Enrico Fermi
Scuola Normale Superiore in Pisa

Fermi graduated from high school in July 1918, having skipped the third year entirely. At Amidei's urging, Fermi learned German to be able to read the many scientific papers that were published in that language at the time, and he applied to the Scuola Normale Superiore in Pisa. Amidei felt that the Scuola would provide better conditions for Fermi's development than the Sapienza University of Rome could at the time. Having lost one son, Fermi's parents only reluctantly allowed him to live in the school's lodgings away from Rome for four years. Fermi took first place in the difficult entrance exam, which included an essay on the theme of "Specific characteristics of Sounds"; the 17-year-old Fermi chose to use Fourier analysis to derive and solve the partial differential equation for a vibrating rod, and after interviewing Fermi the examiner declared he would become an outstanding physicist.

At the Scuola Normale Superiore, Fermi played pranks with fellow student Franco Rasetti; the two became close friends and collaborators. Fermi was advised by Luigi Puccianti, director of the physics laboratory, who said there was little he could teach Fermi and often asked Fermi to teach him something instead. Fermi's knowledge of quantum physics was such that Puccianti asked him to organize seminars on the topic. During this time Fermi learned tensor calculus, a technique key to general relativity. Fermi initially chose mathematics as his major, but soon switched to physics. He remained largely self-taught, studying general relativity, quantum mechanics, and atomic physics.

In September 1920, Fermi was admitted to the physics department. 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. The first was entitled "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 in relativity, it 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/c, where U was the electrostatic energy of the system, and c is the speed of light.

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/c. 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 timeline, 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 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.

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 Einstein equation (E = mc) 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."

In 1924, Fermi was initiated into the Masonic Lodge "Adriano Lemmi" of the Grand Orient of Italy.

In 1923–1924, Fermi spent a semester studying under Max Born at the University of Göttingen, where he met Werner Heisenberg and Pascual Jordan. Fermi then studied in Leiden with Paul Ehrenfest from September to December 1924 on a fellowship from the Rockefeller Foundation obtained through the intercession of the mathematician Vito Volterra. Here Fermi met Hendrik Lorentz and Albert Einstein, and became friends with Samuel Goudsmit and Jan Tinbergen. From January 1925 to late 1926, Fermi taught mathematical physics and theoretical mechanics at the University of Florence, where he teamed up with Rasetti to conduct a series of experiments on the effects of magnetic fields on mercury vapor. He also participated in seminars at the Sapienza University of Rome, giving lectures on quantum mechanics and solid state physics. While giving lectures on the new quantum mechanics based on the remarkable accuracy of predictions of the Schrödinger equation, Fermi would often say, "It has no business to fit so well!"

After Wolfgang Pauli announced his exclusion principle in 1925, Fermi responded with a paper "On the quantization of the perfect monoatomic gas" (Sulla quantizzazione del gas perfetto monoatomico), in which he applied the exclusion principle to an ideal gas. The paper was especially notable for Fermi's statistical formulation, which describes the distribution of particles in systems of many identical particles that obey the exclusion principle. This was independently developed soon after by the British physicist Paul Dirac, who also showed how it was related to the Bose–Einstein statistics. Accordingly, it is now known as Fermi–Dirac statistics. After Dirac, particles that obey the exclusion principle are today called " fermions ", while those that do not are called " bosons ".
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