Ettore Majorana

Ettore Majorana

Ettore Majorana (5 August 1906, Catania, Sicily, Italy27 March 1938 presumed dead) was an Italian theoretical physicist who began promising work on neutrino masses. He disappeared suddenly in mysterious circumstances. Noted for the eponymous Majorana equation.

Life and work

Gifted in Mathematics

Majorana was born in Catania, Sicily. Mathematically extremely gifted, he was very young when he joined Enrico Fermi's team in Rome as one of the "Via Panisperna boys", who took their name from the street address of their laboratory.

He began his university studies in engineering in 1923, but switched to physics in 1928 at the urging of Emilio Segrè."Great Mysteries of the Past", Reader's Digest Association, Pleasantville, New York, 1991, pp. 69-72.] His first papers dealt with problems in atomic spectroscopy.

First published academic papers

His first paper, published in 1928, was written when he was an undergraduate and was coauthored by Giovanni Gentile Jr., a junior professor in the Institute of Physics in Rome. This work was an early quantitative application to atomic spectroscopy of Fermi's statistical model of atomic structure (now known as the Thomas-Fermi model, due to its contemporaneous description by Llewellyn Thomas).

In this paper, Majorana and Gentile performed first-principles calculations within the context of this model that gave a good account of experimentally observed core electron energies of gadolinium and uranium, and of the fine structure splitting of caesium lines observed in optical spectra. In 1931, Majorana published the first paper describing the phenomenon of autoionization in atomic spectra, designated by him as "spontaneous ionization"; an independent paper in the same year, published by Allen Shenstone of Princeton University, first used the term "auto-ionization", which has since become conventional, without the hyphen.

Majorana earned his undergraduate degree in engineering, and completed his physics doctorate, both at the University of Rome La Sapienza.

An important paper (1932) in the field of atomic spectroscopy concerned the behaviour of aligned atoms in time-varying magnetic fields. This problem, also studied by I.I. Rabi and others, led to an important sub-branch of atomic physics, that of radio-frequency spectroscopy. Also in 1932, Majorana published his paper on a relativistic theory of particles with arbitrary intrinsic momentum, in which he developed and applied infinite dimensional representations of the Lorentz group, and gave a theoretical basis for the mass spectrum of elementary particles. Like most of Majorana's papers in Italian, this paper languished in relative obscurity for several decades. (It is discussed in detail by D. M. Fradkin, "Amer. J. Phys.", vol. 34, pp.314-318 (1966)).

Works with Heisenberg, illness, isolation

"At Fermi's urging, Majorana left Italy early in 1933 on a grant from the National Research Council. In Leipzig, Germany, he met Werner Heisenberg, another Nobel Prize winner. In the letters he subsequently wrote Heisenberg, Majorana revealed that he had found not only a scientific colleague but a warm personal friend.""Great Mysteries of the Past", Reader's Digest Association, Pleasantville, New York, 1991, p. 71.] Majorana also travelled to Copenhagen, where he worked with Niels Bohr, yet another Nobel Prize winner, and friend and mentor of Heisenberg.

The Nazis had come to power in Germany just as Majorana arrived there. Subsequently, he studied with Werner Heisenberg in Leipzig, and worked on a theory of the nucleus (published in German in 1933) which, in its treatment of exchange forces, represented a further development of Heisenberg's theory of the nucleus. Majorana's last-published paper, in 1937, again in Italian, concerned his elaboration of a symmetrical theory of electrons and positrons.

"In the fall of 1933, Majorana returned to Rome in poor health, having developed acute gastritis in Germany and apparently suffering from nervous exhaustion. Put on a strict diet, he grew reclusive and became harsh in his dealings with his family. To his mother, with whom he had previously shared a warm relationship, he had written from Germany that he would not accompany her on their customary summer vacation by the sea. Appearing at the institute less frequently, he soon was scarcely leaving his home; the promising young physicist had become a hermit. For nearly four years he shut himself off from friends and stopped publishing."

Majorana, during these same years in which he published these few articles, wrote many small works about several topics: from Geophysics, to Electrical Engineering, from Mathematics to Relativity. These unpublished papers, preserved in Domus galileiana in Pisa, have been recently edited by Erasmo Recami and Salvatore Esposito.

He became full professor of theoretical physics at the University of Naples in 1937, without needing to take an examination because, as certified by official documents, competition board suggested “to appoint Majorana as full professor of Theoretical Physics in a University of the Italian kingdom, for high and well-deserved repute, independently of the competition rules”.

The competition board suggestion was accepted and Majorana taught the chair of Theoretical Physics in Naples. After a few months of teaching, however, it ended with his well-known disappearance.

Work with neutrino masses

Majorana did prescient theoretical work on neutrino masses, a currently active subject of research. He also worked on an idea that mass may exert a small shielding effect on gravitational waves, which did not gain much traction.

His uncle Quirino Majorana was also a physicist.

The year 2006 marked Majorana's centenary, and [ a book] of his (nine) collected papers, with commentary and English translations, was published by the Italian Physical Society.

For the Centenary of Ettore Majorana (1906-1938) [ Electronic Journal of Theoretical Physics] ' (EJTP) has published a special issue (20 articles) dedicated to the modern development of Majorana’s legacy.

On the occasion of the Majorana Centenary in 2006 and the editing of the Special Issue about his Legacy in Contemporary Physics, the Electronic Journal of Theoretical Physics has established a prize in memory of the great Sicilian physicist Ettore Majorana (1906 - 1938). The " [ Majorana Medal] " is an annual prize of excellence for the researchers who showed peculiar creativity, critical sense and mathematical rigour in theoretical physics - in its broadest sense. The recipients of the 2006 Majorana prize were Erasmo Recami (University of Bergamo and INFN) and George Sudarshan (University of Texas), and for the 2007 Majorana Prize; Lee Smolin (Perimeter Institute for Theoretical Physics, Canada), Eliano Pessa (Centro Interdipartimentale di Scienze Cognitive, Universit`a di Pavia and Dipartimento di Psicologia, Universit`a di Pavia Piazza Botta, Italy) and Marcello Cini (Dipartimento di Fisica, Universita’ La Sapienza, Roma, Italy).

Disappearance at sea and theories

Traveling to Naples

Majorana disappeared in unknown circumstances during a return boat trip from Palermo to Naples. Despite several investigations, the truth about his fate is still uncertain. His body has not been found. He had apparently withdrawn a large sum of money from his bank account, prior to making the first trip to Palermo a few days before the return trip. ["Mysteries of the Past", "Reader's Digest" Press, New York 1991.] He may have travelled to Palermo hoping to visit his friend Emilio Segrè, a professor at the university there. But Segrè was in California at that time, September 1938, and as a Jew, was barred from returning to Italy under a 1938 law passed by Benito Mussolini's government.

Immediately after Majorana's disappearance, several people theorized about what could have happened; major hypotheses have included:
*He could have been kidnapped by foreign powers.
*He could have committed suicide (he left two letters which contained a sort of farewell).
*He could have voluntarily disappeared, changed his identity and possibly left Italy.

Voluntary disappearance theory detailed

Some argue for this last hypothesis, conjecturing that after having envisioned the destructive power of atomic energy, Majorana did not want to contribute to its deployment in a fascist state (at that time, Italy was governed by Benito Mussolini). There have been sporadic rumors that he may have been sighted in South America in the 1950s. Also in Italy, a story appeared in the news when a man living on the street claimed that he once was a famous physicist.

The Sciascia hypothesis

The Italian writer Leonardo Sciascia has summarized some of the results of these investigations and these hypotheses in his passionate book "La Scomparsa di Majorana" (Einaudi, 1975 - English translation: "The Moro Affair and The Mystery of Majorana", Carcanet, 1987, ISBN 0-85635-700-6). However, some of Sciascia's conclusions were refuted by certain of Majorana's former colleagues, including E. Amaldi and E. Segrè. The various hypotheses on Majorana's disappearance have been extensively discussed by Erasmo Recami in his book "Il caso Majorana: Lettere, testimonianze, documenti" (Di Renzo Editore, Roma, 2000), and in a journal article (E. Recami, "I nuovi documenti sulla scomparsa del fisico Ettore Majorana", "Scientia", vol. 110, pp.577-588 (1975); English version titled "New Evidence on the Disappearance of the Physicist Ettore Majorana", "Scientia", vol. 110, p. 589 ff. (1975)). In the above-mentioned book and article, Recami discusses critically the various rival explanations concerning Majorana's disappearance, including those advanced by Sciascia in his short book, and presents highly suggestive evidence to the effect that Majorana absconded to Argentina, where he may have earned his living as an engineer.

The theories about Majorana’s disappearance can be summarized as follows:
*Hypothesis of suicide, by Amaldi, Segrè and others;
*Hypothesis of escape to Argentina, by Recami and Artemi (who has developed a detailed if hypothetical reconstruction of the possible escape and life in Argentina of Majorana);
*Hypothesis of escape to a monastery, by Sciascia;
*Hypothesis of kidnapping or killing, to avoid his participation in the construction of an atomic weapon, by Bella, Bartocci and others;
*Hypothesis of escape to become a beggar, ("omu cani" hypothesis), by Bascone.


*"Appunti inediti di Fisica teorica", Zanichelli, 2006. (Edited by E. Recami and S. Esposito)
*Carlo Artemi, "Il plano Majorana: una fuga perfetta" ( The Majorana plan: a perfect escape), De Rocco press, Rome, 2007.
*E. Amaldi, "Ricordo di Ettore Majorana", Giornale di fisica, 9, 1968.
*E. Recami, "Il caso Majorana", Di Renzo Ed., Roma, 2001.
*I. Bascone, "Tommaso l’omu cani amara e miserabile ipotesi sulla scomparsa di Ettore Majorana fisico siciliano al tempo del fascismo", ed. Ananke, 1999.
*I. Licata (ed), Majorana Legacy in Contemporary Physics, Di Renzo Ed., Roma, (2006).
*L. Castellani, "Dossier Majorana, Fratelli Fabbri", 1974 (edited again in 2006).
*L. Sciascia, "La scomparsa di Majorana", Adelphi ed., 1975.
*S. Bella, "Rivelazioni sulla scomparsa di uno scienziato : Ettore Majorana", Italia letteraria, 1975.
*S. Esposito, "Ettore Majorana and his heritage seventy years later", [ arxiv:physics.hist-ph/0803.3602] (2008).
*"Reader's Digest" Association, "Great Mysteries of the Past", Pleasantville, New York, 1991, ISBN 0-89577-377-5, pp. 69-72.
*U. Bartocci, "La scomparsa di Majorana: un affare di stato?", ed. Andromeda, 1999.


::Enrico Fermi

ee also

*List of people who have disappeared
*Majorana equation
*Majorana fermion


For a summary of Majorana's scientific output, see the following article (in Italian): E. Amaldi, "L'opera scientifica di Ettore Majorana", "Physis", vol. X, pp.173-187 (1968).

Majorana's collected papers, accompanied by English translations and commentaries, were published in [ Ettore Majorana Scientific Papers on the occasion of the centenary of the birth] .


External links

* [ CERN Courier: Ettore Majorana: genius and mystery]
* [ Ettore homepage]
* [ Ettore homepage]
* [ Ettore Majorana Foundation and Centre for Scientific Culture]
* [ Majorana Legacy in Contemporary Physics]
* [ Majorana Prize]

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