Fermi’s questions

Accuracy is often defined as how close you are to the ‘true’ value. Yet if something has never been measured before, how do you know that what you measure is even close? For this you need a special toolset to peer into the unknown and an approach that is often attributed to Enrico Fermi, whose questions led to love, friendship and learning.

Fermi grew up in Rome, Italy, playing with his elder brother, Giulio, who was fascinated by airplanes and electricity. Giulio’s sudden death in 1915 hit the family very hard. Enrico’s response was to bury himself in his studies and to read voraciously. Times were hard and their flat was unheated; reading, he would sit on his hands to keep them warm, turning the pages with his tongue.

As a teenager, a friend of his father’s began to guide his interest in science. When Fermi applied for a scholarship at the Reale Scuola Normale in Pisa, the examiner was so astonished by the Fourier series that Fermi used to solve a problem on sound that they invited him for interview to check that there wasn’t some mistake.

It was soon clear that here was a truly exceptional student whose understanding of the new physics – quantum theory and relativity – was well in advance of that of any member of staff. So his numerous pranks – like a stink bomb let off to enliven a particularly dull lecture – were forgiven. He and a couple of friends were given the run of the labs and told to get on with whatever they found interesting. Fermi graduated with the highest marks at age 20.

In 1930, aged 29, Fermi was offered the new chair of theoretical physics in Rome. He surrounded himself with a group of young students, some them childhood friends, others drawn from the highly mathematically oriented engineering school; they became known, toponymically, as the ‘Panisperna Street boys’. He also began to spend time with a young woman called Laura Capon who was very taken by his mix of brilliance and matter of fact directness. Her sister was less impressed; she thought Fermi and his mates ‘a dull bunch of logarithms’.

Maybe this was because Fermi liked to play the slightly nerdy ‘two lire’ game with his friends and students. ‘Each person can put a question to someone and if they don’t give a satisfactory answer they have to pay one lira. But if the person who asked the question can’t give an answer satisfactory to all of us, he or she has to pay two lire.’ It was an opportunity to think about ideas and solve hard problems, at low stakes. And perhaps because Fermi was so often right – he seemed almost infallible in matters of quantum theory – he was nicknamed The Pope.

Was it accident or design?

Fermi’s research turned increasingly nuclear. The discovery by James Chadwick of the ‘neutrone’ (the big neutral thing) gave Fermi the idea that it might penetrate the nucleus. He developed a theory of beta particle decay, renaming the massless, neutral particle that Pauli had invoked to account for spin as the ‘neutrino’ (the little neutral thing). His paper was the foundation of the theory of the electroweak interaction. The neutron experiments also bore fruit when – was it accident or design? – he placed paraffin wax in the neutron beam. Bombarding uranium with the unexpectedly slow neutrons gave scores of radioactive products.

Fermi was convinced he had made new transuranic elements. But Ida Noddack in Germany disagreed. She proposed that the nuclei would split. For once, Fermi was wrong; to his embarrassment the Nobel prize he was awarded in 1938 included his transuranics in the citation.

But 1938 was also the year that Benito Mussolini brought in racial discrimination laws that targeted Jews like Fermi’s wife Laura. The Panisperna team scattered, several emigrating. After collecting his prize in Stockholm, Fermi and his family moved to the US – to New York and Columbia University.

The Einstein-Szilard letter to President Roosevelt of 1939 led to the Manhattan project to weaponise nuclear fission. Fermi built the first self-sustaining nuclear ‘pile’ in Chicago, an experiment that would bring ‘the bomb’ several steps closer, but also seed what is now the Argonne National Lab.

Fermi was present at the ‘Trinity test’ of the first atomic bomb on 16 July 1945. As the shockwave passed he famously scattered a handful of shredded paper into the air. After pacing out how far they had been blown by the blast he guesstimated the yield of the explosion to be 10 kilotonnes, a bit over half the actual yield established by detailed measurement and calculation. Not bad for some mental maths.

That anecdote is probably the origin of the phrase ‘Fermi calculation’. It is an approach taken by John Harte in his wonderful textbook of environmental science Consider a Spherical Cow, as well as by Randall Munroe in his cartoon xkcd. The older I get, the more I think we should spend a lot more time teaching science through such a ballsy, order-of-magnitude approach, focusing on the argument and the model rather than ‘the answer’. To paraphrase George Box, Fermi estimates are not always right, but they are useful.