Distinguished Italian theoretical physicist Tullio Eugenio Regge passed away on 24 October 2014 in Orbassano, Italy, after an acute attack of pneumonia.
Tullio was born on 11 July 1931 in Turin, Italy. After graduating from the University of Turin in 1952 with his laurea in physics, he studied with Robert Marshak at the University of Rochester. From 1958 to 1959, he visited the Max Planck Institute for Physics, directed by Werner Heisenberg, in Munich. In 1961 the University of Turin appointed Tullio as a full professor. He went to Princeton University in 1963, and two years later was made a member of the Institute for Advanced Study (IAS), at the time guided by J. Robert Oppenheimer. In 1979 Tullio was back in Turin as a professor, first at the University of Turin and then at the Polytechnic University.
In 1983 Tullio and I founded the Institute for Scientific Interchange (ISI), today a top research organization in complex systems and data science. We based the institute on the IAS mission to cultivate a legacy of living on the edge of science, with a small, elite group of visionary scientists pursuing their ideas without constraints. Tullio was president of ISI for 20 years, and then honorary president until his death.
Tullio greatly enjoyed popularizing science. From 1989 to 1994, he served as a member of the European Parliament. Among his numerous recognitions were the 1964 Dannie Heineman Prize for Mathematical Physics from the American Physical Society, the 1996 Dirac Medal from the Abdus Salam International Centre for Theoretical Physics, and the 2001 Pomeranchuk Prize from the Institute for Theoretical and Experimental Physics.
The name Regge is part of the lexicon of modern physics—Regge poles, reggeons, Regge calculus, Regge symmetries of 3-j symbols—and the community of physicists resounds with it, something that amused Tullio and about which he enjoyed making practical jokes and puns. His contributions cover most of theoretical physics: general relativity, quantum mechanics and field theory, astrophysics, statistical mechanics, low-temperature physics. Regge poles and Regge calculus exemplify the depth and width of his influence.
The notion of Regge poles, which Tullio proposed in 1957, came out of his bold idea of studying the potential scattering amplitude as a function of angular momentum and analytically continuing the angular momentum to complex values. The amplitude grows as a power of the cosine of the scattering angle, with the energy-dependent exponent equal to the angular momentum that a would-be bound state with that energy would have. Such an exponent, a function of the energy squared, defines a Regge trajectory. Tullio’s ideas inspired the formulation of a theory in which hadrons are bound states lying on Regge trajectories. Within that framework, Gabriele Veneziano formulated his self-consistent scattering amplitude, the precursor of string theory. Regge poles also help us understand glory, that ephemeral optical phenomenon similar to a rainbow.
In 1961 Tullio introduced his piecewise-linear reformulation of general relativity, now universally known as Regge calculus, in an article titled “General relativity without coordinates” in Il Nuovo Cimento. He loved the classics of mathematics and was fascinated by Carl Friedrich Gauss’s “theorema egregium” (remarkable theorem), which proves that any surface’s Gaussian curvature is intrinsic: Although defined as a product of the principal curvatures, which depend on how the surface is immersed in ambient space, it is independent of that space. But in general relativity, as encapsulated by John Wheeler, “Matter tells spacetime how to curve; spacetime tells matter how to move.”
Regge calculus circumvents the difficult formalism of differential geometry through discrete objects that characterize the intrinsic metric structure of curved spacetime, and it reduces Einstein’s equations to a set of expressions that depend only on their value. Such combinatorial objects are simplicial complexes, structures whose constraints are twofold: They have a flat metric in their simplices, and their n-simplices are attached to each other only along pairs of (n − 1)-subsimplices.
The space metrics thus generated are fully characterized by edge lengths. Local coordinates, indispensable in differential geometry, are no longer there, yet the equivalence principle of relativity holds naturally, as the simplex metrics can be chosen to be Minkowskian, and triangulations with vanishing edge lengths let us recover the physical, continuous Lorentz spacetime. Tullio’s winning intuition, inspired by Gauss’s theorem, was to define curvature in that discrete representation in terms of angle deficit and to express the Einstein–Hilbert action only through edge lengths, with no need to resort to the Riemann curvature tensor. Many models of quantum gravity are rooted in Regge calculus.
I have fond memories of Tullio. The first time I met him was at CERN in 1972. His first words to me were, “Did you read Gauss’s original work?” When, embarrassed, I confessed that I had not, he said, “You should. In Latin, of course.” And I did. Later, I asked him how he had conceived the beautiful conceptual scheme of Regge calculus. His answer: “I was sitting at the barber’s shop and I had mirrors both in front and at the back. Looking at my image in the mirror, I saw infinitely many images and images of images, both of my face and of the nape of my neck. I thought how nice it would be to imagine this in four dimensions.”
Besides being a great scientist, Tullio was a cultivated man with a deep love for Mozart’s music, and a warm and gentle human being. His exceptional intellectual vigor and unyielding ethical principles earned him respect as a teacher, mentor, and colleague. With his incredible comprehension of science, deep knowledge, sense of humor, and curiosity, he left an indelible imprint on those who had the fortune of interacting with him. We shall dearly miss him.
