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

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the quantum story

200

Eager to pursue the chemical bonding analogy, Heisenberg further

identiﬁ ed the exchange of charge between the proton and neutron as

involving a change of spin, with zero charge—the neutron—involving

spin in one direction (spin-down) and positive charge—the proton—

involving spin in the opposite direction (spin-up). Converting a neutron

into a proton was then equivalent to ‘rotating’ the spin of the neutron.

It was admittedly a clumsy model, but through it Heisenberg was able

to apply non-relativistic quantum mechanics to the nucleus itself. In a

series of papers published in 1932 he accounted for many observations

in nuclear physics, such as the stability of isotopes (atoms with the same

number of protons but different numbers of neutrons) and alpha-particles

(helium nuclei, consisting of two protons and two neutrons).

However, as a theory of nuclear interactions, its weaknesses were

exposed in experiments performed just four years later. The electron-

exchange model did not allow for any kind of proton–proton interac-

tion, and Heisenberg had assumed that there could therefore be no

strong interaction between protons. In contrast, experiments showed

that the strength of the interaction between protons is comparable to

that between protons and neutrons.

Despite the shortcomings of the theory, Heisenberg’s electron-exchange

model held at least a grain of truth. The exchange of electrons was aban-

doned, but the concept of isospin symmetry was retained. As far as the

strong force is concerned, the proton and the neutron are two sides of the

same coin, or two states of the same particle, the only difference between

them being their isospin.

As Yang searched for a quantum ﬁ eld theory that would preserve isospin

symmetry he quickly got bogged down. But, despite repeated failure, he

did not give up. He became obsessed with the problem. ‘Occasionally an

obsession does ﬁ nally turn out to be something good,’ he later observed.

In the summer of 1953 he made a visit to Brookhaven National Lab-

oratory on Long Island, New York, where he found himself sharing an

ofﬁ ce with a young American physicist called Robert Mills. Mills became

caught up with Yang’s obsession and together they worked on a quantum

ﬁ eld theory for strong interactions. ‘There was no other, more immedi-

ate motivation,’ Mills explained some years later, ‘He and I just asked

a beautiful idea

201

ourselves “Here is something that occurs once. Why not again?” ’ By the

end of the summer they had worked out a solution. It was a solution with

some rather unphysical consequences, however.

The group U(1) is appropriate to describe the symmetry properties of

the quantum ﬁ eld theory of the electron as this involves a single parti-

cle in a single ﬁ eld interacting via a single type of ﬁ eld quantum—the

photon. There is no change of charge in the interaction and so the pho-

ton is not required to carry a charge of its own. Furthermore, the ﬁ eld

is not limited in extent, though it weakens with distance. Consequently,

the force can be carried quite happily by massless particles, able to travel

long distances at high speeds.

However, a quantum ﬁ eld theory of the strong interaction has to

account for the fact that there are now two particles whose charges and

isospins change as a result of the interaction. Also, the force between

the nuclear particles operates over very short distances only, within the

boundary of the nucleus itself.

Yang and Mills reached for the symmetry group SU(2), the special uni-

tary group of transformations of two complex variables. The resulting

ﬁ eld theory satisfactorily preserved the isospin symmetry and introduced

a new ﬁ eld analogous to the electromagnetic ﬁ eld in QED. They called it

the B ﬁ eld. The theory also predicted three new ﬁ eld particles, responsi-

ble for carrying the strong force between the protons and neutrons in the

nucleus, analogues of the photon in QED.

Three particles were needed because of the greater complexity of

the interactions. Two of the three ﬁ eld particles were required to carry

charge, accounting for the change in charge resulting from proton–neu-

tron and neutron–proton interactions. Yang and Mills referred to these

particles as B

and B

−

. The third particle was neutral, like the photon, and

was meant to account for proton–proton and neutron–neutron interac-

tions in which there is no change in charge. This was referred to as B

. It

was found that these ﬁ eld particles interact not only with protons and

neutrons, but also with each other.

It was here that the problems started. The renormalization methods

that had been used so successfully in QED could not be applied to the

Yang–Mills ﬁ eld theory. Worse still, the zeroth-order term in the pertur-

bation expansion indicated that the ﬁ eld particles should be massless,

the quantum story

202

just like the photon. But this was self-contradictory. Japanese physicist

Hideki Yukawa had suggested in 1935 that the ﬁ eld particles of short-

range forces should be heavy, arguing that virtual particles conﬁ ned to

short distances implied short lifetimes and short lifetimes implied large

masses according to the energy–time uncertainty relation.

Massless ﬁ eld

particles for the strong force made no sense.

Yang returned to Princeton, and on 23 February 1954 presented the results

of the work he had done with Mills in a seminar. Oppenheimer was in the

audience, as was Pauli.

It turned out that Pauli had earlier explored some of the same logic

and had arrived at the same puzzling conclusions concerning the masses

of the ﬁ eld particles. He had consequently abandoned the approach. As

Yang drew his equations on the blackboard, Pauli piped up:

‘What is the mass of this B ﬁ eld,’ he asked, anticipating the answer.

‘I don’t know,’ Yang replied, somewhat feebly.

‘What is the mass of this B ﬁ eld,’ Pauli demanded.

‘We have investigated that question,’ Yang replied, ‘It is a very complex

question, and we cannot answer it now.’

‘That is not a sufﬁ cient excuse,’ Pauli grumbled.

Yang, taken aback, sat down to general embarrassment. Oppenheimer

suggested that they let Yang continue. He resumed his lecture, and Pauli

asked no more questions.

It was a problem that simply would not go away. Without mass, the

ﬁ eld particles of the Yang–Mills ﬁ eld theory did not ﬁ t with physical

expectations. If they were massless, as the theory predicted, then no such

particles had ever been observed. Accepted methods of renormalization

wouldn’t work.

Yukawa had suggested that the ﬁ eld particle of the strong force should possess a mass about

200 times that of the electron. When the meson (muon) was discovered in 1937 it was initially

thought to be the particle that Yukawa had proposed.

This was a very difﬁ cult time for Oppenheimer. His ‘Q’ security clearance had been with-

drawn by the Eisenhower administration in December 1953. He was accused of being ‘more

probably than not’ an agent of the Soviet Union. The Atomic Energy Commission’s Personnel

Security Board met in April 1954 to pass judgement on Oppenheimer’s guilt or innocence.

a beautiful idea

203

And yet, it was still a nice theory.

‘The idea was beautiful and should be published,’ Yang wrote, ‘But what

is the mass of the gauge particle? We did not have ﬁ rm conclusions, only

frustrating experiences to show that [this] case is much more involved

than electromagnetism. We tended to believe, on physical grounds, that

the charged gauge particles cannot be massless.’

Yang and Mills published a paper describing their results in Physical

Review in October 1954. They had made no further progress, and turned

their attentions elsewhere.

204

In 1935 Japanese physicist Hideki Yukawa had suggested that the carrier of the force bind-

ing protons and neutrons together in the nucleus would be a particle about 200 times

heavier than the electron. The meson, discovered just two years later, appeared to ﬁ t the

bill. But this was not Yukawa’s ﬁ eld particle. Any carrier of the nuclear force was expected

to interact very strongly with matter. The meson did not.

In 1947 another particle was discovered in cosmic ray experiments performed atop the

Pic du Midi in the French Pyrenees by Bristol University physicist Cecil Powell and his

team. This was found to have a slightly larger mass, 273 times that of the electron, and

came in positive and negative varieties. This was the particle that Yukawa had predicted.

The meson was renamed the mu-meson (subsequently shortened to muon). The new

particle was called the pi-meson (pion). As techniques for detecting particles produced by

cosmic rays became more sophisticated, the ﬂ oodgates opened. The pion was quickly fol-

lowed by the positive and negative K-meson (kaon) and the neutral lambda particle. The

kaons and the lambda behaved rather oddly and, for want of a more scientiﬁ c descriptor,

the physicists awarded the new particles the collective name ‘strange’.

Flush with generous funding from a grateful post-war American administration,

Ernest Lawrence redeployed to peaceful purposes his 184-inch cyclotron, which had been

used during the war to separate uranium isotopes. Physicists at Berkeley’s Radiation

Some Strangeness in the

Proportion

Rochester, August 1960

Yukawa became the ﬁ rst Japanese physicist to receive the Nobel Prize, in 1949. Powell was

awarded the Prize in 1950.

some strangeness in the proportion

205

Laboratory used the cyclotron to discover the neutral pion in 1949. As new synchrotron

accelerators were constructed at Brookhaven National Laboratory in New York, Berkeley

in California, Dubna in Russia, and Geneva in Switzerland there soon followed positive,

negative, and neutral sigma particles, negative and neutral xi particles, the anti-proton,

anti-neutron, and Pauli’s long-anticipated neutrino.

There was more to come. At high energies a number of nucleon ‘resonances’ emerged,

the ﬁ rst associated with an increased scattering of pions from protons. Were these actually

particles? They seemed hardly more than brief ﬂ irtations between pions and nucleons,

surviving for no more than trillionths of trillionths of seconds. Though initially viewed as

excited states of the nucleons, by the late 1950s it was generally accepted that they couldn’t

be ignored. They duly entered the lexicon, as delta particles.

Dirac’s ‘dream of philosophers’ had been shattered by the brute forces unleashed in col-

lisions between particles accelerated to greater and greater energies. Instead of revealing

an underlying simplicity, the experimentalists had uncovered a bewildering complexity,

a veritable ‘zoo’ of particles.

All cried out for an explanation.

Something new and unusual was going on with the strange particles.

The physicists realized that they were witnessing the effects of two dif-

ferent kinds of nuclear force. The strange particles would be produced

through strong-force interactions involving ‘ordinary’ particles, such as

protons and pions. These strange particles would then travel on through

the detector before disintegrating to produce characteristic ‘V’-shaped

tracks. Their relatively long lifetimes suggested that although they were

being produced by the strong force, their decay modes were governed

by a much weaker nuclear force. The same force, in fact, that governs

radioactive beta-decay.

In Princeton, Dutch-born American physicist Abraham Pais became

convinced that this kind of behaviour could not be explained in terms

of the known quantum numbers, those for charge, spin, and isospin. He

suggested that a further quantum number was needed, which he called

N. Ordinary particles possessed N = 0, whereas the new strange particles

possessed N = 1.

The particles were not given these names initially. To avoid confusion, I will continue with

their modern names and refer to their antecedents only when necessary.

the quantum story

206

He ﬁ gured that in strong-force interactions, the mysterious new quan-

tum number N is conserved: the total N for the particles that are pro-

duced must be the same as that for the reacting particles. However, once

produced, the strong force cannot decompose a strange particle with an

odd-numbered N back into ordinary particles with even N. It seemed

that only the weak force could do this, Pais hypothesized, because the

weak force somehow did not respect this even–odd conservation rule.

It all seemed a bit ad hoc, and American physicist Murray Gell-Mann

was not convinced. Gell-Mann was another in the long and illustrious

line of prodigious intellects that came to be applied to problems in quan-

tum physics in the twentieth century. He had been born in New York

in 1929, entered Yale University when he was ﬁ fteen,

and secured his

doctorate at MIT in 1951, aged just 21. He had a short spell at the Institute

for Advanced Study in Princeton before moving to Chicago to work with

Fermi. It was in Chicago that he began to apply himself to the puzzle of

the strange particles.

The scheme that Gell-Mann devised was no less curious, but it was

more comprehensive than that of Pais. Gell-Mann invented the idea of

strangeness, a new property of the strange particles that he later immortal-

ized with the words of Francis Bacon: ‘There is no excellent beauty that

hath not some strangeness in the proportion.’

Although the origin of strangeness was not yet understood, Gell-

Mann argued that, whatever it is, strangeness is conserved in strong-

force interactions, much like electric charge is conserved. Pais realized

that Gell-Mann had properly identiﬁ ed the new quantum number he had

been looking for.

This was no longer about ‘evenness’ and ‘oddness’. If a strange particle

is produced in a strong-force reaction between two ordinary particles,

both with zero strangeness, then conservation of strangeness meant that

it could not be produced on its own. For example, collision of an acceler-

ated negative pion with a proton produces a neutral kaon (with a strange-

ness arbitrarily assigned as +1) and the lambda (strangeness −1). These

particles must always be produced together to conserve the total strange-

ness, in a phenomenon called ‘associated production’. Once created, the

Think about it. What were you doing when you were ﬁ fteen?

some strangeness in the proportion

207

strange particles could not be decomposed except through weak-force

interactions.

Gell-Mann called Courtney Wright, a particle physicist at Brookhaven

National Laboratory, to ask about associated production. If he was right,

then strange particles should always be produced in certain pairings, in

preference to other possible combinations that were feasible simply on

the basis of the available energy of the collision.

‘What possible difference does it make?’ Wright wanted to know. ‘Who

cares?’

‘I care. Please ﬁ nd out,’ Gell-Mann replied.

Wright found out. Gell-Mann was right.

The lack of an underlying explanation for strangeness meant that Gell-

Mann’s solution was not universally embraced by the physics community.

Oppenheimer referred to it in 1956 as a ‘temporary kind of solution’.

The behaviour of the strange particles led to renewed interest in the weak

nuclear force. Fermi had elaborated a detailed theory of beta radioactiv-

ity in the early 1930s. He had recounted his new theory to his colleagues

during Christmas 1933, after a full day skiing in the Italian Alps. Italian

physicist Emilio Segrè described the event: ‘. . . we were all sitting on one

bed in a hotelroom, and I could hardly keep still in that position, bruised

as I was after several falls on icy snow. Fermi was fully aware of the

importance of his accomplishment and said that he thought he would be

remembered for this paper, his best so far.’

Fermi had drawn on comparisons between the weak force that gov-

erns beta radioactivity and electromagnetism. In electromagnetic theory,

two electrons approaching one another experience the electromagnetic

force, exchange a virtual photon, and are deﬂ ected away from each other.

Likewise, Fermi surmised, a neutron experiencing the weak nuclear force

transforms into a proton, exchanging ‘something’ (speculation on which

Fermi was not prepared to be diverted), with an electron and neutrino.

From the resulting electromagnetic-like theory, Fermi was able to deduce

the range of energies (and hence speeds) of the emitted beta-electrons.

In the interests of proper book-keeping, it was subsequently agreed that the electron emit-

ted in beta radioactive decay should be accompanied by an anti-neutrino.

the quantum story

208

With some small adjustments, Fermi’s theory remains valid to this day.

His predictions for the electron energies were shown in 1949 to be correct

in experiments performed at Columbia University by Chinese-American

physicist Chien-Shiung Wu.

Fermi deduced that the strength of the coupling between the neutron–

proton and electron–neutrino ‘currents’ in beta radioactivity is some ten bil-

lion times weaker than the equivalent coupling between charged particles in

electromagnetism. Weak it may be, but the force has some profound con-

sequences. Because of the weak force, neutrons, regarded as ‘fundamental’

nuclear particles almost from the moment of their discovery, are inherently

unstable. The average lifetime of a free neutron is just eighteen minutes.

In the late 1940s it became evident that the interactions governing

absorption and emission of muons were of similar strength. The force

governing the decay modes of the strange particles also fell into the same

range, and it seemed clear that beta radioactivity was simply one com-

mon manifestation of a more widespread phenomenon, which became

known as the Universal Fermi Interaction.

But there was now another problem. One of the inviolate symmetries

of electromagnetism relates to the behaviour of the wavefunctions of

charged particles under reﬂ ection, a property known as parity. If revers-

ing the signs of the particle’s spatial coordinates does not change the sign

of the wavefunction, the particle is said to possess even parity. If the sign

of the wavefunction is reversed, the particle is said to have odd parity.

far as the physicists could tell, in all electromagnetic and nuclear interac-

tions, parity is conserved.

Aside from what was believed to be compelling experimental evidence,

the assumption of parity conservation was also very much the instinct

of physicists. How could it be possible for the immutable laws of nature

to favour such seemingly human conventions of left versus right, up versus

At Columbia University Wu had worked on the Manhattan Project, reﬁ ning the gaseous

diffusion technique that was used to separate U-235 from natural uranium. She is thought to be

the only scientist of Chinese birth to have worked on the Manhattan Project.

This symmetry operation can be thought of as a kind of mirror reﬂ ection which not only

reverses left and right, but also front and back and up and down.

some strangeness in the proportion

209

down, front versus back? Surely, no natural force could be expected to

display such ‘handedness’?

The problem was that two positively charged strange particles, then

named the tau and the theta, looked to all intents and purposes as though

they were one and the same particle. They possessed the same mass and

decay rate. But the positive theta particle decayed into two pions, each

with odd parity. Two particles with odd parity give a total even parity,

as −1 multiplied by −1 gives +1. The tau particle, however, decayed into

three pions, also each with odd parity. Three particles with odd parity

give a total odd parity, as −1 multiplied by −1 multiplied by −1 gives −1.

Dark hints began to emerge that if the tau and theta really were one

particle, then the weak interaction might not respect the conservation of

parity. Could the weak force, after all, be ‘handed’?

Yang and fellow Chinese physicist Tsung-Dao Lee decided to check the

experimental record. What they found was greatly surprising. It turned

out that for weak force interactions there was no experimental evidence in

support of parity conservation. In June 1956 they published a speculative

paper posing the question: Is parity conserved in weak interactions?

The answer came from a series of extremely careful experiments

conducted towards the end of that year by Wu, Eric Ambler, and their

colleagues at the US National Bureau of Standards laboratories in

Washington, DC. These involved the measurement of the direction of

emission of beta-electrons from atoms of radioactive cobalt-60, cooled

to near absolute zero temperature, their nuclei aligned by application of

a magnetic ﬁ eld. A symmetrical pattern of beta-electron emission would

suggest that no direction was specially favoured, and that parity is con-

served. An asymmetrical pattern would suggest that conservation of

parity is violated.

So convinced was Pauli of parity conservation that he was ready to

stake a large sum: ‘I do not believe that the Lord is a weak left-hander,’ he

wrote to Weisskopf in January 1957, ‘and I am ready to bet a very large

sum that the experiments will give symmetric results.’

The experiments were unequivocal. Wu found that the Lord is indeed

a ‘weak left-hander’. Parity is not conserved in weak-force interactions.

Within less than two weeks Pauli was eating his words and thankful that

he had not placed his bet, with money he could ill-afford to lose.