ETTORE MAJORANA
Ettore Majorana was born in Sicily in 1906. An extremely gifted
physicist, he was a member of Enrico Fermi's famous group in Rome in the
1930s, before mysteriously disappearing in March 1938.
The great Sicilian writer, Leonardo Sciascia, was convinced that
Majorana decided to disappear because he foresaw that nuclear forces
would lead to nuclear explosives a million times more powerful than
conventional bombs, like those that would destroy Hiroshima and
Nagasaki. Sciascia came to visit me at Erice where we discussed this
topic for several days. I tried to change his mind, but there was no
hope. He was too absorbed by an idea that, for a writer, was simply too
appealing. In retrospect, after years of reflection on our meetings, I
believe that one of my assertions about Majorana's genius actually
corroborated Sciascia's idea. At one point in our conversations I
assured Sciascia that it would have been nearly impossible - given the
state of physics in those days - for a physicist to foresee that a heavy
nucleus could be broken to trigger the chain reaction of nuclear
fission. Impossible for what Enrico Fermi called first-rank physicists,
those who were making important inventions and discoveries, I suggested,
but not for geniuses such as Majorana. Maybe this information convinced
Sciascia that his idea about Majorana was not just probable, but
actually true - a truth that his disappearance further corroborated.
There are also those who think Majorana's disappearance was related
to spiritual faith and that he retreated to a monastery. This
perspective on Majorana as a believer comes from his confessor,
Monsignor Riccieri, who I met when he came from Catania to Trapani as
Bishop. Remarking on his disappearance, Riccieri told me that Majorana
had experienced "mystical crises" and that, in his opinion, suicide in
the sea was to be excluded. Bound by the sanctity of confessional, he
could tell me no more. After the establishment of the Erice Centre,
which bears Majorana's name, I had the privilege of meeting Majorana's
entire family. No one ever believed it was suicide. Majorana was an
enthusiastic and devout Catholic and, moreover, he withdrew his savings
from the bank a week before his disappearance. The hypothesis shared by
his family and others who had the privilege of knowing him (Fermi's wife
Laura was one of the few) is that he withdrew to a monastery.
Laura Fermi recalls that when Majorana disappeared, Enrico Fermi said
to his wife, "Ettore was too intelligent. If he has decided to
disappear, no-one will be able to find him. Nevertheless, we have to
consider all possibilities." In fact, Fermi even tried to get Benito
Mussolini himself to support the search. On that occasion (in Rome in
1938), Fermi said: "There are several categories of scientists in the
world; those of second or third rank do their best but never get very
far. Then there is the first rank, those who make important discoveries,
fundamental to scientific progress. But then there are the geniuses,
like Galilei and Newton. Majorana was one of these."
A genius, however, who looked on his own work as completely banal:
once a problem was solved, Majorana did his best to leave no trace of
his own brilliance. This can be witnessed in the stories of the neutron
discovery and the hypothesis of the neutrinos that bear his name, as
recalled below by Emilio Segré and Giancarlo Wick (on the neutron) and
by Bruno Pontecorvo (on neutrinos). Majorana's comprehension of the
physics of his time had a completeness that few others in the world
could match.
Oppenheimer's Recollections
Memories of Majorana had nearly faded when, in 1962, the
International School of Physics was established in Geneva, with a branch
in Erice. It was the first of the 150 schools that now form the Centre
for Scientific Culture, which today bears Majorana's name. It is in this
context that an important physicist of the 20th century, Robert
Oppenheimer, told me of his knowledge of Majorana.
After having suffered heavy repercussions for his opposition to the
development of weapons even stronger than those that destroyed Hiroshima
and Nagasaki, Oppenheimer had decided to get back to physics while
visiting the biggest laboratories at the frontiers of scientific
knowledge. This is how he came to be at CERN, the largest European
laboratory for subnuclear physics.
At this time, many illustrious physicists participated in a ceremony
that dedicated the Erice School to Majorana. I myself - at the time very
young - was entrusted with the task of speaking about the Majorana
neutrinos. Oppenheimer wanted to voice his appreciation for how the
Erice School and the Centre for Scientific Culture had been named. He
knew of Majorana's exceptional contributions to physics from the papers
he had read, as any physicist could do at any time. What would have
remained unknown was the episode he told me as a testimony to Fermi's
exceptional opinion of Majorana. Oppenheimer recounted the following
episode from the time of the Manhattan Project, which in the course of
only four years transformed the scientific discovery of nuclear fission
into a weapon of war.
There were three critical turning points during the project, and
during the executive meeting to address the first of these crises, Fermi
turned to Eugene Wigner and said: "If only Ettore were here." The
project seemed to have reached a dead-end in the second crisis, during
which Fermi exclaimed once more: "This calls for Ettore!" Other than the
project director himself (Oppenheimer), three people were in attendance
at these meetings: two scientists (Fermi and Wigner) and a military
general. After the "top secret" meeting, the general asked Wigner, who
this "Ettore" was, and he replied: "Majorana". The general asked where
Majorana was so that he could try to bring him to America. Wigner
replied: "Unfortunately, he disappeared many years ago."
By the end of the 1920s, physics had identified three fundamental
particles: the photon (the quantum of light), the electron (needed to
make atoms) and the proton (an essential component of the atomic
nucleus). These three particles alone, however, left the atomic nucleus
shrouded in mystery: no-one could understand how multiple protons could
stick together in a single atomic nucleus. Every proton has an electric
charge, and like charges repel each other. A fourth particle was needed,
heavy like the proton but without electric charge. This was the
neutron, but no-one knew it at the time.
Then Frédérick Joliot and Irène Curie discovered a neutral particle
that can enter matter and expel a proton. Their conclusion was that it
must be a photon, because at the time it was the only known particle
with no charge. Majorana had a different explanation, as Emilio Segré
and Giancarlo Wick recounted on different occasions, including during
visits to Erice. (Both Segré and Wick were enthusiasts for what the
school and the centre had become in only a few years, all under the name
of the young physicist that Fermi considered a genius alongside Galilei
and Newton). Majorana had explained to Fermi why the particle
discovered by Joliot and Curie had to be as heavy as a proton, even
while being electrically neutral. To move a proton requires something as
heavy as the proton, thus a fourth particle must exist, a proton with
no charge. And so was born the correct interpretation of what Joliot and
Curie discovered in France: the existence of a particle that is as
heavy as a proton but without electrical charge. This particle is the
indispensable neutron. Without neutrons, atomic nuclei could not exist.
Fermi told Majorana to publish his interpretation of the French
discovery right away. Majorana, true to his belief that everything that
can be understood is banal, did not bother to do so. The discovery of
the neutron is in fact justly attributed to James Chadwick for his
experiments with beryllium in 1932.
Majorana's Neutrinos
Today, Majorana is particularly well known for his ideas about
neutrinos. Bruno Pontecorvo, the "father" of neutrino oscillations,
recalls the origin of Majorana neutrinos in the following way: Dirac
discovers his famous equation describing the evolution of the electron;
Majorana goes to Fermi to point out a fundamental detail: " I have found
a representation where all Dirac γ matrices are real. In this
representation it is possible to have a real spinor that describes a
particle identical to its antiparticle."
The Dirac equation needs four components to describe the evolution in
space and time of the simplest of particles, the electron; it is like
saying that it takes four wheels (like a car) to move through space and
time. Majorana jotted down a new equation: for a chargeless particle
like the neutrino, which is similar to the electron except for its lack
of charge, only two components are needed to describe its movement in
space-time - as if it uses two wheels (like a motorcycle). "Brilliant,"
said Fermi, "Write it up and publish it." Remembering what happened with
the neutron discovery, Fermi wrote the article himself and submitted
the work under Majorana's name to the prestigious scientific journal Il Nuovo Cimento (Majorana 1937). Without Fermi's initiative, we would know nothing about the Majorana spinors and Majorana neutrinos.
The great theorist John Bell conducted a rigorous comparison of
Dirac's and Majorana's "neutrinos" in the first year of the Erice
Subnuclear Physics School. The detailed version can be found in the
chapter that opens the 12 volumes published to celebrate Majorana's
centenary. These volumes describe the highlights leading up to the
greatest synthesis of scientific thought of all time, which we
physicists call the Standard Model. This model has already pushed the
frontiers of physics well beyond what the Standard Model itself first
promised, so now the goal is the Standard Model and beyond.
Today we know that three types of neutrinos exist. The first controls
the combustion of the Sun's nuclear engine and keeps it from
overheating. One of the dreams of today's physicists is to prove the
existence of Majorana's hypothetical neutral particles, which are needed
in grand unification theory. This is something that no-one could have
imagined in the 1930s. And no-one could have imagined the three
conceptual bases needed for the Standard Model and beyond.
Particles With Arbitrary Spin
In 1932 the study of particles with arbitrary spin was considered at
the level of a pure mathematical curiosity, and Majorana's paper on the
subject remained quasi-unknown despite being full of remarkable new
ideas (Majorana 1932). Today, three-quarters of a century later, this
mathematical curiosity of 1932 still represents a powerful source of new
ideas. In fact in this paper there are the first hints for
supersymmetry, spin-mass correlation and spontaneous symmetry breaking
(SSB) - three fundamental concepts underpinning the Standard Model and
beyond. This means that our current conceptual understanding of the
fundamental laws of nature was already in Majorana's attempts to
describe particles with arbitrary spins in a relativistically invariant
way.
Majorana starts with the simplest representation of the Lorentz
group, which is infinite-dimensional. In this representation the states
with integer (bosons) and semi-integer (fermions) spins are treated
equally. In other words, the relativistic description of particle states
allows bosons and fermions to exist on equal footing. These two
fundamental sets of states are the first hint of supersymmetry.
Another remarkable novelty is the correlation between spin and mass.
The eigenvalues of the masses are given by a relation of the type m = m0/(J+1/2), where m0
is a given constant and J is the spin. The mass decreases with the
increasing value of the spin, the opposite of what would come, many
decades later, in the study of the strong interactions between baryons
and mesons (now known as Regge trajectories). As a consequence of the
description of particle states with arbitrary spins, this remarkable
paper also contains the existence of imaginary mass eigenvalues. We know
today that the only way to introduce real masses without destroying the
theoretical description of nature is through the mechanism of SSB, but
this could not exist without imaginary masses.
In addition to these three important ideas, the paper also
contributed to a further development: the formidable relation between
spin and statistics, which would have led to the discovery of another
invariance law valid for all quantized relativistic field theories, the
celebrated PCT theorem.
Majorana's paper shows first of all that the relativistic description
of a particle state allows the existence of integer and semi-integer
spin values. However, it was already known that the electron must obey
the Pauli exclusion principle and that it has semi-integer spin. Thus
the problem arose of understanding whether the Pauli principle is valid
for all semi-integer spins. If this were the case it would be necessary
to find out the properties that characterize the two classes of
particles, now known as fermions (semi-integer spin) and bosons (integer
spin). The first of these properties are of statistical nature,
governing groups of identical fermions and groups of bosons. We now know
that a fundamental distinction exists and that the anticommutation
relations for fermions and the commutation relations for bosons are the
basis for the statistical laws governing fermions and bosons.
The spin-statistics theorem has an interesting and long history, the
main players of which are some of the most distinguished theorists of
the 20th century. The first contribution to the study of the correlation
between spin and statistics comes from Markus Fierz with a paper where
the case of general spin for free fields is investigated (Fierz 1939). A
year later Wolfgang Pauli comes in with his paper also "On the
Connection Between Spin and Statistics" (Pauli 1940). The first proofs,
obtained using only the general properties of relativistic quantum field
theory and which include microscopic causality (also known as local
commutativity), are due to Gerhart Lüders and Bruno Zumino, and to N
Burgoyne (Lüders and Zumino 1958; Burgoyne 1958). Another important
contribution, which clarifies the connection between spin and
statistics, came three years later with the work of G F Dell'Antonio
(Dell'Antonio 1961).
It cannot be accidental that the first suggestion of the existence of
the PCT invariance law came from the same people engaged in the study
of the spin-statistics theorem, Lüders and Zumino. These two outstanding
theoretical physicists suggested that if a relativistic quantum field
theory obeys the space-inversion invariance law, called parity (P), it
must also be invariant for the product of charge conjugation
(particle-antiparticle) and time inversion, CT. It is in this form that
it was proved by Lüders in 1954 (Lüders 1954). A year later Pauli proved
that PCT invariance is a universal law, valid for all relativistic
quantum field theories (Pauli 1955).
This paper closes a cycle started by Pauli in 1940 with his work on
spin and statistics where he proved already what is now considered the
classical PCT invariance, as it was derived using free non-interacting
fields. The validity of PCT invariance for quantum field theories was
obtained in 1951 by Julian Schwinger, a great admirer of Majorana
(Schwinger 1951). It is interesting to read what Arthur Wightman,
another of Majorana's enthusiastic supporters, wrote about this paper by
Schwinger: "Readers of this paper did not generally recognize that it
stated or proved the PCT theorem" (Wightman 1964). It is similar for
those who, reading Majorana's paper on arbitrary spins, have not found
the imprinting of the original ideas discussed in this short review of
the genius of Majorana.
Link:
http://cerncourier.com/cws/article/cern/29664
[A self Portrait]