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

Подождите немного. Документ загружается.

the quantum story

230

can be eliminated from the theory through their ‘absorption’ into the

description of the Yang–Mills bosons. The Nambu–Goldstone bosons

cease to exist as independent massless particles, becoming a new ‘degree

of freedom’ of the Yang–Mills bosons.

The process by which the Yang–Mills bosons are meant to acquire mass

is mathematically complex, but there are several analogies that can help

us to visualize what is going on. The hypothetical vacuum ﬁ eld required

to break the symmetry (which is now called a Higgs ﬁ eld) acts selectively

on the Yang–Mills ﬁ eld particles. To these particles, the Higgs ﬁ eld behaves

like molasses. These particles quickly get ‘bogged down’, their motion

impeded through interactions with the ﬁ eld resulting in behaviour that

appears to all intents and purposes like the motion of massive particles.

CERN physicists use another analogy to explain the Higgs mechanism

to politicians. Imagine a cocktail party in which a room is uniformly popu-

lated with physicists quietly drinking cocktails and chatting among them-

selves. This is equivalent to the vacuum containing the Higgs ﬁ eld. A noted

celebrity physicist (no doubt a Nobel Laureate) enters the room and causes

something of a stir. This is the massless Yang–Mills boson. The physicists

gravitate in the direction of the celebrity in order to engage her in conver-

sation and, before too long, a throng has gathered around her which slows

down her progress as she crosses the room.

This resistance to accelaration

of the Yang–Mills boson is equivalent to the acquisition of mass.

A massless particle with spin 1 (boson) has two degrees of freedom corresponding to trans-

verse polarization states (in the photon these are associated with left-circular and right-circular

polarization states). After application of the Higgs mechanism, the spin 1 boson ‘absorbs’ the Nambu–

Goldstone boson to yield a third, longitudinal, degree of freedom. Consequently the acceleration

of the particle is resisted by the ﬁ eld, and we recognise this as the acquisition of mass.

This is a variation of the analogy devised by physicist David Miller at University College Lon-

don, in which the ‘ﬁ eld’ of cocktail-drinking physicists is replaced by political party workers, and

the celebrity physicist by former Prime Minister Margaret Thatcher. Miller submitted his analogy

to a competition to explain the Higgs mechanism in simple terms, established in 1993 by the Sci-

ence Minister, William Waldegrave. Miller’s was one ﬁ ve winning entries. Waldegrave was con-

vinced that the search for the Higgs boson was worth Britain’s annual contribution to CERN.

It’s worth noting that in the symmetry-breaking of the U(1) gauge ﬁ eld of electromagnetism

associated with superconductivity, the massless photons of the gauge ﬁ eld can acquire mass

in precisely the same way. The result is the Meissner effect, ﬁ rst discovered in 1933 by Walther

Meissner and R. Ochsenfeld. If a superconductor is cooled below its transition temperature in

the presence of a weak-to-moderate magnetic ﬁ eld, the ﬁ eld photons become massive and the

‘lines of force’ of the ﬁ eld can no longer penetrate the interior of the superconductor. The ﬁ eld

is forced to ﬂ ow around the outside of the material.

the ‘god particle’

231

The theory had implications not only for the massless bosons of the

ﬂ edgling electro-weak theory, but for all particles. It was believed that the

Higgs ﬁ eld was responsible for breaking the symmetry of the entire uni-

verse in the early stages of the hot ‘big bang’. Just as the iron atoms start

to crystallize, breaking the symmetry in a cooling ferromagnet, so the

phase angle of the Higgs ﬁ eld ‘crystallized’ to a speciﬁ c value as the early

universe cooled. This crystallization created a ‘false’ vacuum, a baseline

energy state higher than the zero-energy true vacuum. This symmetry-

breaking mechanism affected the particles created in the early universe

in different ways. The photons of the electromagnetic force were unaf-

fected, and remained massless. But the bosons of the weak force picked

up the energy trapped in the false vacuum in the form of acquired mass.

Indeed, it appears that all massive particles acquire their mass this way.

Whilst this does seem as though something (mass) is being conjured

from ‘nothing’ (the false vacuum, ﬁ lled with the Higgs ﬁ eld), it is fair to

say that the theory is not without its consequences. There is no quan-

tum ﬁ eld without a quantum particle, and the particle of the Higgs

ﬁ eld is called the Higgs boson. Stretching the cocktail party analogy a

little further, the Higgs boson is like a softly spoken rumour about

the celebrity, passed between the physicists as they wait for her to

arrive. Now the physicists cluster together in order to hear the rumour,

resulting in the creation of resistance (mass) even in the absence of

the celebrity. This clustering is equivalent to a massive Higgs boson.

The acquisition of mass by otherwise massless ﬁ eld particles is then

identiﬁ ed as arising from interactions between these particles and the

Higgs boson.

The Higgs mechanism did not win converts immediately. Higgs him-

self had some difﬁ culties getting his papers published. He sent the second

Because of the actions of the Higgs mechanism in endowing mass to the Yang–Mills par-

ticles, and its subsequent adoption as the mechanism by which all particles acquire mass, the

mechanism has acquired an almost theological status, at least outside the community of prac-

ticing physicists. In their 1993 popular book The God Particle: If the Universe is the Answer, What is

the Question?, Nobel Laureate Leon Lederman and science writer Dick Teresi elevated the Higgs

boson to the status of the ‘God particle’. Higgs insists that Lederman had originally wanted

to call it ‘that goddamn particle’ but his publisher wouldn’t let him (see The Guardian, 30 June

2008).

the quantum story

232

of his two papers initially to the European journal Physics Letters in July

1964, but it was rejected by the editor as unsuitable. Years later, Higgs

wrote:

I was indignant. I believed that what I had shown could have impor-

tant consequences in particle physics. Later, my colleague Squires, who

spent the month of August 1964 at CERN, told me that the theorists

there did not see the point of what I had done. In retrospect, this is not

surprising: in 1964 the European particle theory scene was dominated

by S-matrix theorists. Quantum ﬁ eld theory was out of fashion, and I

had rashly formulated my description of the mass-generating mecha-

nism in terms of linearised classical ﬁ eld theory, quantized by invoking

the de Broglie relations.

Perhaps surprisingly, the mechanism had little immediate impact on

those who might have beneﬁ ted most from it. By his own admission, it

seems that by this time Glashow had quite forgotten his earlier attempts

to develop a uniﬁ ed theory of the weak and electromagnetic forces, a

theory which predicted massless W

, W

−

, and Z

particles which needed

somehow to be massive. ‘His amnesia unfortunately persisted through

1966,’ Higgs wrote. Glashow attended a lecture on the mass-generating

mechanism that Higgs delivered at Harvard that year, yet failed to put

two and two together.

It was Weinberg who eventually made the connection although he,

too, did not immediately see the relevance of the Higgs mechanism.

Weinberg spent the years 1965–67 working on the effects of sponta-

neous symmetry breaking in strong-force interactions described by

an SU(2) × SU(2) field theory. The result of symmetry-breaking is the

masses of the nucleons and Nambu–Goldstone bosons which could

be approximated as the pions. At the time this all seemed to make

sense and, far from trying to evade the Goldstone theorem, he now

positively welcomed the predicted extra particles. This was a devel-

opment ‘. . . which suddenly seemed to change the role of [Nambu–]

Goldstone bosons from that of unwanted intruders to that of wel-

come friends.’

the ‘god particle’

233

But after a couple of years pursuing this line of reasoning, Weinberg

realized that it wasn’t going to bear fruit. It was at this point that he was

struck by another idea:

At some point in the fall of 1967, I think while driving to my ofﬁ ce at MIT,

it occurred to me that I had been applying the right ideas to the wrong

problem.

Weinberg had been applying symmetry-breaking to the strong force.

He now realized that the mathematical structures he had been trying to

apply to strong-force interactions were precisely what were needed to

resolve the problems with weak-force interactions and the massive bos-

ons these interactions implied. ‘My God,’ he exclaimed to himself, ‘this is

the answer to the weak interaction!’

Weinberg was well aware that if the masses of the W

, W

−

, and Z

particles were added by hand to Glashow’s SU(2) × U(1) ﬁ eld theory

of the weak and electromagnetic forces, then the result was rendered

unrenormalizable. He now wondered if breaking the symmetry using

the Higgs mechanism would endow the particles with mass, eliminate

the unwanted Nambu–Goldstone bosons, and yield a theory that could

be renormalized.

There remained the problem of the weak neutral currents, inter-

actions involving the neutral Z

particle for which there was still no

experimental support. He decided to avoid the problem altogether by

restricting his theory to leptons—electrons, muons, and neutrinos.

He had by now become wary of the hadrons, particles affected by the

strong force, and especially the strange particle decays which were the

principal ground for the experimental exploration of weak-force inter-

actions.

Neutral currents would still be predicted, but in a model consisting only

of leptons these would involve interactions with the neutrino. The neu-

trino had proved difﬁ cult enough to ﬁ nd experimentally in the ﬁ rst place,

and he may have ﬁ gured that ﬁ nding weak neutral currents involving

these particles would present sufﬁ cient experimental challenges that he

could predict them with little fear of immediate contradiction.

the quantum story

234

Weinberg published a paper detailing an ‘electroweak’ uniﬁ ed theory

for leptons in November 1967. This was an SU(2) × U(1) ﬁ eld theory

reduced to the U(1) symmetry of ordinary electromagnetism by sponta-

neous symmetry-breaking, which gave mass to the W

, W

−

, and Z

par-

ticles, whilst leaving the photon massless. He estimated the mass-scales

of the weak-force bosons, about 80 GeV for the W particles and 90 GeV

for the Z

and predicted some properties of what would become known

as the Higgs boson. He was not able to prove that the theory was renor-

malizable but felt conﬁ dent that it was.

Salam, too, had ﬁ nally woken to the possibilities afforded by the

Higgs mechanism early in 1967 and had independently arrived at much

the same formalism. He decided against publishing until he had had an

opportunity properly to incorporate hadrons in the model.

Nobody took much notice. Those few who did pay attention tended to be

critical. The mass problem had been ﬁ xed through some ‘smoke-and-mir-

rors’ trick involving a hypothetical ﬁ eld and another hypothetical boson.

It seemed as though the quantum ﬁ eld theorists were continuing to play

games with ﬁ elds and particles, according to obscure rules that few under-

stood. Physicists simply ignored them and got on with their science.

Weinberg later drew an analogy with Plato’s famous allegory of pris-

oners in the cave, which he set out in The Republic. The prisoners held cap-

tive in the cave have no knowledge or experience of the outside world.

All that they experience are shadows cast on one wall of the cave. Their

world is a world of crude appearances of objects which they mistake for

the objects themselves, ‘literally nothing but the shadows of the images’.

Weinberg wrote:

We are in such a cave, imprisoned by the limitations on the sorts of experi-

ments we can do. In particular, we can study matter only at relatively low

temperatures, where symmetries are likely to be spontaneously broken,

so that nature does not appear very simple or uniﬁ ed. We have not been

able to get out of this cave, but by looking long and hard at the shadows

on the cave wall, we can at least make out the shapes of symmetries, which

though broken, are exact principles governing all phenomena, expres-

sions of the beauty of the world outside.

PART V

Quantum

Particles

This page intentionally left blank

237

Weinberg’s use of Plato’s allegory of the cave may have reﬂ ected something of the mood

among quantum ﬁ eld theorists in the late 1960s. Theirs was a largely thankless task.

They had strained to make sense of the shadows cast on the cave wall, and had spent

much time blundering around in the dark. They had tried hard to make their approaches

ﬁ t the shadows as best they could, patching the theory or ﬁ nding ‘work-arounds’ when

the mathematics became particularly truculent. There had been breakthroughs, but few

acknowledged their success in what had by now become an unfashionable discipline. It

was not at all clear where this was leading.

Experimental particle physicists were presented with a different task. Their mission

was to shine more light in the cave, sharpening and clarifying the shadows so they bet-

ter reﬂ ected the underlying reality that created them. In the 1960s, this meant building

bigger and bigger particle accelerators.

In October 1957 the American administration had experienced a deep sense of frus-

trated impotence as the Soviet Union’s Sputnik I satellite bleeped provocatively overhead

on its 98-minute orbit of the earth.

This sense had been compounded by the completion

that year of a 10-GeV proton synchrotron by the Joint Institute for Nuclear Research in

Dubna, 120 kilometres north of Moscow. At the time this was the world’s largest particle

accelerator, beating the Cosmotron’s 3 GeV at Brookhaven and the Bevatron’s 6.2 GeV

Deep Inelastic Scattering

Stanford, August 1968

You can listen to Sputnik’s telemetry on a NASA website: http://history.nasa.gov/sputnik

the quantum story

238

at Berkeley’s Radiation Laboratory. CERN soon followed in 1959 with a 26-GeV proton

synchrotron in Geneva.

As the race for Cold War technological supremacy reached white heat in the 1960s,

American particle physicists were among the beneﬁ ciaries as funding for high-energy

physics was greatly increased. The Alternating Gradient Synchrotron was constructed

at Brookhaven in 1960, capable of operating at 33 GeV. These were all proton accelera-

tors, designed to smash protons into stationary targets, including other protons. Their

basic aim was the creation of exotic new particles and the study of strong- and weak-

force interactions. The outcomes of these experiments involved long and complex analysis,

however. As Feynman explained, proton–proton collisions were ‘. . . like smashing two

pocket watches together to see how they are put together.’

This emphasis on high-energy hadron collisions came at the cost of subtlety. When

construction commenced in 1962 of a new $114-million 20-GeV linear electron accelera-

tor at Stanford University in California, it was dismissed by many particle physicists as

an irrelevant machine, capable only of second-rate experiments. But American theorist

James Bjorken understood that the de Broglie wavelengths of high-energy electrons would

be far smaller than the diameter of the proton.

Such electrons could probe the interior of

protons in ways that heavy-particle collisions could not. In particular, they could reveal

the existence or otherwise of point-like constituents deep inside the proton.

In astonishing experiments that would mirror the fabled 1909 Geiger–Marsden experi-

ments which revealed the interior structure of the atom,

the scattering of electrons from

protons in the new Stanford accelerator would reveal the interior structure of the proton.

The experimentalists would ﬁ nally have an opportunity to catch up with some of the

more outrageous conclusions of the theorists.

The Stanford Linear Accelerator Center (SLAC) was built on 400 acres of

Stanford University grounds about ﬁ ve kilometres west of the main cam-

pus, at the foot of the Los Altos hills about 60 kilometres south of San

Francisco.

The three-kilometre accelerator is linear, rather than circu-

lar, because bending electron beams into a circle using intense magnetic

Remember that according to the de Broglie relation, l = h/p, the higher the speed (and hence

momentum, p) of an electron, the shorter its wavelength.

See Chapter 3.

It is situated close to the San Andreas fault. In the event of a major earthquake it has been

suggested that it might be renamed the Stanford Piecewise Linear Accelerator Center (SPLAC).

See Woit, p. 23.

deep inelastic scattering

239

ﬁ elds results in dramatic energy loss through emission of X-ray synchro-

tron radiation. The accelerator reached its 20-GeV design beam energy

for the ﬁ rst time in 1967.

The aim was to examine electrons scattered off various targets posi-

tioned at the end of the accelerator, using large and elaborate electron

spectrometers. When an electron collides with a proton, three differ-

ent types of interaction may result. The electron may bounce relatively

harmlessly off the proton, exchanging a virtual photon, changing the

electron’s velocity and direction, but leaving the particles intact. This,

so-called ‘elastic’ scattering yields electrons with relatively high scattered

energies clustered around a peak.

In a second type of interaction, the collision with the electron may

exchange a virtual photon which kicks the proton into one or more excited

energy states. The scattered electron comes away with less energy as a

result, and a chart of scattered energy versus yield shows a series of peaks or

‘resonances’ corresponding to different excited states of the proton. Such

scattering is ‘inelastic’, as new particles (such as delta particles and pions)

may be created, although both electron and proton emerge intact from the

interaction. In essence, the energy of the collision, and of the exchanged

virtual photon, has gone into the creation of new particles.

The third type of interaction is called ‘deep inelastic’ scattering, in

which much of the energy of the electron and the exchanged virtual

photon goes into destroying the proton completely. A spray of different

hadrons emerges and the scattered electron recoils, now with consider-

ably less energy.

It was this last type of scattering that interested James Bjorken. Now in

his early thirties, Bjorken had obtained his doctorate at Stanford Univer-

sity and had recently returned to California after a spell at the Niels Bohr

Institute in Copenhagen. Just before SLAC was completed, he had devel-

oped an approach to predicting the outcomes of electron–proton colli-

sions using a rather esoteric quantum ﬁ eld theoretic approach known as

current algebra.

In this model, the electron is treated as a point-particle surrounded

by a cloud of virtual particles which ﬂ icker into and out of existence.

The proton is a different matter, however. At the time it was possible to

conceive the structure of the proton in two distinct ways. It could be