Mário Schenberg (born Mayer Schönberg ar. ''Mário Schönberg'', ''Mario Schonberg'', ''Mário Schoenberg'' 2 July 1914 – 10 November 1990) was a Brazilian

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and writer.

Early life

Schenberg was born in

Recife Recife ( , ) is the Federative units of Brazil, state capital of Pernambuco, Brazil, on the northeastern Atlantic Ocean, Atlantic coast of South America. It is the largest urban area within both the North Region, Brazil, North and the Northeast R ...

, Brazil as Mayer Schönberg. His parents were

Russian Jews The history of the Jews in Russia and areas historically connected with it goes back at least 1,500 years. Jews in Russia have historically constituted a large religious and ethnic diaspora; the Russian Empire at one time hosted the largest po ...

of German origin. From early on he showed remarkable ability for mathematics, enchanting himself with geometry, which had a strong influence on his works. He took the primary and secondary courses in Recife. Because of his family's financial limitations, he was not able to study in Europe. He then entered the Faculty of Engineering of Recife in 1931.

Scientific work

The Urca process

Widely regarded as one of Brazil's most important

theoretical physicist Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena. This is in contrast to experimental physics, which uses experi ...

s, Schenberg is best remembered for his contributions to

astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the ...

, particularly the theory of nuclear processes in the formation of

supernova A supernova (: supernovae or supernovas) is a powerful and luminous explosion of a star. A supernova occurs during the last stellar evolution, evolutionary stages of a massive star, or when a white dwarf is triggered into runaway nuclear fusion ...

stars. He provided the inspiration for the name of the so-called '' Urca process'', a cycle of nuclear reactions in which a nucleus loses energy by absorbing an

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

and then re-emitting a beta particle plus a

neutrino A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that i ...

-antineutrino pair, leading to the loss of internal supporting pressure and consequent collapse and explosion in the form of a supernova. George Gamow (1904–1968) was inspired to name the process Urca after the name of a

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in Rio de Janeiro, when Schenberg remarked to him that "the energy disappears in the nucleus of the supernova as quickly as the money disappeared at that roulette table".

Schönberg–Chandrasekhar limit

Together with Indian physicist Subrahmanyan Chandrasekhar (1910–1995), he discovered and published in 1942 the so-called Schönberg–Chandrasekhar limit, which is the maximum mass of the core of a star that can support the overlying layers against gravitational collapse, once the core

hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...

is exhausted.

Quantum physics and geometric algebra

In the

University of São Paulo The Universidade de São Paulo (, USP) is a public research university in the Brazilian state of São Paulo, and the largest public university in Brazil. The university was founded on 25 January 1934, regrouping already existing schools in ...

had Schönberg interacted closely with

David Bohm David Joseph Bohm (; 20 December 1917 – 27 October 1992) was an American scientist who has been described as one of the most significant Theoretical physics, theoretical physicists of the 20th centuryDavid Peat Who's Afraid of Schrödinger' ...

during the final years of Bohm's exile in Brazil,Interview with Basil Hiley
conducted by Olival Freire on January 11, 2008, Oral History Transcript, Niels Bohr Library & Archives, American Institute of Physics and, in 1954, Schönberg demonstrated a link among the quantized motion of the Madelung fluid and the trajectories of the de Broglie–Bohm theory. He wrote a series of publications of 1957/1958 on geometric algebras that stand in relation to

quantum physics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

and

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...

. He pointed out that those algebras can be described in terms of extensions of the commutative and the anti-commutative Grassmann algebras which have the same structure as the ''boson algebra'' and the ''fermion algebra'' of

creation and annihilation operators Creation operators and annihilation operators are Operator (mathematics), mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilatio ...

. These algebras, in turn, are related to the symplectic algebra and

Clifford algebra In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished subspace. As -algebras, they generalize the real number ...

, respectively.F. A. M. Frescura, B. J. Hiley
Algebras, quantum theory and pre-space
p. 3–4 (published in Revista Brasileira de Fisica, Volume Especial, Julho 1984, Os 70 anos de Mario Schonberg, pp. 49–86) In a paper published in 1958, Schönberg suggested to add a new

idempotent Idempotence (, ) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of pl ...

to the Heisenberg algebra, and this suggestion was taken up and expanded upon in the 1980s by Basil Hiley and his co-workers in their work on algebraic formulations of quantum mechanics; this work was performed at Birkbeck College where Bohm had become professor of physics in the meantime. Schönberg's ideas have also been cited in connection with algebraic approaches to describe relativistic phase space. His work has been cited, together with that of Marcel Riesz, for its importance to Clifford algebras and mathematical physics in the proceedings of a workshop held in France in 1989 which had been dedicated to these two mathematicians.

Politics and life

Schenberg was a member of the Brazilian Communist Party and professor of the

Articles

His articles include: * M. Schönberg: ''Quantum kinematics and geometry'', Il Nuovo Cimento (1955–1965), vol. 6, Supplement 1, pp. 356–380, 1957,
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* M. Schönberg, S. Chandrasekhar: ''On the Evolution of the Main-Sequence Stars'', Astrophysical Journal, vol. 96, no. p. 161 ff., 1942
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Legacy

* Mario Schenberg Graviton, a spherical, resonant-mass, gravitational wave detector.

References

{{DEFAULTSORT:Schenberg, Mario 1914 births 1990 deaths People from Recife Brazilian people of Russian-Jewish descent Brazilian people of German-Jewish descent Brazilian physicists Jewish Brazilian writers Jewish socialists Jewish scientists Brazilian communists University of São Paulo alumni Academic staff of the University of São Paulo 20th-century Brazilian scientists 20th-century Brazilian people Presidents of the Brazilian Physical Society