Editing Enrico Fermi (section)

== ''Scuola Normale Superiore'' in Pisa ==
[[File:Enrico Fermi giovane.jpg|right|thumb|upright|Enrico Fermi as a student in Pisa]]
Fermi graduated from high school in July 1918, having skipped the third year entirely. At Amidei's urging, Fermi learned [[German language|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.{{sfn|Segrè|1970|pp=11–13}}{{sfn|Fermi|1954|pp=20–21}} 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 [[Euler–Bernoulli beam theory#Dynamic beam equation|vibrating rod]], and after interviewing Fermi the examiner declared he would become an outstanding physicist.{{sfn|Segrè|1970|pp=11–13}}<ref>{{cite web |url=http://mathematica.sns.it/autori/1173/ |title=Edizione Nazionale Mathematica Italiana – Giulio Pittarelli |publisher=Scuola Normale Superiore |language=it |access-date=6 May 2017 |archive-date=17 December 2017 |archive-url=https://web.archive.org/web/20171217014929/http://mathematica.sns.it/autori/1173/ |url-status=live }}</ref>

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.{{sfn|Segrè|1970|pp=15–18}} During this time Fermi learned [[tensor calculus]], a technique key to [[general relativity]].{{sfn|Bonolis|2001|p=320}} 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]].{{sfn|Bonolis|2001|pp=317–319}}

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.{{sfn|Segrè|1970|p=20}} 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" (''{{lang|it|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 (physics)|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" (''{{lang|it|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<sup>2</sup>, where U is the electrostatic energy of the system, and c is the [[speed of light]].{{sfn|Bonolis|2001|pp=317–319}}

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<sup>2</sup>. 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.<ref>{{cite journal |title=Über einen Widerspruch zwischen der elektrodynamischen und relativistischen Theorie der elektromagnetischen Masse |language=de |journal=Physikalische Zeitschrift |volume=23 |pages=340–344 |url=https://en.wikisource.org/?curid=1059488 |access-date=17 January 2013 |archive-date=3 February 2021 |archive-url=https://web.archive.org/web/20210203233214/https://en.wikisource.org/?curid=1059488 |url-status=live }}</ref> That year, Fermi submitted his article "On the phenomena occurring near a [[world line]]" (''{{lang|it|Sopra i fenomeni che avvengono in vicinanza di una linea oraria}}'') to the Italian journal ''{{ill|I Rendiconti dell'Accademia dei Lincei|it|Rendiconti 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]].{{sfn|Bertotti|2001|p=115}}{{sfn|Bonolis|2001|p=321}}

[[File:World line2.svg|left|thumb|A [[light cone]] is a three-dimensional surface of all possible light rays arriving at and departing from a point in [[spacetime]]. Here, it is depicted with one spatial dimension suppressed. The timeline is the vertical axis.]]
Fermi submitted his thesis, "A theorem on probability and some of its applications" (''{{lang|it|Un teorema di calcolo delle probabilità ed alcune sue applicazioni}}''), to the ''Scuola Normale Superiore'' in July 1922, and received his [[Laurea#Former status of the Laurea degree|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 to embrace 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.{{sfn|Bonolis|2001|p=321}}

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 [[Mass–energy equivalence|Einstein equation]] ({{nowrap|''E'' {{=}} ''mc''<sup>2</sup>}}) was an enormous amount of [[nuclear potential energy]] to be exploited.<ref>{{Cite web |last=Service |first=Multimedia |title=[as] radici – Le masse nella teoria della relatività (1923) |url=https://www.asimmetrie.it/le-masse-nella-teoria-della-relativita |access-date=23 July 2023 |website=Asimmetrie |language=it-it}}</ref> "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."{{sfn|Bonolis|2001|p=321}}

In 1924, Fermi was initiated into the [[Masonic Lodge]] "Adriano Lemmi" of the [[Grand Orient of Italy]].<ref>{{cite web|url=http://www.goilombardia.it/massoni-illustri/enrico-fermi|title=Enrico Fermi L'Uomo, lo Scienziato e il Massone|language=it|access-date=4 March 2015|archive-url=https://web.archive.org/web/20160320065006/http://www.goilombardia.it/massoni-illustri/enrico-fermi|archive-date=20 March 2016|url-status=dead}}</ref>

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 vapour. He also participated in seminars at the Sapienza University of Rome, giving lectures on quantum mechanics and [[solid state physics]].{{sfn|Bonolis|2001|pp=321–324}} 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!"{{sfn|Hey|Walters|2003|p=61}}

After [[Wolfgang Pauli]] announced his [[Pauli exclusion principle|exclusion principle]] in 1925, Fermi responded with a paper "On the quantization of the perfect monoatomic gas" (''{{lang|it|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 [[physical system|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]].{{sfn|Bonolis|2001|pp=329–330}} After Dirac, particles that obey the exclusion principle are today called "[[fermion]]s", while those that do not are called "[[boson]]s".{{sfn|Cooper|1999|p=31}}