# Enrico Fermi and Scuola Normale Superiore

June 26, 2021Fermi finished high school in July 1918 and, with Amidei’s support, applied to the Scuola Normale Superiore in Pisa.

Because they had lost their other son, his family did not allow him to move out of the house at first, but they later granted his request. The school in Pisa offered students free housing, but the entrance exam, which required writing an essay, was extremely difficult. The theme given was “Specific characteristics of sounds”. 17-year-old Fermi derived and solved the partial differential equation and applied it to a vibrating rod, using Fourier analysis to do so. The examiner interviewed Professor Giuseppe Pittarelli Fermi from Sapienza University and said that the exam he gave was at the doctoral level and Fermi entered the school with the first place.

During his years at the Scuola Normale Superiore, he befriended another student, Franco Rasetti, and they were friendly enough to joke with, and later began working together. Luigi Puccianti, director of the Fermi physics laboratory in Pisa, told Fermi that he had little to teach and that Fermi had to teach him something. Fermi’s knowledge of quantum physics reached such a level that Puccianti asked him to organize seminars on the subject. During this time Fermi learned the tensor calculus developed by Gregorio Ricci and Tulli Levi-Civita, which is necessary to illustrate the principles of the general theory of relativity. Fermi first chose mathematics, but later switched to physics. He taught himself general relativity, quantum mechanics, and atomic physics.

In September 1920, Fermi was accepted into the physics department. Since there were only three students in the department (Fermi, Rasetti and Nello Carrara), Puccianti allowed them to use the lab as they wished. Fermi decided to investigate x-ray crystallography, and the three of them worked together to produce the Laue photograph, an x-ray image of a crystal. In 1921, Fermi’s third year at university, Fermi published his articles in the Italian magazine Nuovo Cimento. The title of his first article was “Dynamics of an electric charge system in a solid and translational motion”. Weight was expressed as a tensor, something that moves and is displaced in three-dimensional space. In classical mechanics weight was a scalar value, but in relativity it changes with speed. The second article was “On the electrostatics of a uniform gravitational field consisting of electromagnetic charges and electromagnetic currents”. Using general relativity, Fermi found that the weight of a charge is U/c2 (where U is the electrostatic energy of the system and c is the speed of light).

The first article expressed the contradiction between the theory of electrodynamics and the theory of relativity in terms of the calculation of electromagnetic weight (4/3 U/c2 in electrodynamic theory). Fermi raised this issue the following year in an article on “A conflict between the electrodynamic and relativity theories explaining electromagnetic weight,” and stated that this contradiction was a consequence of relativity. This article was of high reputation and was translated into German and published in the German journal Physikalische Zeitschrift in 1922. In the same year, Fermi submitted his article “Events taking place near timelines” to the Italian journal I Rendiconti dell’Accademia dei Lincei. In this article he discussed the Equivalence principle and presented the Fermi coordinates. He proved that space near timelines behaves like Euclidean space.

Fermi presented his thesis entitled “A theorem on probability and its applications” to the Scuola Normale Superiore in July 1922 and received his diploma at the age of 21. His thesis was on x-ray diffraction pictures. Theoretical physics was not yet recognized as a discipline in Italy, and only theses on experimental physics were accepted in this field. For this reason, Italian physicists later accepted ideas such as relativity from Germany. This wasn’t a problem for him, as Fermi was pretty good at laboratory experiments.

While writing an addendum to August Kopff’s The Mathematical Theory of Relativity, he realized that the potential for an enormous amount of nuclear energy resides within Einstein’s famous equation E = mc2. “It seems unlikely that this monstrous amount of energy will be released in the near future, because when this event occurs the first job of this burst of energy will be to tear apart the physicist who created it,” Fermi said.

In 1924, Fermi was taken to the Adriano Lemmi lodge of the Italian Freemasons.

Fermi decided to go abroad and became a semester student of Max Born at the University of Göttingen. Here he met with Werner Heisenberg and Pascual Jordan. Fermi later studied at Leiden with Paul Ehrenfest on a Rockefeller scholarship, which was granted to him by mathematician Vito Volterra from September to December 1924. Fermi met Hendrik Lorentz and Albert Einstein here and became friends with Samuel Goudsmit and Jan Tinbergen. From January 1925 until late 1926 Fermi taught mathematical physics and theoretical mechanics at the University of Florence, where he and Rasetti conducted experiments on the effect of magnetic fields on mercury vapor.