**The Infinity Puzzle: How the quest to understand quantum field theory led to extraordinary science, high politics, and the world's most expensive experiment by Frank Close**

**Literary Review, December 2011**

‘A desk or table, a chair, paper and pencils,’ was what Einstein asked for in 1933 when he arrived at the Institute for Advanced Study in Princeton. Then he remembered one last item: ‘Oh yes, and a large wastebasket, so I can throw away all my mistakes.’ In the next two decades before his death in 1955 there were plenty of them, but Einstein had earned the right to make those mistakes in search of his holy grail – a unified field theory.

In 1864 the Scottish physicist
James Clerk Maxwell showed that electricity and

magnetism were different
manifestations of the same underlying phenomenon – electromagnetism. His great
achievement was to encapsulate the disparate behaviour of electricity and
magnetism into a set of four elegant mathematical equations that were to be the
crowning glory of nineteenth-century physics.

Einstein sought a single,
all-encompassing theoretical structure that would unify electromagnetism with
his theory of gravity, the general theory of relativity. Such a unification was
the logical next step for Einstein, but few were convinced, for in the
twentieth century two new forces were discovered and given names that alluded
to their strengths relative to the electromagnetic: the so-called strong and
weak forces.

The strong force is the binding
force that holds atomic nuclei together; conversely the weak force destabilises
nuclei, causing a form of radioactivity that plays an essential role in the way
that the sun produces its energy. As the years passed the belief grew that
these four forces – electromagnetism, gravity, and the strong and weak forces –
would be reunited in a Theory of Everything.

With the exception of general
relativity, physicists have been able to ‘quantize’ the other three forces,
since quantum mechanics deals with the atomic and sub-atomic domain. In effect
they managed to get three trains running on the same size track. The quantum
gravity train is still stuck at the station. In The Infinity Puzzle Oxford particle physicist Frank Close tells the
tale of quantum field theory – the attempts to understand and then unite
electromagnetism and the strong and weak forces.

In the 1930s the union of
Maxwell’s theory of electromagnetism, Einstein’s theory of special relativity,
and quantum mechanics gave birth to a theory of the electromagnetic force known
as quantum electrodynamics, or QED. However, in the bowels of the theory lurked
a monster – infinity. The equations of QED kept predicting that the chance of
some things occurring was ‘infinite’. When infinity pops up in physics it
spells disaster since, as Close explains, it is ‘proof that you are trying to
apply a theory beyond its realm of applicability’. In the case of QED, if you
can’t calculate something as basic as a photon – a particle of light –
interacting with an electron without getting infinity, you haven’t got a
theory.

It was the late 1940s before a
way was found to solve the infinity puzzle in QED by a process called
renormalisation. The calculations of many properties of atoms and their
constituent particles, including those for the mass and charge of an electron, gave
infinity as the answer. However, these two quantities of the electron had
already been measured to a high degree of precision using other methods and the
results were sufficient to provide benchmarks for anything else physicists
wished to compute in QED. Instead of infinity, many of the answers now turned
out to be finite and correct. Some physical quantities that have been
calculated using renormalisation agree with earlier experiments to an accuracy
of one part in a trillion, which is an order of magnitude akin to the diameter
of a hair when compared to the width of the Atlantic.

Renormalisation may have been
inelegant but its ‘recipe for extracting sensible answers for QED worked’.
Those who cooked it up independently of each other – Richard Feynman, Julian
Schwinger and Sin-Itiro Tomonaga – won a share of the 1965 Nobel Prize in
Physics.

Gerard 't Hooft |

It may be a collective
enterprise but, as Close’s book reveals, science is full of wrong turns,
partial answers, missed opportunities and misunderstandings. How could it be otherwise,
since the dispassionate, logic-driven stereotype of the scientist is a fiction?
The physicists in The Infinity Puzzle ‘experience the same
emotions, pressures and temptations as any other group of people, and respond
in as many ways’.

A timeline of who did what
when, together with a glossary, could be added to the paperback, to help
readers as they grapple with gauge invariance, parity violation, spontaneous
symmetry breaking, gluons, colour, the Higgs boson and SU(2)xU(1). Yet Close
has succeeded in humanising a dramatic era of physics in what is my science
book of the year. Some sections of his narrative are difficult because of the
inherent nature of the ideas he’s trying to explain. But then, it took
exceedingly clever people to devise them.

‘Hold Infinity in the palm of
your hand,’ William Blake wrote in the ‘Auguries of Innocence’. Frank Close
does a fabulous job of reconstructing how physicists like Feynman and ’t Hooft
managed to do exactly that.