This year is the centenary of the birth of Ettore Majorana, one of the major Italian physicists of all times. In this note we briefly sketch a few biographical details about Ettore Majorana and introduce and discuss the main points of Majorana's 10th article. In his article Majorana explicitly considers quantum mechanics as an irreducible statistical theory because the theory is not able to describe the time evolution of a single particle or atom in a precise environment at a deterministic level. This lack of determinism at the level of an elementary physical system motivated him to suggest a formal analogy between statistical laws observed in physics and in the social sciences. We hope the occasion of the centenary of the birth of Ettore Majorana will be useful to remember and to reconsider not only his exceptional achievements in theoretical physics but also his fresh and original views on the role of statistical laws in physics and in other disciplines such as the social sciences.
Ettore Majorana, perhaps the greatest Italian theoretical physicist of this century (Enrico Fermi compared him to Galilei and Newton), disappeared misteriously from Naples in 1938, when he was 31. In the first part of this work we outline his scientific personality (on the basis of letters, documents, testimonies collected by us in about twenty years) and the significance of some parts of his publications. In the second part of this paper we set forth some brief information about the unpublished scientific manuscripts left by E.Majorana and known to us till this moment (most of which are depos…
This agile small "book" (in Italian) is an introduction to the life and work of Ettore Majorana, the brightest Italian theoretical physicist of the XX century, regarded by Enrico Fermi as the best theoretician of his time in the world. It consists of ten smooth chapters, only few of them being moderately technical, and of three Appendices: (i) about his inaugural lecture on physics at the University of Naples; (ii) about some notes of his, on the role of the statistical laws in physics and in the social sciences; and (iii) with a recapitulatory biographic outline. The present material is mainl…
Ettore Majorana proposed an important improvement to the Thomas-Fermi statistical model for atoms, with a communication at the general meeting of the Italian Physical Society, held in Rome, on December 29th, 1928, regularly published on Nuovo Cimento. This communication did not receive any mention, neither in the numerous publications of Fermi and his associates on the subject, nor in the further reconstructions of the life and activity of Ettore Majorana. The Majorana proposal was not accepted by Enrico Fermi for years, and forgotten. However, it was finally exploited, without reference, in t…
We analyze in some detail the course of Theoretical Physics held by Ettore Majorana at the University of Naples in 1938, just before his mysterious disappearance. In particular we present the recently discovered "Moreno Paper", where all the lecture notes are reported. Six of these lectures are not present in the collection of the original manuscripts conserved at the Domus Galilaeana in Pisa, consisting of only ten lectures.
An account is given of some topical unpublished work by Ettore Majorana, revealing his very deep intuitions and skilfulness in Theoretical Physics. The relevance of the quite unknown results obtained by him is pointed out as well.
We review the introduction in physics of the concepts of an elementary space length and of a fundamental time scale, analyzing some related unknown contributions by Ettore Majorana. In particular, we discuss the quasi-Coulombian scattering in presence of a finite length scale, as well as the introduction of an intrinsic (universal) time delay in the expressions for the retarded electromagnetic potentials. Finally, we also review a special model considered by Majorana in order to deduce the value of the elementary charge, in such a way anticipating key ideas later introduced in quantum electrod…
We give, for the first time, the critical complete text of a manuscript by Ettore Majorana, conserved in the same file of the lecture notes for his course on Theoretical Physics at the University of Naples. He probably refers to a seminar delivered in that University. Some passages reveal a physical interpretation of the Quantum Mechanics which anticipates of several years the Feynman approach in terms of path integrals, independently of the underlying mathematical formulation.
The mentioned article was written by Ettore Majorana, in a partially educational way, for a journal of Sociology; but he gave up publishing it (and threw it away). It appeared posthumous, thanks to Giovanni Gentile Jr. (the inventor of "parastatistics") in "Scientia" 36 (1942) 58-66. It has not been re-published, in Italian, till the beginning of 2006, when we made known some abridgements of it by Italian newspapers and by the journal "Fisica in Medicina". We don't know when was it written: perhaps in 1930. However, its central theme was still alive in Majorana's mind in 1934: in fact, on July…
After a quick historical account of the introduction of the group-theoretical description of Quantum Mechanics in terms of symmetries, as proposed by Weyl, we examine some unpublished papers by Ettore Majorana. Remarkable results achieved by him in frontier research topics as well as in physics teaching point out that the Italian physicist can be well considered as a follower of Weyl in his reformulation of Quantum Mechanics.
In this paper we present a panoramic view of the main scientific articles published by Ettore Majorana, the brightest Italian theoretical physicist of the XX century (actually, Enrico Fermi regarded him as the brighest in the world of his time, and compared him to Galileo and Newton; even if to some people Majorana is often known mainly for his mysterious disappearance in 1938, when he was 31). Extensive information and comments are added with regard to the scientific manuscripts left unpublished by him. We also outline his life, the biographical data being based on letters, documents, testimo…
We analyze in some detail the course of Theoretical Physics held by Ettore Majorana at the University of Naples in 1938, just before his mysterious disappearance. In particular we give an account of the recently retrieved "Moreno Paper", where the lecture notes are reported. Six of these lectures are not present in the collection of the original manuscripts deposited at the Domus Galilaeana in Pisa, consisting of only ten lectures.
We present and analyze in detail an unknown theory of ferromagnetism developed by Ettore Majorana as early as the beginnings of 1930s, substantially different in the methods employed from the well-known Heisenberg theory of 1928 (and from later formulations by Bloch and others). Similarly to this, however, it describes successfully the main features of ferromagnetism, although the key equation for the spontaneous mean magnetization and the expression for the Curie temperature are different from those deduced in the Heisenberg theory (and in the original phenomenological Weiss theory). The theo…
The physicists working in several areas of research know quite well the name of Ettore Majorana, since it is currently associated to fundamental concepts like {\it Majorana neutrinos} in particle physics and cosmology or {\it Majorana fermions} in condensed matter physics. But, probably, very few is known about other substantial contributions of that ingenious scholar, and even less about his personal background. For non specialists, instead, the name of Ettore Majorana is usually intimately related to the fact that he disappeared rather mysteriously on March 26, 1938, just seventy years ago, …
We give an accurate historical and scientific account of a previously unknown manuscript written by Ettore Majorana in French. The retrieved text deals with Quantum Electrodynamics by using the formalism of field quantization, and it is here reported, for the first time, in translation. It is likely related to an invited talk for a conference at Leningrad (or Kharkov) in 1933 (or 1934) which, however, Majorana never attended. Probably this manuscript refers to the last missing papers of the ``Senatore folder'', given by Majorana to one student of his at the University of Naples in 1938, just b…
We show that a number of apparently separate extravagant Majorana's actions, including those connected with his disappearance are united by the invariant of behavior. It is based on "carrying into life" the principles of quantum theory. We argue that the underlying motive force in the story of his disappearance consisted in existential intention to overcome the fixed frame of personal identity and dichotomy "life - death" and mimic breakthrough to plurality of worlds.
We report on the retrieval of the last missing papers of the "Senatore folder", given by Majorana to one student of his in Naples in 1938, just before his disappearance. The mentioned manuscript is conserved at the Domus Galilaeana in Pisa (Italy), and was written in French, probably for a conference in Leningrad (or in Kharkov) in 1933 (or in 1934). Majorana was invited to attend to such a conference but, actually, he did not tke part to it. The retrieved text deals with quantum electrodynamics by using the formalism of field quantization. It is here reported, for the first time, in translati…
At the kind request of the Editor of Hadronic Journal, and of TEC/TNRG (Usa), we recall in this article some elementary historical information about the role played by Ettore Majorana[1-17] with regard to the Neutron, and to the Neutrino. Often we do explicitly insert direct quotations from the original written statements --in particular by Edoardo Amaldi[22-24]--, which in some cases, and for some topics, constitute the main available evidence. We also discuss some recent, unjustified rumors about Ettore Majorana and Enrico Fermi. [Keywords: Ettore Majorana; Neutron; Neutrinos; Enrico Fermi; …
In 1927, just after he obtained a full professorship, Enrico Fermi delivered his first course on Theoretical Physics at the Institute of Physics in Rome. The following year Edoardo Amaldi, Emilio Segre' and Ettore Majorana became students of that course. The lectures given in 1927-28, whose content may be easily reconstructed, probably had a deep impact in forming such young students, who participated actively in the Physics researches carried on in Rome soon after. In this perspective, the case of Ettore Majorana is certainly the most important one: as a lecturer, in 1933-36 he planned to giv…
We present a panoramic view of the main scientific manuscripts left unpublished by the brightest Italian theoretical physicist of the XX century, Ettore Majorana. We deal in particular: (i) with his very original "study" notes (the so-called "Volumetti"), already published by us in English, in 2003, c/o Kluwer Acad.Press, Dordrecht & Boston, and in the original Italian language, in 2006, c/o Zanichelli pub., Bologna, Italy; and (ii) with a selection of his research notes (the so-called "Quaderni"), that we shall publish c/o Springer, Berlin. We seize the present opportunity for setting forth a…
We report on theoretical courses by Fermi and Majorana, giving evidence of the first appearance and further development of Quantum Mechanics teaching in Italy. On the basis of original documents, we make a comparison between Fermi's and Majorana's approaches. A detailed analysis is carried out of Fermi's course on Theoretical Physics attended by Majorana in 1927-28. Three (previously unknown) programs on advanced Physics courses submitted by Majorana to the University of Rome between 1933 and 1936 and the course he held in Naples in 1938 complete our analysis: Fermi's phenomenological approach…
This article, in English, represents part of the invited talk delivered by the author at the "Internat.Conf.Majorana Legacy and Phys. XXI century" held at Dep. of Phys.,University of Catania, Italy, in Oct.2006: Conference organized for celebrating the 100th anniversary of the birth (in Catania) of the Italian theoretical physicist Ettore Majorana; probably the brightest Italian theoretician of the XX century (Enrico Fermi regarded him as the brightest in the world of his time), even if to some people Majorana is still known chiefly for his mysterious disappearance, in 1938, when he was 31. In…
Sicily has played an important role in the development of the new research area named "Econophysics". In fact some key ideas supporting this new hybrid discipline were originally formulated in a pioneering work of the Sicilian born physicist Ettore Majorana. The article he wrote was entitled "The value of statistical laws in physics and social sciences". I will discuss its origin and history that has been recently discovered in the study of Stefano Roncoroni. This recent study documents the true reasons and motivations that triggered the pioneering work of Majorana. It also shows that the desc…
Ettore Majorana was a member of Enrico Fermi's research group in Rome, Italy. Fermi did regard Majorana as much brihter than himself as far as theoretical physics was concerned (more information can be found particularly in the arXives' e-print physics/9810023, in Italian, and refs therein, and also in the recent multilanguage arXiv:0708.2855v1 [physics.hist-ph]). In 1937 Majorana partecipated in the national Italian competition, for a chair in theoretical phyics, requested by Emilio Segre' at that time at Palermo University: Other competitors being GC.Wick, G.Racah, and G.Gentile jr. After a …
We focus here on the work of the italian physicist Ettore Majorana, and more particularly on his 1937 article on the symmetrical theory of the electron and the positron, probably one of the most important theory for contemporary thought. We recall the context of this article (Dirac relativistic electron wave equation) and analyze how Majorana deduces his own equation from a very general variational principle. After having rewritten Majorana equation in a more contemporary language, we study its implications in condensed matter physics and their possible applications in quantum computing. Final…
We comment on a recent paper announcing the discovery of a previously unknown publication of Ettore Majorana on the Thomas-Fermi atomic model. In pointing out that such a publication was not written by Majorana, we correct some misunderstandings and clarify the historical and scientific relevance of the "forgotten publication".
In the centennial of Ettore Majorana's birth (1906-1938?), we re-examine some aspects of his fundamental scientific production in atomic and molecular physics, including a not well known short communication. There, Majorana critically discusses Fermi's solution of the celebrated Thomas-Fermi equation for electron screening in atoms and positive ions. We argue that some of Majorana's seminal contributions in molecular physics already prelude to the idea of exchange interactions (or Heisenberg-Majorana forces) in his later workson theoretical nuclear physics. In all his papers, he tended to emph…
We give, for the first time, the English translation of a manuscript by Ettore Majorana, which probably corresponds to the text for a seminar delivered at the University of Naples in 1938, where he lectured on Theoretical Physics. Some passages reveal a physical interpretation of the Quantum Mechanics which anticipates of several years the Feynman approach in terms of path integrals, independently of the underlying mathematical formulation.
In 1932 Ettore Majorana proposed an infinite-component relativistic wave equation for particles of arbitrary integer and half-integer spin. In the late 80s and early 90s it was found that the higher-derivative geometric particle models underlie the Majorana equation, and that its (2+1)-dimensional analogue provides with a natural basis for the description of relativistic anyons. We review these aspects and discuss the relationship of the equation to the exotic planar Galilei symmetry and noncommutative geometry. We also point out the relation of some Abelian gauge field theories with Chern-Sim…
In 1932 Ettore Majorana published an article proving that relativity allows any value for the spin of a quantum particle and that there is no privilege for the half integer spin. The Majorana idea was so innovative for the time that the scientific community understood its importance only towards the end of the thirties. This paper aims to highlight the depth of the scientific thought of Majorana that, well in advance of its time, opened the way for modern particle physics and introduced for the first time the idea of a universal quantum equation, able to explain the behavior of particles with …
In Europe (e.g., in Italy), and in the States, the opinion is widely spreading that the negative consequences of modern progress are the fault of "Science". A lively debate on this topic took place among the famous writer Leonardo Sciascia and Italian physicists like Edoardo Amaldi and Emilio Segre', when Sciascia wrote his known book about the disappearance of Ettore Majorana, a book that presented Majorana (a very reserved theoretical physicist) as an example of the scientist that keeps his discoveries secret when afraid of possible evil applications. We wish to contribute now to such a ques…
