Sep 292018

Enrico Fermi, the nuclear physicist was born in Rome on this date in 1901. The scientific school where I taught for 2 years in Mantua was named Enrico Fermi technical school and liceo (in Italian), so I feel the need to give him an extra nod even though I covered his supervision of the first sustained nuclear chain reaction here:  Now I can be a tad more general.

Fermi was the third child of Alberto Fermi, a division head (Capo Divisione) in the Ministry of Railways, and Ida de Gattis, a primary school teacher. One of Fermi’s first sources for his study of physics was a book he found at the local market at Campo de’ Fiori in Rome, the 900-page Elementorum physicae mathematicae(1840), which was written in Latin by Jesuit Father Andrea Caraffa, a professor at the Collegio Romano. It covered mathematics, classical mechanics, astronomy, optics, and acoustics, insofar as these disciplines were understood when the book was written. Fermi befriended another scientifically inclined student, Enrico Persico, and together the two worked on scientific projects such as building gyroscopes and trying to measure the acceleration of Earth’s gravity accurately (a young Galileo). Fermi’s interest in physics was further encouraged by his father’s colleague Adolfo Amidei, who gave him several books on physics and mathematics, which he read and assimilated quickly.

Fermi finished secondary school in July 1918 and, at Amidei’s urging, applied to the Scuola Normale Superiore in Pisa. The school provided free lodging for students, but candidates had to take a difficult entrance exam that included an essay. The given theme was “Specific characteristics of Sounds”. The 17-year-old Fermi chose to derive and solve the partial differential equation for a vibrating rod, applying Fourier analysis in the solution. The examiner, Professor Giulio Pittarelli from the Sapienza University of Rome, interviewed Fermi and praised him, saying that he would become an outstanding physicist in the future.

During his years at the Scuola Normale Superiore, Fermi teamed up with a fellow student, Franco Rasetti, with whom he would indulge in light-hearted pranks and who would later become Fermi’s close friend and collaborator. In Pisa, Fermi was supervised by the director of the physics laboratory, Luigi Puccianti, who acknowledged that there was little that he could teach Fermi, and frequently asked Fermi to teach him something instead. Fermi’s knowledge of quantum physics reached such a high level that Puccianti asked him to organize seminars on the topic. During this time Fermi learned tensor calculus, a mathematical technique invented by Gregorio Ricci and Tullio Levi-Civita that was needed to demonstrate the principles of general relativity. Fermi initially chose mathematics as his major field, but soon switched to physics. He remained largely self-taught, studying general relativity, quantum mechanics, and atomic physics.

In September 1920, Fermi was admitted formally as a teacher in the physics department even though he was still an undergraduate. Since there were only three students in the department—Fermi, Rasetti, and Nello Carrara—Puccianti let them freely use the laboratory for whatever purposes they chose. Fermi decided that they should research X-ray crystallography, and the three worked to produce a Laue photograph—an X-ray photograph of a crystal. During 1921, his third year at the university, Fermi published his first scientific works in the Italian journal Nuovo Cimento, “On the dynamics of a rigid system of electrical charges in translational motion” (Sulla dinamica di un sistema rigido di cariche elettriche in moto traslatorio). A sign of things to come was that the mass was expressed as a tensor—a mathematical construct commonly used to describe something moving and changing in three-dimensional space. In classical mechanics, mass is a scalar quantity, but within relativity mass changes with velocity. The second paper was “On the electrostatics of a uniform gravitational field of electromagnetic charges and on the weight of electromagnetic charges” (Sull’elettrostatica di un campo gravitazionale uniforme e sul peso delle masse elettromagnetiche). Using general relativity, Fermi showed that a charge has a weight equal to U/c2, where U was the electrostatic energy of the system, and c is the speed of light.

A Fermiac

The first paper seemed to point out a contradiction between the electrodynamic theory and the relativistic one concerning the calculation of the electromagnetic masses, as the former predicted a value of 4/3 U/c2. Fermi addressed this the next year in a paper “Concerning a contradiction between electrodynamic and the relativistic theory of electromagnetic mass” in which he showed that the apparent contradiction was a consequence of relativity. This paper was sufficiently well-regarded that it was translated into German and published in the German scientific journal Physikalische Zeitschrift in 1922. That year, Fermi submitted his article “On the phenomena occurring near a world line” (Sopra i fenomeni che avvengono in vicinanza di una linea oraria) to the Italian journal I Rendiconti dell’Accademia dei Lincei. In this article he examined the Principle of Equivalence, and introduced the so-called “Fermi coordinates”. He proved that on a world line close to the time line, space behaves as if it were a Euclidean space.

Fermi submitted his thesis, “A theorem on probability and some of its applications” (Un teorema di calcolo delle probabilità ed alcune sue applicazioni), to the Scuola Normale Superiore in July 1922, and received his laurea at the unusually young age of 20. The thesis was on X-ray diffraction images. Theoretical physics was not yet considered a discipline in Italy, and the only thesis that would have been accepted was one on experimental physics. For this reason, Italian physicists were slow in embracing the new ideas like relativity coming from Germany. Since Fermi was quite at home in the lab doing experimental work, this did not pose insurmountable problems for him, and ended up making him something of a rara avis, a nuclear physicist equally at home with both theoretical and experimental physics.

While writing the appendix for the Italian edition of the book Fundamentals of Einstein Relativity by August Kopff in 1923, Fermi was the first to point out that hidden inside the famous Einstein equation (E = mc2) was an enormous amount of nuclear potential energy to be exploited. “It does not seem possible, at least in the near future”, he wrote, “to find a way to release these dreadful amounts of energy—which is all to the good because the first effect of an explosion of such a dreadful amount of energy would be to smash into smithereens the physicist who had the misfortune to find a way to do it.” Well, he did go on to find a way to do it, and was not smashed to smithereens. Unfortunately, many people were in Hiroshima and Nagasaki, and Fermi, after helping a team in Los Alamos develop the first atomic bombs in the US, became a staunch advocate for the limitation of nuclear weapons, especially after Russians invented a fusion bomb.

I could go on, but, combined with my post on Fermi’s CP-1 pile, you have a very good outline of his life’s work. I do wonder, more often than I would like, what goes into the making of geniuses such as Fermi. How can a teenager, barely starting as an undergraduate be more capable in his field than the head of the department?  A friend of mine who is a noted mathematician pointed out that mathematics and theoretical physics are often revolutionized by very young scholars, partly because their minds are agile and flexible, and partly because their lives are not cluttered with distractions. When they marry and have children their creativity begins to fade, although their work may still be very good.

One of the measures of Fermi’s greatness is the number of diverse things that are named after him: schools, roads, concepts in physics, devices, buildings, departments, and a trans-uranic element – fermium. This gives me an idea for creating a dessert in his honor: the Fermi Pile Tiramisu. Look at this photo for the general idea:

You need a package of ladyfinger biscuits, tiramisu custard, and high quality cocoa. Here is my recipe for the custard again:

Put 4 egg yolks and half a cup of sugar in the top of a double boiler. Bring the water in the bottom to a steady simmer, and make sure that the water does not touch the top part of the boiler. Whisk the sugar and egg yolk mixture vigorously for around 8 minutes. It will expand to a froth and cook. (Hint: you are not making scrambled eggs). Remove from the heat and fold in 1 pound (½ kg) of mascarpone. In a separate bowl whisk 1 cup of heavy cream to stiff peaks. Fold the mascarpone-egg mix into the cream. Chill in the refrigerator overnight.

Next day, make a base of custard and embed a layer of ladyfingers in it. Sprinkle some cocoa over the ladyfingers and then start layering custard and biscuits, finishing with custard and a generous shower of cocoa. Play with this concept to suit yourself.