Ettore Majorana: A Question Still Waiting for an Answer
Most physicists are remembered for what they answered. Majorana is remembered for a question, and for the fact that he was not there to see anyone try to answer it. He published very little, disappeared at thirty-one, and left behind a piece of mathematics that eighty-seven years later still divides the possible universes into two - one in which the neutrino is its own antiparticle, and one in which it is not.
The Physics
Paul Dirac's 1928 equation predicted that every fermion has an antiparticle with the same mass and opposite charge. The positron was found four years later and the framework has held for every charged fermion since.
Majorana noticed that the mathematics allows something else if the particle has no charge to reverse. In that case the particle and its antiparticle can be the same object. His 1937 paper worked this out as a symmetric theory of the electron and positron, and the resulting objects are now called Majorana fermions.
At the time this was a formal curiosity, because no suitable particle was known. The neutrino was still a hypothesis, and it would not be detected for another nineteen years. Today it is the only candidate among known fermions: quarks carry electric and colour charge, charged leptons carry electric charge, and only the neutrino carries neither.
The distinction is not academic. If the neutrino is a Majorana particle, lepton number is not conserved, the seesaw mechanism becomes available to explain why neutrino masses are so small, and leptogenesis becomes a viable account of why the universe contains matter. If it is not, all three of those lines close.
The Man
Majorana was born in Catania in 1906 and joined Enrico Fermi's group in Rome, the circle later known as the Via Panisperna boys. Fermi's assessment of him is quoted often and worth quoting again: there are various categories of scientists, people of second or third rank who do their best but do not go very far; there are first-rank people who make discoveries of great importance; and then there are geniuses like Galileo and Newton. Majorana, he said, was one of those.
He published almost nothing. In 1932 he worked out a model of the nucleus built from protons and neutrons before James Chadwick announced the neutron's discovery, and did not publish it. Colleagues describe him working out results and then losing interest in writing them down.
In 1937 he was appointed to a chair of theoretical physics at Naples, without the usual competition, on the strength of his reputation. He had been in poor health and largely withdrawn for several years.
The 1937 paper on the symmetric theory was his last publication.
The Disappearance
On 25 March 1938 Majorana withdrew his savings and boarded a ship from Naples to Palermo. He sent a letter to the director of the Naples institute apologising for what he intended, then a telegram and a second letter asking him to disregard the first. He is recorded as having boarded the return ship from Palermo to Naples on the night of 25 to 26 March. He was never seen again with certainty.
No body was found. The main hypotheses have been suicide, withdrawal into a monastery, and emigration under another identity, and none has ever been established. Italian prosecutors reopened the case and closed it in 2015, concluding that he was probably alive in Venezuela between 1955 and 1959, based on witness testimony and a photograph. That is an official conclusion, not a proof, and it is not universally accepted.
It is worth resisting the pull of the story here. The disappearance is genuinely unresolved, the evidence is thin in every direction, and the honest position is that nobody knows. The temptation to prefer the most interesting explanation is exactly the temptation this site tries to avoid elsewhere.
What is not in doubt is the physics he left. It was largely ignored for decades, because there was no particle to apply it to and no way to test it.
The Question Today
The practical test is neutrinoless double beta decay. If the neutrino is its own antiparticle, a rare nuclear process becomes possible in which two neutrons convert to two protons emitting two electrons and no neutrinos at all. Several large experiments have been searching for decades, using different isotopes so that no single systematic error can produce a false signal.
Nothing has been found. Half-life limits now exceed 10^26 years, which constrains the possibilities without settling them: a null result is consistent with the neutrino being a Dirac particle, and also with it being Majorana if the mass contributions happen to cancel.
So the question stands where Majorana left it, sharpened by eighty-seven years of theory and by detectors he could not have imagined. It is one of the few genuinely fundamental questions that a currently running experiment could answer.
There is a lesson in the shape of that. A good question can outlive the person who asked it by a century, and being unanswered is not the same as being unanswerable - the distinction our page on leptogenesis draws in another context.
Frequently asked questions
What is a Majorana particle?
A fermion that is identical to its own antiparticle. Only an electrically neutral particle can be one, which makes the neutrino the sole candidate among known fermions.
What happened to Ettore Majorana?
He disappeared on the night of 25 to 26 March 1938 while travelling by ship between Palermo and Naples. No body was found. Suicide, withdrawal to a monastery and emigration have all been proposed, and none has been established.
Did the 2015 investigation solve it?
No. Italian prosecutors closed the case concluding he was probably alive in Venezuela between 1955 and 1959, based on testimony and a photograph. That is an official hypothesis rather than proof, and it is not universally accepted.
Why does the Majorana question still matter?
Because the answer determines whether lepton number is conserved, whether the seesaw mechanism can explain the smallness of neutrino masses, and whether leptogenesis can explain why the universe contains matter.
How could it be settled?
Through neutrinoless double beta decay, which is only possible if the neutrino is its own antiparticle. Experiments have searched for decades without a detection, and current limits exceed half-lives of 10^26 years.
