU(2)

× U(1) theory and Gell-Mann offered encouragement. ‘What you’re doing

is good,’ Gell-Mann told him, ‘But people will be very stupid about it.’ Gell-

Mann also extended an invitation for Glashow to join him at Caltech.

When such weak-force interactions involve charged intermediaries they are called charged

‘currents’, as they involve the ﬂ ow of charge from one particle to another. By analogy, the weak-

force interactions involving the exchange of neutral force particles are sometimes referred to as

neutral currents.

Glashow originally referred to the neutral particle as B, by analogy with Yang and Mills,

but it is now commonly referred to as the Z

some strangeness in the proportion

213

Gell-Mann decided to present Glashow’s as yet unpublished

work at

the next high-energy physics conference, to be held in Rochester, New

York, from 25 August to 1 September 1960. The Rochester conferences,

ﬁ rst established in 1950, were intended to mirror the exclusive tradition

of the Shelter Island and Pocono conferences, but included experimental

particle physicists as well as theoreticians. Glashow had thus far articu-

lated the theory in Schwinger’s impenetrable style, and Gell-Mann now

offered a translation in a language that more physicists would under-

stand. The reaction from conference participants was underwhelming.

In truth, the theory did not seem to have that much going for it.

Nobody had yet been able to solve the problem of how the W

, W

−

, and

particles were supposed to acquire their mass. Just as Yang and Mills

had discovered, the ﬁ eld theory predicted that the force carriers should

be massless, like the photon. The carriers of the weak force needed to be

massive particles, however, and adding the masses ‘by hand’ rendered the

theory unrenormalizable.

Then there was the problem of the Z

. The existence of a neutral force

carrier could be expected to be manifested experimentally in the form

of weak neutral currents. No such currents could be found in any of the

strange particle decays, which by now had become the particle physi-

cists’ principal point of reference for weak-force interactions.

Glashow’s explanation was never likely to ﬁ nd much favour with the

experimentalists. He argued that the Z

was so much more massive than

the charged W particles that interactions involving the Z

were simply

out of reach of the largest particle accelerators.

The theoreticians had reached an impasse. High-energy physicists

had run riot, triggering an explosion of particles that had left the theo-

reticians clutching at straws. Quantum ﬁ eld theory was in the doldrums

and, in any case, wasn’t the only theoretical game in town.

Some declared that quantum ﬁ eld theory was dead.

Glashow’s paper was published in the journal Nuclear Physics in November 1961.

By the early 1960s, the physicists had notched up 30 ‘fundamental’ particles, including

the anti-particles but excluding the delta particles. If there was to be any hope of making

sense of the by now bewildering array of electrons, photons, protons, neutrons, muons,

pions, kaons, the lambda, sigma, xi, and delta particles, it was going to be necessary to

ﬁ nd some rigorous way of classifying them, beyond ‘ordinary’ and ‘strange’. Names had

proliferated. Responding to a question from one young physicist, Fermi remarked: ‘Young

man, if I could remember the names of these particles, I would have been a botanist.’

The particles were classiﬁ ed according to their characteristic ‘quantum numbers’, their

values of electric charge, spin, isospin, and strangeness. It was possible to distinguish two

basic types. There are ‘matter’ particles that are the stuff of material substance and there

are ‘force’ particles, the quanta of the ﬁ elds responsible for transmitting forces between

matter particles.

Matter particles are fermions—they possess half-integral spins.

These include the

leptons: the electron, muon, neutrino, and their anti-particles,

and the baryons, includ-

ing the proton, neutron, lambda (L), sigma (S ), xi (X) particles, and their anti-particles.

Three Quarks

for Muster Mark!

New York, March 1963

Fermions are named for Enrico Fermi.

The leptons (from the Greek leptos, meaning small) are the lighter fermions which do not

experience the strong nuclear force.

The baryons (from the Greek barys, meaning heavy) are heavier fermions with masses equal

to or greater than the proton mass. Baryons experience the strong nuclear force.

214

three quarks for muster mark!

215

Force particles are bosons—they possess integral spins.

They include the photon and the

group of particles collectively known as ‘mesons’, the pions (p) and the kaons (K).

these, the mesons carry the strong force and, together with the baryons, constitute a par-

ticle category called the hadrons.

The spin-½ baryons possess positive (proton, S

), neutral (neutron, S

, L

, and X

) and

negative (S

−

and X

−

) electric charges and strangeness values of zero (proton, neutron), −1 (S

, L

, and S

−

) and −2 (X

and X

−

). The spin-0 mesons possess positive (K

, p

), neutral

, p

, and K

−

, the anti-particle of K

) and negative (p

−

, K

−

) electric charges and strange-

ness values of +1 (K

, K

), zero (p

, p

−

) and −1 (K

−

, K

−

). The spin-³⁄

delta particles all

possess zero strangeness and electric charges ranging from −1 to +2 (D

−

, D

, and D

Baryons are classed according to their ‘baryon number’, B, designated as +1 for all

baryons, −1 for all anti-baryons. A similar ‘lepton number’, l, can be deﬁ ned with the

value +1 for all leptons and −1 for all anti-leptons. Protons and neutrons therefore possess

B = +1, l = 0. Electrons possess B = 0, l = +1. All force particles (all bosons) possess B = 0,

l = 0. These are important characterizations, as the physicists discovered that in particle

interactions, baryon and lepton numbers are conserved.

It was clear that amidst this confusion of particle categories there must be a pattern,

a particle equivalent of Dmitri Mendeleev’s periodic table of the elements. The question

was: What is this pattern and does it have an underlying explanation? The question was

answered in two stages. Gell-Mann and Israeli physicist Yuval Ne’eman independently

identiﬁ ed the pattern in 1961.

The explanation took a little while longer.

The search began in earnest for some kind of underlying simplicity. It was

the physicists’ instinct that there could not be this many fundamental par-

ticles, and that somehow it should be possible to rationalize their number

by ﬁ nding the ‘real’ fundamental particles that constituted all the rest.

Bosons are named for the Indian physicist Satyendra Nath Bose. Spin-zero bosons are also

possible, but these are associated with matter ﬁ elds rather than force ﬁ elds.

Note that although it was originally called the meson, the muon (the ‘heavy’ electron) is a

lepton and does not belong in the class of mesons with pions and kaons. Confused?

From the Greek hadros, meaning thick or heavy.

This was not the only approach available. American theoretician Geoffrey Chew had

offered an alternative ‘bootstrap’ model based on S-matrix theory, in which each particle is

constructed from the others. In this ‘nuclear democracy’, no particle is more important or

fundamental than any other.

the quantum story

216

a certain extent, physicists have adopted this kind of approach throughout

the history of their science, but the beginnings of an attempt to apply this

to the new particles that had begun to emerge in cosmic ray and particle

accelerator experiments were ﬁ rst published by Fermi and Yang in 1949.

Inﬂ uenced by Marxist theories of dialectical materialism, in the early

1950s Japanese physicist Shoichi Sakata and his colleagues had adopted

the proton, neutron, and lambda particles as precisely this kind of funda-

mental ‘triplet’, from which they tried to build other particles. Gell-Mann

tried much the same approach, but it was never really clear why these par-

ticles should be regarded as more ‘fundamental’ than the others. ‘It was a

big mess,’ Gell-Mann admitted, ‘I didn’t like it, and I didn’t publish it.’

These early attempts failed because the theorists were pushing for an

underlying explanation before a proper pattern had been established.

This was a bit like trying to ﬁ gure out the fundamental building blocks

of the elements without ﬁ rst appreciating the position that each element

occupies in the periodic table.

Gell-Mann believed that the framework for such a pattern could be

provided by a global symmetry group.

However, although possessed of

a prodigious intellect and familiar with the work of Yang and Mills, in

1959 he was unfamiliar with group theory. He had sat through lectures

on the subject, but had always thought it rather abstract and irrelevant to

anything of importance in physics.

He knew he needed a larger continuous symmetry group than U(1)

or SU(2) to accommodate the range and variety of particles that were

then known, but was quite unsure how to proceed. By this time he was

working as a visiting professor at the Collège de France in Paris. Not sur-

prisingly, copious quantities of good French wine consumed over lunch

with his French colleagues did not immediately help to point the way to

a solution.

Note that this was a global, rather than local, symmetry group. Gell-Mann was searching

for a way of classifying the particles. He was not yet seeking to develop a Yang–Mills ﬁ eld theory

of the strong force based on a local gauge symmetry.

It did not seem to aid conversation either. The colleagues with whom Gell-Mann was drink-

ing were mathematicians who could have solved his problem almost immediately, but they

never talked about it.

three quarks for muster mark!

217

Glashow’s visit to Paris in March 1960 therefore prompted more

than noises of encouragement from Gell-Mann concerning Glashow’s

attempts to unify the weak and electromagnetic forces. Once he got

past the relatively impenetrable Schwinger terminology that Glashow

was using, Gell-Mann was intrigued by Glashow’s SU(2) × U(1) theory.

He began to understand how it might be possible to expand the sym-

metry group to higher dimensions. Not that the SU(2) × U(1) approach

was the solution, as the expansion it offered (to a total of four ﬁ eld par-

ticles or bosons: the photon, W, and Z particles) was insufﬁ cient for his

purposes.

He was nevertheless suitably impressed. Thus inspired, he now tried

theories with more and more dimensions:

I worked through the cases of three operators, four operators, ﬁ ve opera-

tors, six operators, and seven operators, trying to ﬁ nd algebras that did not

correspond to what we would now call products of SU(2) factors and U(1)

factors. I got all the way up to seven dimensions and found none . . . At that

point, I said, ‘That’s enough!’ I did not have the strength after drinking all

that wine to try eight dimensions.

Glashow chose to accept Gell-Mann’s offer to join him at Caltech and,

shortly after his return from Paris, the two physicists searched for a

solution together. But it was only after a chance discussion with Caltech

mathematician Richard Block that Gell-Mann discovered that the Lie

group SU(3) offered the structure he had been searching for. In Paris he

had given up just as he was about to discover this for himself.

The simplest, or ‘irreducible’ representation of SU(3) is a fundamental

triplet. Sakata and his colleagues had actually tried to construct a model

based on the SU(3) symmetry group and had used the proton, neutron,

and lambda particles as the fundamental representation. Gell-Mann had

already been down this road, and had no wish to repeat his experiences.

He simply skipped over the fundamental representation and turned his

attention to the next.

In mathematical terms, the representations of the SU(3) symmetry

group can be combined according to the formula: 3 × 3 × 3 = 1 + 8 + 8 +

10. This implies a pattern consisting of a ‘singlet’, a couple of ‘octets’ of

the quantum story

218

particles, and a ‘decimet’ of particles. Gell-Mann focused his attentions

on the octets.

He found that he could ﬁ t the spin-½ baryons into one such octet, essen-

tially a hexagonal pattern with points determined by values of electric charge

and strangeness and with two particles, the S

and L

, positioned in the cen-

tre of the pattern.

He found that he needed to place the proton, neutron, and

lambda particle in this pattern, and must have felt justiﬁ ed in his decision to

resist the temptation to ascribe these to the fundamental representation.

When Gell-Mann put together an octet for the spin-0 mesons, he found

that he could assign only seven particles to the pattern. One particle, the

meson equivalent of the L

, was ‘missing’. Emboldened, he speculated

that there did exist an eighth spin-0 meson with an electric charge of

zero and zero strangeness. He called it the chi.

Gell-Mann drew back from speculating on the members of the decimet,

as only the four delta particles were known at the time and to predict the

existence of another six new particles must have appeared to be a step too

far. In any case, he had already achieved a major breakthrough with the

octets. Consequently, he chose to call his approach the ‘Eightfold Way’, a

tongue-in-cheek reference to the teachings of Buddha on the eight steps to

Nirvana.

He completed his work on the Eightfold Way during Christmas

1960 and it was published as a Caltech preprint in early 1961.

The particle he had predicted to complete the meson octet was found

a few months later by American physicist Luis Alvarez and his team in

Berkeley, as a three-pion resonance. They called the new particle the eta, h.

Yuval Ne’eman was a colonel in the Israeli army when he was granted

leave by Moshe Dayan to pursue physics in London whilst working as

a defence attaché at the Israeli Embassy. His was an unlikely career in

The singlet representation—a one-member group—is nevertheless relevant. The phi

meson, discovered in the early 1960s, is an example.

In some representations, hypercharge is used instead of strangeness. The hypercharge

number is simply the strangeness plus the baryon number. In the case of the spin-½ baryons,

the hypercharge is then equal to the strangeness +1. This centres the pattern on zero charge and

zero hypercharge.

These are: right views, right intention, right speech, right action, right living, right effort,

right mindfulness, and right concentration.

three quarks for muster mark!

219

physics. Where Gell-Mann had gone to Yale at the tender age of ﬁ fteen,

Ne’eman, a native of Tel Aviv, had joined the Haganah, the Jewish under-

ground, in what was then the British Mandate for Palestine. He had com-

manded an infantry battalion in the 1948 Arab-Israeli war.

Initially intending to study relativity at King’s College, London, he found

that the city trafﬁ c made it impossible for him to get there from the Embassy

in Kensington so he switched to Imperial College and particle physics. At

Imperial College he was pointed in the direction of Abdus Salam.

Ne’eman worked in the evenings and at weekends, bringing ideas to

Salam which Salam would patiently point out had been worked out

years previously by other, more distinguished physicists. Salam began to

grow impatient, but Ne’eman’s conﬁ dence with the theory was growing.

A search for potential symmetry groups that might accommodate the

–

Strangeness

–2

–1

Electric

Charge

Electric

Charge

Spin–½ Baryons

Spin–0 Mesons

–1

0+1

fig 12 The Eightfold Way. Gell-Mann found that he could ﬁ t the spin-½ baryons,

including the neutron (n), and proton (p) and the spin-0 mesons into two octet rep-

resentations of the global symmetry group SU(3). But there were only seven particles

in the representation for the spin-0 mesons. One particle, the meson equivalent of

the K

, was missing. This particle was found a few months later by Luis Alvarez and

his team in Berkeley. They called it the eta, g.