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Life of Ettore Majorana

The Great Inquisitor

Ettore Majorana was born in Catania on August 5th 1906 into a cultured family: Already as a child, Ettore showed signs of being a child prodigy, and at the age of four he mastered arithmetic, while at seven he already excelled at chess.

He studied with the Jesuits at the Istituto Massimo in Rome, and in 1923 he graduated from high school; in the autumn of the same year, he enrolled in the two-year preparatory course for engineering at the University of Rome. His reputation as a mathematical genius, who never shied away from dispensing advice and explanations to many of his fellow students, began to spread during this period. At the end of his two-year course, he enrolled in the Scuola di Applicazione degli Ingegneri. At the end of 1927, the circle around Enrico Fermi was gradually being created: Emilio Segrè had switched from engineering to physics and often praised the exceptional qualities of Ettore Majorana. Their first meeting took place in the autumn of that year when Fermi had just found an approximate solution to a problem he was studying. It has been reported that during their conversation Fermi spoke about his recent research and quickly outlined the general lines of the model, showing the tables where the various numerical values were collected and that Majorana recalculated the same table in just under 24 hours. Shortly afterwards he left the engineering faculty to enroll in physics.

In his new environment Majorana impressed everyone with his strong intelligence, his deep understanding of phenomena and his exceptional critical spirit, which differentiated him from  his colleagues. These characteristics soon earned him the name of “Grand Inquisitor”. Majorana graduated in July 1929 with top marks under the guidance of Fermi with a thesis entitled “On the mechanics of radioactive nuclei”, which was one of the first works on nuclear physics in the Roman environment which at that time was focusing on the study of atoms.

The newly formed group of Ragazzi di Via Panisperna had been created to function as a perfect “physics machine” and revolved around the figure of Fermi, the “Pope” of Italian physics, who was seen as an absolute authority. Majorana, on the other hand, was a reflective person, with a deep-rooted capacity for analysis who carried out his research in complete autonomy, since the work of a theoretical physicist requires patience and extreme concentration. Relations were not exactly jovial, while in fact Majorana cultivated friendly relations with the other boys in Via Panisperna. Of the young physicists who revolved around Fermi, Majorana was the only one who never held an official position in Rome. The consequence of this different view of things led Majorana to a detached attitude towards the group, rarely attending the institute but always showing sincere willingness when his great skill was required. As reported by Edoardo Amaldi and Bruno Pontecorvo, Majorana was the only one who could discuss scientific problems with Fermi as an equal.

After graduating and becoming a free lecturer, he did not acquire any official position within the Institute of Physics, and at the end of 1932 Majorana asked the National Research Council for a scholarship for a stay abroad in Leipzig and Copenhagen, which was accepted also thanks to a letter of support from Fermi. Majorana arrived in Leipzig at Werner Heisenberg’s court on 19 January 1933. His German stay was very profitable for Majorana. The exciting atmosphere of the centre run by Heisenberg, which hosted some of the most important theoretical physicists of the time, aroused a particular fascination in the young Italian physicist compared to the backward Italian environment, where theoretical physics was still confined to a practically nonexistent state. In Leipzig Majorana published three articles, and, above all, he made crucial contribution to the nucleus model proposed by Heisenberg by providing some fundamental corrections. Heisenberg praised the work of the physicist from Catania over and over again, both at the seminars held in Leipzig and during the Solvay Congress in 1933, and he gave him all the credit. After a brief one-month stay in Copenhagen with Niels Bohr, Ettore returned to Italy in August 1933.

On his return from Leipzig, in spite of the scientific success he had acquired, relations with Via Panisperna did not improve, indeed they grew progressively more distant. When some of the most important discoveries in the field of nuclear physics were being made at the Institute of Physics, Ettore, the forerunner of these studies, was absent. This hiatus was only interrupted in 1937 with the publication of a paper, probably his most important, “Symmetric theory of the electron of the positron”, which set aside the theory of negative energy states of the famous physicist Paul Dirac, for a more general theory in which it is possible to describe neutral particles as Majorana particles, identical to their antiparticles.

In the spring of the same year, the University of Palermo, at the behest of Emilio Segrè, announced a competition for professorships in theoretical physics. There were many good candidates and the winning trio were: Gian Carlo Wick, Giulio Racah and Giovanni Gentile, Jr. Majorana surprisingly decided to take part, completely overturning the possible results of the competition. The commission thus nominated Majorana for a chair of “clear fame” at the University of Naples.  He arrived in Naples in January 1938 and regularly held his series of lectures, 21 in total, until 25 March. That same day he took a steamer from Naples bound for Palermo. On landing in Sicily he wrote an initial letter to Antonio Carrelli, director of the Institute of Physics in Naples.

“I have made a decision that was by now inevitable. There is not a single grain of selfishness in it, but I realise the trouble my sudden disappearance will cause you and the students. For this reason, too, please forgive me”.

In a second letter, also addressed to Carrelli, he wrote:

“The sea has refused me and I shall return tomorrow to the Hotel Bologna. However, I intend to give up teaching. Don’t take me for an Ibsenian girl because the case is different. I am at your disposal for further details”.

This is Ettore Majorana’s last letter, and his disappearance and possible death caused astonishment and dismay in the world of physics and beyond. Like Galileo and Newton, nothing more has been heard of this genius, and to borrow the words that Anatole Dauman said about Chris Marker, “to speak of the life of this secret man is to challenge his disapproval”.

Ettore Majorana: la fisica

Majorana’s contributions

Ettore Majorana, whose genius has often been compared, even by Fermi himself, to that of Galilei and Newton, researched theoretical physics over a relatively short period of about ten years. This led to the publication of nine articles plus a posthumous one edited by his friend Giovanni Gentile, Jr.

The first articles, written at the turn of the 1920s and 1930s, mainly concerned problems of atomic and molecular physics. As Amaldi points out, these papers are striking for their high intellectual class and reveal a deep knowledge of the theoretical apparatus and of the smallest details of experimental data, as well as an uncommon ability to exploit the properties of symmetry (so dear to physicists) to simplify the most difficult problems, and an uncommon ability to calculate, as Majorana proved on several occasions. From this period, a classic and much cited article is “Atoms oriented in a variable magnetic field”, published in 1932, where Majorana obtained important results that are the theoretical basis for a method still used in experiments today.

At the Institute in Rome, and in Italy in general, the first work on the application of quantum mechanics to nuclear physics is represented by Majorana’s thesis, where he treated α decay in a rigorous manner. From that moment on Majorana no longer took any official interest in nuclear physics. His interest resurfaced towards the end of January 1932, when the first results of Frédéric Joliot and Irène Curie on penetrating radiation arrived in Rome, where they hypothesized a new type of interaction between gamma rays and protons. This proposal was greeted by Majorana with a shake of his head and a “they haven’t understood anything, they have discovered the neutral proton—a term he used to indicate the neutron—and they haven’t even noticed it”. It was not taken seriously at the time, but shortly afterwards a memoir by James Chadwick appeared in the journal Nature announcing the discovery of the neutron.

The discovery of this new particle radically changed the understanding of the atomic nucleus. Between June and December 1932 Werner Heisenberg published a series of papers showing that a model of a nucleus made up of protons and neutrons could be constructed using quantum mechanics. The idea was that neutrons and protons are bound by a complex system of forces, which also includes the so-called “exchange force”, an exquisitely quantum term that arises from the impossibility of distinguishing identical particles, such as neutrons and protons, at least in the context of strong interactions. These forces allowed the particles under consideration to exchange position, spin and electric charge. Heisenberg also retained the doubt of whether to consider the neutron as a real elementary particle or to identify it as consisting of a proton and an electron, a consideration that was suggested by the emission of electrons in radioactive processes such as, for example, in β decay.

Amaldi stated that Majorana tried to develop an analogous theory of nuclei already before these works appeared. Majorana’s decision to go to Leipzig to work with “Herr Professor” Heisenberg was influenced by the publication of these papers, which were considered conceptually correct but were seen as incomplete. Everything changed with Majorana’s article “On nuclear theory”, which was also published in the well-known and important journal Zeitschrift für Physik. The basic ideas were the same as those adopted by the German physicist, but Majorana made substantial changes to the exchange forces: their sign was changed from negative to positive, spin no longer took part in this mechanism, and protons and neutrons, in exchanging their positions, did not make any real change inside the nucleus. With these corrections the theory matched perfectly with the experimental results, greatly improving Heisenberg’s previous theory.

From then on it was referred to as the Heisenberg–Majorana theory of exchange forces. It was Majorana’s scientific triumph. These results brought him international fame in the nuclear field, placing him on a par with Enrico Fermi and Bruno Rossi, so much so that in 1935 he was invited to take part in an international conference at the Technical Physical Institute of Leningrad. Unfortunately this conference was held only two years later, without Majorana’s participation.

Shortly before his departure for Leipzig, Majorana published “Relativistic theory of particles with arbitrary intrinsic angular momentum”, which can be considered the birth of theoretical physics in the field of elementary particles. In 1928 the English physicist Paul Dirac had derived his very famous quantum and relativistic equation for the electron and was convinced that such a description was only possible in the case of particles having a medium spin. Majorana, convinced of the contrary, began to derive equations analogous to Dirac’s, “although somewhat more complicated”, which allow particles with any value of spin, even zero. Majorana tackled the difficult mathematical problem with the help of group theory, a branch of mathematics that has many important applications in physics, anticipating the work that the physicist-mathematician Eugene Wigner carried out years later. Majorana’s results were well ahead of his time and were misunderstood by most of the scientific community.

On his return from Germany Majorana’s long period of silence was interrupted by the publication of his last article, perhaps the most important, entitled “Symmetrical theory of the electron and positron” in which he developed the idea of particle–antiparticle symmetry and where what are now commonly known as Majorana’s neutrinos and fermions appeared.

Majorana completely eliminated the idea of the Dirac sea and negative energy states, constructing, in the most natural way possible, a theory of elementary neutral particles in which the particle under examination is identified with its own antiparticle, thus abandoning the need to introduce them. The most famous example that could meet this type of requirement, as reported by Majorana himself, could be the neutrino, theorised only sometime before by Pauli.

An honourable mention goes to his last article, published posthumously, “The value of statistical laws in physics and social sciences”, which shows Majorana’s multifaceted interests.  To date, many unpublished writings have been found and are being studied but some important scientific traits can be noted: The extreme precision in his work (pages and pages of calculations made and remade). Many seem to have a certain influence on the progress of scientific research even today.