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

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the quantum story

380

The astronomer Carl Sagan was attending a meeting on the search

for extraterrestrial life in another part of the building. He was drawn to

the ceremony during a coffee break and, standing in the doorway, wit-

nessed the signing. ‘In the front row a young man in a wheelchair was,

very slowly, signing his name in a book that bore on its earliest pages the

signature of Isaac Newton,’ Sagan wrote. ‘When at last he ﬁ nished, there

was a stirring ovation. Stephen Hawking was a legend even then.’

381

The success of the standard model in the mid-1970s led inevitably to questions about

its SU(3) × SU(2) × U(1) symmetry properties. Why this particular combination? Was

there a higher symmetry group that would properly unify both the strong force and the

electro-weak force? A number of different approaches had been tried, but in 1974 Sheldon

Glashow was convinced he had a solution. With Harvard postdoctoral fellow Howard

Georgi, he developed a so-called grand uniﬁ ed theory based on the SU(5) symmetry

group. They declared it the ‘gauge group of the world’.

The theory proliferated more Higgs particles. It also allowed transformations

between quarks and leptons. This meant that a quark inside a proton could in principle

transform into a lepton. ‘And then I realized that this made the proton, the basic build-

ing block of the atom, unstable,’ Georgi said. ‘At that point I became very depressed

and went to bed.’

Admittedly, the time required for proton decay was longer than the age of the universe,

but it was a prediction that nevertheless could be checked experimentally. By the early

1980s, the experimental results appeared unequivocal: the proton is more stable than

Georgi and Glashow’s SU(5) quantum ﬁ eld theory suggested.

The First Superstring

Revolution

Aspen, August 1984

These experiments involved searching for a single proton decay event from a large vol-

ume of protons shielded from cosmic rays. As Carlo Rubbia explained: ‘. . . just put half a dozen

graduate students a couple of miles underground to watch a large pool of water for ﬁ ve years.’

Quoted in Woit, p. 104.

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382

Another approach emerged in the early 1970s from theorists in the Soviet Union

and was independently rediscovered in 1973 by CERN physicists Julius Wess and Bruno

Zumino. This was called supersymmetry. It featured ‘super-multiplets’ of particles which,

for the ﬁ rst time, connected the matter particles—fermions—with the bosons that car-

ried forces between them. It also proliferated more particles. For every fermion, the theory

predicted a corresponding boson. This meant that for every particle in the standard model,

the theory required a massive supersymmetric partner with a spin different by ½. The

partner for the electron was called the selectron (a shortening of supersymmetric-electron).

Quarks are partnered by squarks. Supersymmetric partners of the photon, W, and Z par-

ticles are the photino, wino, and zino. These particles may exist at the TeV energy scale,

but to date they have not been found.

In supersymmetry, a ‘super-gauge’ particle acting on a target fermion or boson changes

the spin of the target particle by ½. This kind of change affects the space–time properties of

the target particle, such that it is slightly displaced.

Forces such as electromagnetism can-

not do this. They can change the direction of motion, momentum, and energy of the par-

ticle but they cannot displace it in space–time in this way. This displacement is equivalent

to a gauge transformation characteristic of the gravitational force. A super-gauge theory is

also therefore a theory of gravity. Such theories are collectively called supergravity, and the

super-gauge particle is the gravitino, with spin ³⁄

, the super-partner of the graviton.

There are many different types of supersymmetric transformation, and theories with

more than one transformation are called extended supersymmetric theories. These theo-

ries are classiﬁ ed according to the number of supersymmetry ‘generators’ they posses. The-

ories with 32 generators, called N = 8 supersymmetry, automatically produce gravitons.

They are also theories of supergravity.

For a time, theories of N = 8 supergravity were very popular. In April 1980, Stephen

Hawking used his inaugural lecture as Lucasian Professor of Mathematics at Cambridge,

a position once held by Newton and Dirac, to declare that the end of physics was in sight.

He believed that there was a 50:50 chance that N = 8 supergravity would prove to be the

ultimate unifying theory for all physical forces.

But there was yet another approach. It had lurked in the background, largely ignored or

dismissed. Yet it would soon overtake all these efforts, to become the dominant candidate

as the theory of everything.

Actually, a supersymmetry transformation is equivalent to the square-root of an inﬁ nitesi-

mal translation in space.

Theories with more than 32 generators are possible but predict massless particles with spin

greater than 2, which are thought not to exist in nature.

the first superstring revolution

383

In 1968, whilst puzzling over experimental data from high-energy strong-

force particle collisions, young Italian postdoctoral physicist Gabriele

Veneziano at CERN had noticed a pattern. The probabilities for two

particles to scatter from each other at different collision angles—called

scattering amplitudes—appeared to conform to a formula ﬁ rst devised

by the eighteenth-century Swiss mathematician Leonhard Euler. This is

Euler’s beta function, or the Euler integral of the ﬁ rst kind.

Veneziano had no idea why the data conformed to this function and

could therefore say nothing about the underlying physics. But identify-

ing elegant, if empirical, mathematical connections between data is usu-

ally an important ﬁ rst step to a subsequent revelation.

So it was to prove.

Told about Veneziano’s discovery by an enthusiastic colleague, young

Yeshiva University professor Leonard Susskind was struck by the simplic-

ity of the mathematical relationship describing the scattering amplitudes.

‘I worked on it for a long time,’ he later explained, ‘ﬁ ddled around with it,

and began to realize that it was describing what happens when two little

loops of string come together, join, oscillate a little bit, and then go ﬂ ying

off. That’s a physics problem that you can solve. You can solve exactly for

the probabilities for different things to happen, and they exactly match

what Veneziano had written down. This was incredibly exciting.’

Similar discoveries were made independently by Danish physicist

Holger Nielsen at the Niels Bohr Institute in Copenhagen and by Yoichiro

Nambu in Chicago. Instead of treating fundamental particles as point-

particles, they were imagined instead as strings—small, one-dimensional

ﬁ laments of energy. In such a theory the different particles would not

be translated into different strings, but into different vibrational patterns in

one common string type. The mass of a particle is just the energy of its

string vibration, with charge and spin being more subtle manifestations.

It was a breathtaking idea.

Susskind drafted a paper outlining a quantum theory of strings and

submitted it to the journal Physical Review Letters. It was promptly rejected.

Susskind was deeply perturbed. He returned home nervous and upset.

He took a tranquiliser and slept for a while, waking to join some friends

who were visiting that evening for a few drinks. The combination of tran-

quiliser and alcohol didn’t agree with him, and he passed out.

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384

Having tried—and failed—to get the editor of Physical Review Letters to

reconsider, Susskind resubmitted his paper to the journal Physical Review

D in July 1969. It was published in 1970, to no acclaim. The reaction of

the physics community to the idea of particles as strings was typiﬁ ed

by an encounter with Murray Gell-Mann. After lecturing at an interna-

tional conference on fundamental high-energy interactions held at Coral

Gables in Florida, Gell-Mann headed back to his motel. He got stuck in

the elevator with Susskind.

‘What do you do?’ Gell-Mann asked.

‘I’m working on this theory that hadrons are like rubber bands, these

one-dimensional stringy things,’ Susskind explained.

Gell-Mann just laughed.

But, in fairness, string theory in this early form did not seem to have an

awful lot going for it. For one, it was a theory of bosonic strings only—it could

not accommodate ‘particles’—string vibrational patterns—with half-integral

spin. This was a signiﬁ cant stumbling block for a theory that was supposed to

be about the strong nuclear force. It was also a theory in a twenty-six-dimen-

sional space–time, rather than the more familiar four. Worse still, it predicted

the existence of tachyons, hypothetical particles that travel only at speeds faster

than light and wreak untold damage on the principles of cause-and-effect.

But within a matter of a few months one of the problems of early string

theory had been solved. In the spring of 1971 French physicist Pierre Ram-

ond, working at the National Accelerator Laboratory in Chicago, ﬁ gured

out how to make the transformations between bosons and fermions that

formed the basis for what was later to be called supersymmetry. It meant

that the string (or, more correctly, supersymmetric string or superstring)

vibrational patterns for fermions had been found.

Within a few years some of the other problems had been resolved, too.

The number of dimensions required for the superstrings to vibrate in had

reduced from twenty-six to ten: nine spatial dimensions and one time

dimension. Though this was still a lot more than the four dimensions of

our everyday world, it was at least a step in the right direction. And the

tachyons were now gone.

In Princeton, American theoretical physicist John Schwarz watched the

development of early string theory with great interest. He had also been

the first superstring revolution

385

struck by the implications of Veneziano’s work and in 1969 began collab-

orating on string theory with David Gross. They were joined in Princeton

by two French theorists, André Neveu and Joël Scherk who, by American

standards, had the equivalent of PhDs but had yet to secure their doctorat

in the French system. They were assigned to Schwarz as graduate stu-

dents, but when he suggested they take a course in quantum mechanics

they explained that they didn’t need one. Schwarz sent them away.

They came back a short time later to show him some results they had

derived for the scattering of strings. It quickly became clear to Schwarz

that they really didn’t need a graduate course on quantum mechanics.

Schwarz was among those physicists who identiﬁ ed in 1972 that super-

strings would need to vibrate in just ten space–time dimensions, but his

work on string theory was not enough to earn him a tenured position at

Princeton. Gross, however, was promoted. It was about this time that he

resolved to ﬁ nish off quantum ﬁ eld theory once and for all, by showing

that there was no class of renormalizable theory that was asymptotically

free.

The early 1970s was a bad time in the American market for academic

physics. A few months later Schwarz was offered a research associate

position at Caltech.

The summer of 1973 saw asymptotic freedom and the birth of what

was to become QCD, which quickly became established as the theory of

the strong force. There seemed little need for any further work on strings.

But Schwarz and Scherk were not ready to let go. Scherk came to Caltech

in January 1974 and they resolved to continue their collaboration:

I think we were kind of struck by the mathematical beauty; we found the

thing a very compelling structure. I don’t know that we said it explicitly,

but we must have both felt that it had to be good for something, since it

was just such a beautiful, tight structure. So, one of the problems that we

had had with the string theory was that in the spectrum of particles that it

gave, there was one that had no mass and two units of spin. And this was

just one of the things that was wrong for describing strong nuclear forces,

because there isn’t a particle like that. However, these are exactly the prop-

erties one should expect for the quantum of gravity.

See Chapter 26, p. 261–262.

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386

If the problem of providing a theoretical description of the strong force

had been solved, then the problem of providing a quantum theory of

gravity had not. Superstring theory not only promised to accommodate

all the particles of the Standard Model then known, it also predicted a

particle with the properties of the graviton. Superstring theory was not a

theory of the strong force. It was potentially a theory of everything.

It was a revelation. Superstrings come in two forms: open and closed.

Open strings have loose ends that can be thought of as representing

charged particles and their anti-particles, one at either end, with the

string vibration representing the particle carrying the force between

them. Open strings therefore predict both matter particles and their

forces. But the theory also demands closed strings. When a particle and

anti-particle annihilate, the two ends of the string join up and the result

is a closed string.

But if there are closed strings then there are also gravitons and the

force of gravity. Rather than try to force ﬁ t quantum theory and gen-

eral relativity together, superstring theory appeared to be saying that all

nature’s forces are just different vibrational patterns in open and closed

strings. In superstring theory these forces are automatically uniﬁ ed.

It offered an enticing possibility. All the ‘fundamental’ particles then

known—their masses, charges, spins—the forces between them and all

the Standard Model parameters that could not be derived from ﬁ rst prin-

ciples, could be subsumed into a single theory with just two fundamental

constants. These were the constants that determine the tension of the

string and the coupling between strings.

Nobody was interested.

In the meantime, Hawking declared that black holes could radiate

and momentum began to build for supersymmetry and supergravity.

Schwarz continued his collaboration with both Neveu and Scherk and

published papers on supersymmetric Yang–Mills ﬁ eld theories. He also

coll aborated with British physicist Michael Green at Queen Mary College,

London. Together they resolved various murky aspects of the different

types of superstring theory that had by then emerged, which they called

Type I, Type IIA, and Type IIB.

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387

Although their work continued to be largely ignored, the theory was

winning a few advocates. Among them was Gell-Mann, who had by now

been won round, and Princeton mathematical physicist Edward Witten.

By the early 1980s, Witten was already a phenomenon. He had studied

history and linguistics at Brandeis University, graduating in 1971. He went

on to study economics at the University of Wisconsin and contributed

to George McGovern’s presidential campaign. After McGovern’s over-

whelming defeat by Richard Nixon in 1972, Witten abandoned politics

and moved to Princeton to study mathematics. He transferred to phys-

ics shortly afterwards. He became one of Gross’s graduate students,

securing his PhD in 1976. Four years later, he was a tenured professor at

Princeton.

Schwarz and Green would visit Princeton and discuss their progress

with Witten. As Schwarz later explained: ‘. . . in our discussions with him

it became very clear that one of the really important problems that we

had to think about was something called anomalies. We had been aware

of this ourselves to some extent, but I think in our discussions with

Edward it became even clearer to us how important this was.’

These ‘gauge anomalies’ relate to the mathematical consistency of the

superstring theory after making certain quantum corrections. If the cor-

rections destroy certain symmetries, then the theory might no longer

make mathematically consistent predictions. Different versions of the

theory have different symmetry properties. Type IIA superstring theory

is mirror-symmetric, and the physicists could be conﬁ dent that this

theory would exhibit no anomalies. But look in a mirror. The world we

inhabit is not mirror-symmetric.

In 1984, Witten and Spanish physicist Luis Alvarez-Gaumé pointed

out that there could be further anomalies due to the gauge ﬁ eld of

gravitation, but also showed that in a low-energy approximation Type

IIB theory these anomalies cancelled. This seemed encouraging, but

the Type IIB theory cannot accommodate Yang–Mills ﬁ elds of the kind

required by the Standard Model.

This left all hopes pinned on the Type I superstring theory. In the

summer of 1984, Green and Schwarz retreated to Aspen to think on the

problem some more.

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388

The Type I superstring theory in principle accommodates an inﬁ nite

number of different symmetry groups. Green and Schwarz had to ﬁ nd

one symmetry group in which the gauge anomalies would cancel. The

question was: which one?

A clue came from studying a number of Feynman diagrams derived

from string interactions. A couple of these diagrams gave formulas for

the anomalies that looked very similar. Schwarz wondered if these contri-

butions might cancel for a speciﬁ c choice of symmetry group. They then

went into a seminar. At the end of the seminar, Green said: ‘SO(32)’.

It checked out. In a low-energy approximation, both Yang–Mills and

gravitational anomalies canceled in a Type I superstring theory based on the

symmetry group SO(32), a group of rotations in a 32-dimensional space.

Before Green and Schwarz could tell anyone about what they had dis-

covered, Schwarz was obliged to act the part of Gell-Mann in a caba-

ret that had been organized at the Aspen Center. The same cabaret had

been put on ten years before. Gell-Mann himself had jumped up from

the audience and declared that he had found the theory of everything, at

which point he was carried away by men in white coats.

Schwarz now reprised the role, but with a twist. He ran up on stage

and instead declared: ‘I ﬁ gured out how to do everything. Based on string

theory with a gauge group SO(32), the anomalies cancel! It’s all consist-

ent! It’s a ﬁ nite quantum theory of gravity! It explains all the forces!’ The

audience, not realizing this was the ﬁ rst public announcement of their

discovery, laughed as Schwarz was carried off.

Green and Schwarz returned to Caltech and started to write up their

results. Witten had heard rumours from Aspen, and called to ﬁ nd out

more. They sent him a draft manuscript by Federal Express.

Things then happened very quickly.

The Green–Schwarz paper was submitted to Physics Letters in

September 1984. Witten submitted his ﬁ rst paper on superstrings to the

same journal later that same month. At Princeton, David Gross, Jeffrey

Harvey, Emil Martinec, and Ryan Rohm found another version of the

theory, called heterotic (or hybrid) superstring theory, in which the

anomalies cancelled. They submitted their paper to the journal Physical

Review Letters in November 1984.

The ﬁ rst superstring revolution had begun.

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389

There remained the puzzle of strings vibrating in a ten-dimensional

space–time. To a certain extent, the idea of spatial dimensions additional

to the familiar right-left, backwards-forwards, up-down dimensions had

been anticipated by German mathematician Theodor Kaluza in 1919. He

sent Einstein a draft paper showing how the two forces then known—

electromagnetism and gravity—could be uniﬁ ed in a single theoretical

framework which required four spatial dimensions. In 1926, Oscar Klein

had suggested that the extra dimension might be rolled up so small and

tight, with a radius equal to the Planck length, that it would remain for-

ever inscrutable. The resulting framework became known as Kaluza–

Klein theory.

But why stop at one hidden dimension? If there could be one such

dimension, why couldn’t there be two, or three, or nine? The point about

superstring theory was that it demanded precisely nine spatial dimen-

sions for the strings to vibrate in, no more and no less. It was necessary

to assume that the six additional spaces are curled up in a small bundle

so that we can’t experience them. Superstring theory had something to

say about the shape of these extra dimensions, but it had nothing to say

about their size.

In 1985, Princeton physicists Philip Candelas, Gary Horowitz, Andrew

Strominger, and Witten published a paper explaining that the topol-

ogy of the six extra dimensions had already been found as the solution

to an abstract problem in mathematics by Eugenio Calabi in 1957 and

Shing-tung Yau in 1978. According to this theory, at every point in our

familiar three-space, there lies a six-dimensional Calabi–Yau shape, so

small that it is beyond the reach of experimental instruments.

Each ‘hole’ in the Calabi–Yau shape gives rise to a family of low-energy

string vibrations. A Calabi–Yau shape would therefore produce three

families of vibrational patterns, corresponding to the three generations

of particles in the Standard Model.

But this was not plain sailing. Although the theory demands that the

extra dimensions curl up into a Calabi–Yau shape, there are potentially

hundreds of thousands of such shapes that would satisfy this require-

ment. Each candidate comes with its own set of free constants which

determine its size and shape. Each produces a different version of par-

ticle physics.