For many people, Ettore Majorana remains the Italian physicist who disappeared in 1938. For contemporary physics, however, the real “Majorana case” concerns a 1937 paper that still guides research today on the neutrino, antimatter, and the possibility that matter may not be, in an absolute sense, “forever”. We discuss this with Francesco Vissani, research director at the Gran Sasso National Laboratories of the National Institute for Nuclear Physics and creator of the Asimov Prize for scientific communication in upper secondary schools. By Andrea Monti – Originally published in MIT Technology Review Italia.
MIT Technology Review Italia: When people speak about Ettore Majorana, they almost always begin with his disappearance. You, however, argue that the real Majorana case is something else. Where should we begin?
Francesco Vissani: We must begin with Majorana the physicist, not Majorana the literary figure or national mystery. Ettore Majorana was an outstanding Italian physicist who disappeared when he was still very young, and this is also why his figure has acquired an almost mythical dimension. But the scientifically decisive point lies elsewhere.
Majorana grew up in Enrico Fermi’s school between the 1920s and the 1930s, in an environment of extraordinary quality. That school was also born from the political and cultural intuition of Orso Mario Corbino, a Sicilian liberal who understood how science could become a factor of civil progress. Corbino invested in Fermi, recognised his exceptional nature, and helped build around him a group destined to change twentieth-century physics.
There is also a common trait between Corbino and Majorana: both belonged to that enlightened, ambitious, progressive Sicilian bourgeoisie, bound to a very strong historical and scientific tradition. The Majorana family included rectors, politicians, and scientists of great distinction. His uncle, Quirino Majorana, was a very well-known physicist, perhaps more famous than his nephew at the time, even though he did not accept relativity. Ettore was therefore born into an intellectually very demanding environment.
He studied with the Jesuits, and this probably matters: it is a training that teaches discipline, control of thought, and rigour. He then began engineering, until Corbino, who carried out a kind of scouting of the best young people, brought him into contact with Fermi.
MIT Technology Review Italia: What did Majorana find in Fermi’s group?
Francesco Vissani: He found a scientifically formidable environment, but also a strongly hierarchical one. Fermi is one of the great physicists of the century; we know that. He would become one of the fathers of nuclear physics and atomic energy, win the Nobel Prize, and build a school of international standing. But the Roman environment was not necessarily the one in which Majorana received the fullest recognition.
When Majorana went to Leipzig to work with Werner Heisenberg, he found a different openness. In Germany, he received very strong public consideration, perhaps greater than he had received in Italy. For an ambitious, rigorous, intellectually tense person like him, that recognition mattered a great deal.
Then something fundamental happened. After returning from Heisenberg, Majorana was twenty-seven years old and shut himself away at home. While Fermi’s group was discovering neutron physics, that is, entering modern nuclear physics, he disappeared from the scientific scene. This, in my view, is Majorana’s first disappearance. Not the one in 1938, but the intellectual and scientific disappearance that preceded the better-known biographical affair.
MIT Technology Review Italia: So the real Majorana case begins before his physical disappearance?
Francesco Vissani: Exactly. It begins there. After about four years of almost total silence, we are in 1937, at a dramatic moment for Italy and Europe. Corbino is still alive, Fermi’s group is still respected, and the first chairs in theoretical physics since the one obtained by Fermi in 1926 are announced.
Fermi is chair of the committee. He has three very clear candidates in mind: Giancarlo Wick, Giulio Racah, and Giovanni Gentile junior, son of the philosopher Giovanni Gentile. They were physicists of international stature, not minor figures. There were also other very strong candidates, such as Giuseppe “Beppe” Occhialini, to give an idea of the level of the competition.
At the very moment the competition is announced, Majorana comes out with a paper that he had evidently kept in a drawer. It is difficult to think this was a coincidence. He publishes a revolutionary article, a work whose consequences extend as far as the research now being conducted at the Gran Sasso National Laboratories and in other laboratories around the world.
MIT Technology Review Italia: Which paper are we talking about?
Francesco Vissani: The 1937 paper on the symmetrical theory of the electron and the positron. Today we often associate Majorana above all with the neutrino, but the title of the paper clearly speaks of the electron and the positron. He is talking about antimatter.
The point is that this paper is even deeper than has generally been recognised. In the history of physics, one tends to attribute the theoretical understanding of antimatter to Paul Dirac. That is correct, but it is not enough. Majorana takes a further step: he clarifies conceptually and formally something that remained highly problematic in Dirac.
Dirac had produced a very powerful theory, but one accompanied by a conceptual construction that was difficult to accept: the so-called Dirac sea. According to this image, there would exist negative-energy states occupied by electrons. A “hole” in that sea would behave like a particle with the opposite charge: the positron.
From a formal point of view, the scheme works, but conceptually it is arduous. One ends up giving ontological consistency to an absence. In that view, the positron is the hole left by a negative-energy electron.
Majorana, instead, shows how to empty that sea. He proposes a scheme in which there is no need to imagine an invisible ocean of negative electrons. Particles with negative energy are reformulated as particles of opposite charge, with the same mass and with symmetrical properties. It is an extraordinary operation of conceptual purification.
MIT Technology Review Italia: You have spoken of a kind of axiomatization of antimatter.
Francesco Vissani: Yes, but I would also use a more accessible expression: conceptual clarification. Majorana builds a coherent formal system to describe facts that had been acquired, but had not yet been ordered in a satisfactory way.
It is a passage similar, in conceptual importance, to the relationship between Babylonian mathematics and Euclid’s Elements. Not because knowledge did not exist before, but because at a certain point that knowledge is organised into a more essential, clearer, more powerful framework.
Majorana starts from relativity and quantum mechanics, but draws from them a much more modern scheme. He shows, among other things, that matter particles with half-integer spin, such as the electron, must obey Fermi statistics and the exclusion principle. What had previously been a principle or a hypothesis enters a broader formal system.
MIT Technology Review Italia: So Dirac and Majorana were saying the same thing in different words?
Francesco Vissani: Today, with hindsight, we can say that they were describing aspects of the same problem. But historically it is not so simple.
Dirac’s scheme, however unpleasant from the point of view of natural philosophy, was effective. In 1931 it was formulated in a complete way; in 1932 Carl Anderson observed the positron. At that point, much resistance fell away. The theory received very strong experimental confirmation.
But Majorana does something different. He does not merely make an already existing theory more elegant. He eliminates a cumbersome conceptual construction and shows that antimatter can be described without the Dirac sea. It is a profound difference. Dirac opens the road; Majorana cleans it up, makes it more symmetrical, more natural, closer to the language of modern physics.
MIT Technology Review Italia: Antimatter is also one of the most abused concepts in scientific communication. Anti-worlds, the destruction of the universe, catastrophic scenarios. How much of this is physics and how much is imagination?
Francesco Vissani: The imaginative framework was already there. Literature had long played with the idea of opposite worlds, negative matter, mirror universes. When a mathematical theory of antimatter arrived, this imagery found a scientific foothold.
The problem arises when scientific theories are applied outside their proper domain. It happens often. Think of quantum mechanics, used today as a universal metaphor for anything whatsoever, from emotions to consciousness. It is dangerous to decontextualise scientific theories. Quantum mechanics was born as a theory of the atom. If we then turn it into a general metaphysics of reality, we risk producing arguments that are highly suggestive but scientifically irrelevant.
Something similar happens with antimatter. Certainly, matter and antimatter can annihilate each other. Certainly, contact between particles and antiparticles produces energy. But we are not talking about a theory that predicts the end of the universe if two concepts come into contact. We are talking about well-defined physical processes, in well-defined contexts.
MIT Technology Review Italia: Yet antimatter also has a real cosmological role.
Francesco Vissani: Yes. The cosmological question is serious. We are fairly certain that the primordial universe was extremely rich in both matter and antimatter. In the very first instants after the Big Bang, the hot plasma of the universe must have contained particles and antiparticles: electrons and positrons, protons and antiprotons, and so on.
The problem is that the observable universe today is made almost entirely of matter. We do not see large quantities of anti-atoms. If significant regions of antimatter existed, we would expect gamma-ray emissions that we do not observe. So there is a fundamental question: why did the universe choose, so to speak, matter?
This is where Majorana can return to the scene. The Majorana neutrino, if it exists, would be a neutral particle that coincides with its own antiparticle. It would be matter and antimatter at the same time. A particle of this type could offer a key to understanding the asymmetry between matter and antimatter in the universe.
MIT Technology Review Italia: In what sense could the neutrino be matter and antimatter at the same time?
Francesco Vissani: This is possible only for neutral particles. A charged particle cannot coincide with its own antiparticle, because the antiparticle has the opposite charge. But the neutrino has no electric charge. Therefore, at least in principle, it could be a Majorana particle: a particle identical to its own antiparticle.
If that were the case, a very interesting scenario would open up. There could exist processes in which the neutrino acts as a bridge between matter and antimatter. In technical terms, one of the most important processes is the creation of a pair of electrons in the nuclear transition that classical textbooks call “neutrinoless double beta decay”. It is a transformation hypothesised as early as the late 1930s by Wendell Furry, starting precisely from Majorana’s ideas.
In an ordinary nuclear process, when protons and neutrons change, charge and energy are conserved through the emission of particles, including electrons or positrons and neutrinos. But if the neutrino were a Majorana particle, then in some very rare cases two virtual neutrinos could annihilate each other, and the final process would produce only two electrons, precisely, without observable neutrinos.
This would be enormous. It would mean observing a process in which electronic matter is created in a very concrete sense. It would not be the creation of matter in a mythological or religious sense, but it would be a fundamental physical piece in understanding whether atomic matter is truly eternal or whether it can come into being and disappear.
MIT Technology Review Italia: So Lavoisier’s idea that nothing is created, nothing is destroyed, everything is transformed would no longer hold?
Francesco Vissani: In part, it has already ceased to hold. Twentieth-century physics taught us that mass and energy are equivalent. Einstein’s formula, E = mc², says precisely this. Fermi’s theory of beta decay describes transformations between particles. In stars, for example, hydrogen becomes helium through processes in which protons turn into neutrons, with the emission of positrons and neutrinos.
These processes are physiological, in the sense that they belong to the ordinary functioning of nature. The Sun shines because nuclear reactions of this kind take place inside it. We have observed solar neutrinos and we know that those reactions really occur.
The radical novelty, in the Majorana case, is something else: the possibility that atomic matter may not be “forever”. That there may exist a process in which matter, in the strict sense, is created or destroyed according to precise physical rules. This is one of the reasons why research on the Majorana neutrino is so important.
MIT Technology Review Italia: Let us return to 1937. Majorana publishes a revolutionary paper. How is it received?
Francesco Vissani: Fermi immediately understands that the paper is enormous. And this also creates a practical problem. There was already a competition set up with three expected winners. Majorana’s arrival, with an article of that magnitude, upsets the balance.
The solution is political and academic: Minister Giuseppe Bottai grants Majorana a chair for exceptional merit, through a procedure analogous to the one used for Guglielmo Marconi after the Nobel Prize. Majorana becomes a professor, not in Palermo, which would have been the natural seat of the competition and also his land of origin, but in Naples.
From a scientific point of view, however, reception is slower. The paper is read, also because Majorana enjoyed a certain international visibility thanks to Heisenberg. But metabolising it takes time. Furry grasps an important consequence two years later. Then, in 1941, Wolfgang Pauli publishes a review paper that recognises some of the acquisitions, but does not really bring out the scale of Majorana’s contribution to antimatter.
Thus the paper is not forgotten, but it is partly reduced in scope. Even today many physicists associate Majorana almost exclusively with the neutrino. That is correct, but incomplete. The 1937 paper also concerns, and I would say first of all concerns, antimatter.
MIT Technology Review Italia: You have just published a study in the history of physics on this point. What did you try to show?
Francesco Vissani: I tried to recover the forgotten aspect of Majorana’s contribution to the theory of antimatter. My thesis is that Majorana was not only the physicist who hypothesised a particular nature of the neutrino. He was also the person who gave a conceptually clearer, deeper, and more modern formulation of the theory of antimatter.
His contribution is one of mental purification. He eliminates the Dirac sea, that is, a construction now abandoned, and proposes a more symmetrical structure. In a certain sense, Majorana opens the door to the quantum field theory of fermions, even if he does not call it that. He does not yet have the language that would later become standard, but he is already thinking in that direction.
The surprising thing is that it was enough to read the title of the paper: “Symmetrical Theory of the Electron and Positron”. Not “Theory of the Neutrino”. Majorana was also talking about electrons, positrons, antimatter. Quite simply, for a long time we did not look at that paper with sufficient attention.
MIT Technology Review Italia: What kind of resistance did this rereading encounter?
Francesco Vissani: At first the reviewers were perplexed. Perhaps also because I am a particle physicist active in research, not a historian of science in the strict sense. There was an understandable diffidence: I was entering a territory that was not formally mine.
One of the reviewers even accused me, somewhat paradoxically, of cheering for Majorana because he was Italian. I replied on the merits. The point was not to claim a national priority. The point was to read the texts, reconstruct the passages, and understand what had actually been said by Dirac, by Fock, by Oppenheimer, by Furry, by Heisenberg, and by Majorana.
The reviewers also pointed out intermediate passages that I had not considered sufficiently. They were right. I studied them, integrated them, and in the end the main thesis remained standing. Indeed, the comparison made it more solid.
MIT Technology Review Italia: So it was not an ideological controversy, but a historical and technical discussion.
Francesco Vissani: Exactly. The point was to distinguish the contributions. Some physicists and mathematicians had modified Dirac’s formal schemes to make them more practicable. They did important work. But Majorana operates at a different level. He does not merely straighten the walls: he rethinks the architecture of the building.
The metaphor is simple, but it works. Others are bricklayers; Majorana is the architect. He proposes an intellectual construction of impressive clarity and precision.
MIT Technology Review Italia: Does this story also say something about the relationship between physics and the history of physics?
Francesco Vissani: A great deal. The history of physics is not a dead discipline; it is not a chronicle of things that have already happened. It can change the way we understand the meaning of a theory. It can reopen paths. It can make us see that some ideas were accepted in a less clear form than was possible, or that certain intuitions were reduced in relation to their original scope.
Majorana himself said, in substance, that we often think the schemes with which we describe reality are necessary ones. But those who truly work in science realise that this is not so. There is much of our humanity, our creativity, our imagination. And also of our limits.
Naturally, science needs self-limitation. It must set boundaries, define contexts, and establish rules. But within those boundaries there is always a dimension of conceptual choice. Mathematics can guide us, but it can also confuse us if we use it badly or insert it into baroque mental schemes.
For this reason, at times it would be useful to return to speaking of natural philosophy. Physics is not a religion for new priests of mathematics. It is a rigorous way of questioning nature.
MIT Technology Review Italia: Was your work possible precisely because you are not only a historian, but also someone who “gets his hands into the engine”?
Francesco Vissani: I would say yes and no. I would not want to be unfair to historians of science, who do essential work. But it is true that I found myself in a particular position.
I am also a teacher. For years I have explained these things to students. And for years I had a reservation about the way they were presented: great formulas, but little thought. I saw enormous mathematical expressions, but I wondered what physical idea sustained them. How does a person come to write a formula half a metre long? What is the vision that guides it?
At a certain point I did something apparently obvious: I went back to read the original articles. It is more difficult than it seems, because the language, the mathematics, and the mental schemes change. But precisely for that reason it is useful. In the end I identified the core of the problem and decided to confront it.
MIT Technology Review Italia: In this story there is also a curious episode connected with Treccani.
Francesco Vissani: Yes. I realised that the Treccani entry on Majorana did not recount that work correctly. I asked who had written the original entry and discovered that part of it went back to Quirino Majorana, Ettore’s uncle, who neither understood nor accepted relativity. This explained certain things.
I reported the matter. A text by Giovanni Gentile junior, a physicist and friend of Majorana, written in the 1940s, also emerged. Today the entry has been corrected so that, in my view, it better reflects the historical dimension of Majorana’s work.
It is a small episode, but a significant one. Even encyclopaedias, even authoritative syntheses, can preserve partial readings. The history of science also serves this purpose: to reopen dossiers that seemed closed.
MIT Technology Review Italia: There is almost a paradox: Giovanni Gentile junior, son of the idealist philosopher, becomes one of Majorana’s few scientific interlocutors.
Francesco Vissani: It is interesting, yes. Giovanni Gentile junior is Majorana’s only true co-author. Majorana almost always writes alone; the only article with two signatures is with Gentile. They were friends, confidants, interlocutors.
I would not say that this proves anything in favour of idealism. But it is true that both Majorana and Gentile seem to have a particular relationship with physics and mathematics: as though they were almost eternal objects, disembodied, superior to contingency. In Majorana, this attitude produces formulas of impressive definitiveness. Some of his constructions seem to have been written once and for all.
MIT Technology Review Italia: In the end, what remains today of the real Majorana case?
Francesco Vissani: At least three things remain.
The first is historical: Majorana is not only the disappeared physicist. He is a protagonist in the theoretical construction of antimatter.
The second is conceptual: his work shows that a theory is not made only of correct formulas, but also of architectural clarity. Dirac had an effective scheme; Majorana sees its deeper form.
The third is experimental: the Majorana neutrino, if it exists, could help us understand why the universe is made of matter and not antimatter. Research on neutrinoless double beta decay has precisely the purpose of verifying whether observable processes exist in which particles of matter are created — in this specific case, electrons. This is one of the main objectives of the experiments currently under way at the Gran Sasso laboratory.
The Majorana case, therefore, is not closed. It does not concern only a young genius who disappeared in 1938. It concerns a still open question: what is matter, really? And above all: is it truly eternal, or can it come into being and disappear according to laws that we are still trying to understand?