This biography sheds new light on the life and work of physicist Ettore Majorana (including unpublished contributions), as well as on his mysterious disappearance in March 1938. Majorana is held by many, including Nobel Laureate, Enrico Fermi, to have been a genius of the rank of Galilei and Newton. In this intriguing story, the author, himself a leading expert on the work of Majorana, supplements the existing literature with new insights, anecdotes and personal accounts of contemporaries (...) of Majorana. (shrink)

Il s’agit d’affronter la « figure » d’Ettore Majorana et d’en proposer un premier « profil philosophique ». La question des « fictions » apparaît alors centrale chez Majorana. On établit ensuite la dimension surrationaliste et européenne de ses affinités électives avec Giovanni Gentile Junior. Les deux oeuvres sont restituées dans le cadre d’un mathématisme constructif et inductif (Gaston Bachelard, puis Robert Blanché) qui s’oppose au géométrisme classique (Emile Meyerson) et au pythagorisme spiritualiste (Arthur Eddington).

We give an accurate historical and scientific account of a practically 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 English 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 is one of the last missing (...) papers of the “Senatore folder”, given by Majorana to one student of his at the University of Naples in 1938, just before his disappearance. (shrink)

Cet article retrace la carrière des publications d’Ettore Majorana en analysant les citations dont elles ont fait l’objet depuis le début des années 1930. Cette approche met en évidence la redécouverte, au milieu des années 1960, de l’article de 1937 portant sur les particules de spin quelconque et permet d’identifier les personnes à l’origine du travail de promotion de l‘œuvre de Majorana, dont la visibilité s’est accrue depuis le milieu des années 1970. L’étude des co-citations fait voir (...) le réseau conceptuel dans lequel les travaux de Majorana s’insèrent. (shrink)

We give an accurate historical and scientific account of a practically 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 English translation. It is likely related to an invited talk for a conference at Leningrad in 1933 which, however, Majorana never attended. Probably this manuscript is one of the last missing papers of the “Senatore (...) folder,” given by Majorana to one student of his at the University of Naples in 1938, just before his disappearance. (shrink)

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.

The two-electron atom is the simplest nontrivial quantum system not amenable to exact solutions. Today, its relevance in the development of quantum mechanics and its pedagogical value within the realm of atomic physics are widely recognized. In this work, an historical review of the known different methods and results devised to study such a problem is presented, with an emphasis to the calculations of the ground state energy of helium. Then we discuss several, related, unpublished results obtained around the same (...) years by Ettore Majorana, which remained unknown till recent times. Among them a general variant of the variational method appears to be particularly interesting, even for current research in atomic and nuclear physics: it takes directly into account, already in the trial wavefunction, the action of the full Hamiltonian operator of a given quantum system. Further relevant contributions, specialized to the two-electron problem, include the introduction of the remarkable concept of an effective nuclear charge different for the two electrons (thus generalizing previous known results) and an application of the perturbative method, where the atomic number Z was treated effectively as a continuous variable. Finally a survey of results, relevant mainly for pedagogical reasons, is given; in particular we focus on simple broad range estimates of the helium ionization potential, obtained by suitable choices for the wavefunction, as well as on a simple alternative to Hylleraas’ method, which led Majorana to first order calculations comparable in accuracy with well-known order 11 results derived, in turn, by Hylleraas. (shrink)

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 works on theoretical (...) nuclear physics. In all his papers, he tended to emphasize the symmetries at the basis of a physical problem, as well as the limitations, rather than the advantages, of the approximations of the method employed. (shrink)

A complete theoretical model describing artificial disintegration of nuclei by bombardment with α-particles, developed by Majorana as early as 1930, is discussed in detail jointly with the basic experimental evidences that motivated it. By following the quantum dynamics of a state resulting from the superposition of a discrete state with a continuum one, whose interaction is described by a given potential term, Majorana obtained (among the other predictions) the explicit expression for the integrated cross section of the nuclear (...) process, which is the directly measurable quantity of interest in the experiments. Although this is the first application of the concept of quasi-stationary states to a Nuclear Physics problem, it seems also that the unpublished Majorana work anticipates by several years the related seminal paper by Fano on Atomic Physics. (shrink)

Il s’agit d’affronter la « figure » d’Ettore Majorana et d’en proposer un premier « profil philosophique ». La question des « fictions » apparaît alors centrale chez Majorana. On établit ensuite la dimension surrationaliste et européenne de ses affinités électives avec Giovanni Gentile Junior. Les deux oeuvres sont restituées dans le cadre d’un mathématisme constructif et inductif (Gaston Bachelard, puis Robert Blanché) qui s’oppose au géométrisme classique (Emile Meyerson) et au pythagorisme spiritualiste (Arthur Eddington).

In this philosophical detective story, Giorgio Agamben reads the mysterious 1938 disappearance of atomic physicist Ettore Majorana as an intentional and decisive objection to how quantum physics had reduced the real to probability.

The mental representation of one’s own body does not necessarily correspond to the physical body. For instance, a dissociation between perceived and actual reach-ability has been shown, that is, individuals perceive that they can reach objects that are out of grasp. We presented participants with 3D pictures of objects located at four different distances, namely near-reaching space, actual-reaching space, perceived-reaching space and non-reaching space. Immediately after they were presented with function, manipulation, observation or pointing verbs and were required to judge (...) if the verb was compatible with the object.Participants were faster with function and manipulation verbs than with observation and pointing verbs. Strikingly, with both function and manipulation verbs participants were faster when objects were presented in actual than the perceived reaching space. These findings suggest that our knowledge of the world is implicitly built online through behaviour, and is not necessarily reflected in explicit estimates or conscious representations. (shrink)

This paper gives two complete and elementary proofs that if the speed of light over closed paths has a universal value c, then it is possible to synchronize clocks in such a way that the one-way speed of light is c. The first proof is an elementary version of a recent proof. The second provides high precision experimental evidence that it is possible to synchronize clocks in such a way that the one-way speed of light has a universal value. We (...) also discuss an old incomplete proof by Weyl which is important from an historical perspective. (shrink)

The strongly innovative theory of whole-parts relations outlined by Husserl in his Third logical Investigation—to which he attributed a basic value for his entire phenomenology—has recently attracted a renewed interest. Although many important issues have been clarified (especially by Kit Fine) the subject seems still worth being revisited. To this aim Husserlian universes are introduced. These are lower bounded distributive lattices endowed with a unary operation of defect and a binary relation of isogeneity. Husserl's contents are identified with nonzero elements (...) of a Husserlian universe and the dependence relations among contents are defined and studied starting from the idea that the defect of xis what x needs in order to ‘exist’ i.e., in order to be ‘closed’ with respect to the closure operation defined as the sup of x and its defect. It turns out that there are (at least) eight dependence relations which are worth to be considered. Many other questions concerning the world of contents (among them the proofs of the famous Husserl's Sätze) may now be discussed and clarified. Then the theory of species and genera is developed. Ultimate species (for short: species) are identified with equivalence classes of contents modulo isogeneity, and species in general (for short: genera) are identified with arbitrary unions of species. On the basis of the relation obtaining among two contents when they are isogeneous to two contents the first of which is a part of the second it becomes possible to develop a rather satisfying interpretation of Husserl's theory of the dependencies among species and genera and of the material a priori laws. By strengthening the notion of Husserlian universe into the notion of rigid Husserlian universe, the theory of species and genera obtains a stronger version. Three models of the theory are exhibited. The first one, suggested by combinatorial-topological considerations, identifies contents with finite non-empty sets of natural numbers; the second one identifies contents with non-empty sets of formulas of a formal language; the third one (not totally ‘rigid’) identifies contents with positive integers. (shrink)

This special issue re-evaluates the 1950s as a period of transnationalism in ideas and political practices, offering innovative insights into political history and political ideas. Without setting the national and transnational spheres against each other, the issue argues that the dialectics between the two was a defining element of Europe in this period. The articles explore transnational cooperation and exchanges among intellectuals, politicians and trade unionists, showing how they were changing in their interaction. The editorial sets out from the research (...) on the postwar configuration of Europe based on the retake of the nation state, combining it with new research of transnational history and putting out some methodological innovations. The editorial also highlights some significant themes across the articles: the central role of translation and localisation, the interaction with local interests and disputes, the Cold War, the acceleration of European integration, the rise of the Third World, the tensions between hope and fear or between nihilism and rebirth of Europe, the centrality of science. (shrink)

Catholic Philosophy has long acknowledged the primary place of Metaphysics, and a primary question of metaphysicians is “what is Metaphysics about?” This paper engages this primary metaphysical question through the lens of Scholastic dispute over the adequate subject matter of Metaphysics. Chrysostom Iavelli defended the position that the subject of Metaphysics is real being common to God and creatures against the position of his predecessor Dominic Flandrensis who had argued that it is categorical being to the exclusion of uncreated being. (...) I find Flandrensis’s position represented in the writings of notable contemporary Thomists, but not Iavelli’s. This paper, offers a sixteenth-century Thomist’s position on the subject matter of Metaphysics as a challenge to current Thomist consensus. It attempts to prompt a re-investigation of the reasons behind the current consensus both as a philosophical position and as an interpretation of St. Thomas Aquinas. (shrink)

La logique cartésienne est introuvable parce qu’on a cherché une logique qui n’existe pas, c’est-à-dire une logique classique sur le modèle des manuels de la tradition réformée. La puissance transgressive de Descartes, même dans ce domaine, a été radicale : il a bafoué l’Arbre de Porphyre, vidé de sens la théorie des catégories, montré l’inutilité du syllogisme pour la recherche scientifique. Sans efficacité, à son avis, fut le renouveau d’une logique fondée sur des normes préconstituées. Il se « limite » (...) pourtant à suggérer, sur le modèle des procédés mathématiques, une attitude de pensée centrée sur l’intuitus et dont les relations sont garanties par les notions de « série » et de respectus. La transgression cartésienne a été si bouleversante que « Descartes logicien » devient un auteur maudit et l’attitude qu’il aurait voulu inspirer n’a connu aucune fortune, à telle enseigne que même la Logique de Port-Royal qu’on voudrait cartésienne consacre un grand espace à la syllogistique.Undiscoverable is the Cartesian logic, because scholars looked for a logic that does not exist, i.e. a classical logic after the model of traditional, more or less reformed, manuals. Descartes’ transgressive power was radical even in this domain : he scorned Phorphyrius Tree, voided the theory of categories of all meaning, showed the uselessness of syllogism for scientific research. Just as totally ineffective was, in his view, the renewal of a logic founded on preconstituted norms. He therefore « limits » himself to suggest, after the model of mathematical procedures, an attitude of thought centered on intuitus and whose relationships are guaranteed by the notions of « series » and respectus. The Cartesian transgression turned out to be so upsetting that « Descartes the logician » became a wicked author and the attitude he had meant to inspire had no fortune whatsoever, to such a point that even the Logic of Port-Royal – purportedly Cartesian – leaves much room to syllogistics. (shrink)

Per uscire dalle aporie delle proprie conseguenze, la scienza deve vedere riconosciuto l'atto come uno dei propri principi fondamentali (accanto all'ente e alla parola). Scienza è, infatti, mettere in relazione le cose (la "natura") con delle leggi matematiche (vale a dire con dei simboli e dei concetti). Ma mettere in relazione è un atto. Sicché, la scienza si fonda su tre principi (ente, parola, atto) e sui corrispettivi campi filosofici (ontologia, logica, etica). Tenere conto di quest'ambito triadico serve a mostrare (...) che l'epistemologia non è un sapere neutro e descrittivo, ma è un prendere partito: al tempo stesso dal punto di vista etico, politico, morale e giuridico. (shrink)

This article considers the attempt by a prominent fifteenth-century follower of Thomas Aquinas, Dominic of Flanders, to address John Duns Scotus’ most famous argument for the univocity of being. According to Scotus, the intellect must have a concept of being that is univocal to substantial and accidental being, and to finite and infinite being, on the grounds that an intellect cannot be both certain and doubtful through the same concept, but an intellect can be certain that something is a being (...) while doubting whether it is a substance or accident, finite or infinite. The article shows how Flandrensis’ reply in defence of analogy of being hinges on a more fundamental disagreement with Scotus over the division of the logically one. It also shows how Flandrensis’ answer to this question commits him to a position on the unity of the concept of being that lies between the positions of Scotus and of Flandrensis’ earlier Thomistic sources. (shrink)

The relationship between fear and courage has been discussed in terms of opposite though mutually involving notions. However, their link has not been inquired extensively. Recently, new light has been shed on the topic thanks to recent empirical evidence within emotion theories that stress the role played by perception and/or cognition in the experience of fear, as well as the role played by the “emotional virtue” of courage in fear regulation. Questions arise whether fear has a fundamentally perceptual structure or (...) is a biologically-grounded natural kind, and whether such an emotion-related virtue as courage is intrinsically or extrinsically related to fear. This paper considers the last problem first, then enlarges the picture to fear modeling, finally drives some conclusions which aim at deepening the relationship between fear and courage. As a result, it emerges that the emotion of fear has a conceptual, emotional, situational and subjective dimension. Assuming fear as a possible emotional center within the subject’s cognitive experience, the virtue of courage appears to balance the excess and lack of fear, and is consequently related to rational thoughts and consistent behavior, laying the foundations for a new Aristotelian-Thomistic account for it. (shrink)