How we travelled beyond infinity

Amanda Gefter, contributor

Frank Close tells the human story of how we solved The Infinity Puzzle - once the bane of physics

INFINITY. In mathematics, it's a curiosity. In physics, it's a disease. It reared its head back in the 1940s, with quantum electrodynamics (QED), the theory of electromagnetism.

QED's equations predicted that the electron's mass and charge were infinite. But physicists had already measured those values and found them to be finite. They were almost ready to abandon quantum field theory altogether, but within the decade physicists Richard Feynman, Julian Schwinger and Sin-Itiro Tomonaga independently found the solution: a mathematical trick known as renormalisation.

In The Infinity Puzzle, physicist Frank Close explores the history of renormalisation and physicists' decades-long quest to banish infinity once and for all. The key to renormalisation was knowing that an electron's charge and mass vary depending on the length scale at which you measure them. That's because its interactions with its own electric field and virtual particles in the quantum vacuum grow larger the closer you look, skyrocketing to infinity as you zoom in on the "naked" electron.

Renormalisation involved resetting the electron's naked mass and charge to the finite empirical values, cancelling out all infinities. With this fix, QED made predictions more accurate than any other theory in physics. Of course, it was not a particularly satisfying solution. Instead of predicting the electron's mass and charge from first principles, the theory's mathematics had to be tweaked with experiment-bought information to make the sums work out. Feynman referred to it as "hocus-pocus" - but it worked.

In his thoroughly researched and well-crafted narrative, Close traces the labyrinthine path trodden by physicists over the following decades as they tackled the infinities of two more forces: the weak force, which powers radioactivity and allows the sun to shine, and the strong force, which binds quarks into the protons and neutrons at the heart of every atom. He focuses on the triumphs and failures of the physicists behind the equations, providing a realistic view of how theoretical physics really progresses - the all-too-human endeavour fraught with personal ambitions, rivalries, alliances, errors and plain historical accident.

The difference between a Nobel prize and a name long-forgotten could lie with a journal editor's mood, or whether a physicist has been scheduled to speak first or last at a conference. Sometimes a missed opportunity is a physicists' own fault for not sticking to their guns or not seeing what's right in front of them. Ron Shaw discovered the Yang-Mills equations before Chen Ning Yang or Robert Mills, but after some discouraging words from his professor, Abdus Salam, decided not to publish. Gerard 't Hooft, having proven that the unified electroweak force was renormalisable - winning a Nobel for his trouble - missed out on a second Nobel when he "didn't realize that in the course of his work, he had also stumbled on the key to the strong interaction". That oversight determined the fates of David Gross, Frank Wilczek and David Politzer, who later shared a Nobel for finding that very key.

It's refreshing to read a popular physics book that doesn't revisit the same well-trodden ground of so many before it. At times, though, the physics gets lost in the narrative and I found myself wishing that Close would delve deeper into the meaning of the infinity puzzles. Early in the book he writes: "The philosophy of renormalisation is one of the most difficult, and controversial, in all of particle physics." But disappointingly he never returns to explore its implications.

In the end, Close concludes: "The outcome of the revolution that pursuit of the Infinity Puzzle helped inspire is that physics has for the first time a testable theory about the origins of the material universe." That's exciting, but the missing ingredient is gravity - the one force whose infinities have yet to be tamed. Why gravity is so stubborn, and how something like string theory might provide the solution, is a fascinating topic in its own right. That human drama is still unfolding.

Book Information
The Infinity Puzzle
by Frank Close
Published by: Oxford University Press/Basic Books
?16.99/$28.99

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