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

electrical engineer Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

art critic An art critic is a person who is specialized in analyzing, interpreting, and evaluating art. Their written critiques or reviews contribute to art criticism and they are published in newspapers, magazines, books, exhibition brochures, and catalogu ...

and writer.

Early life

Schenberg was born in

Recife That it may shine on all (Matthew 5:15) , image_map = Brazil Pernambuco Recife location map.svg , mapsize = 250px , map_caption = Location in the state of Pernambuco , pushpin_map = Brazil#South Am ...

, Brazil. His parents were Russian-Jews of German origin. From early on he showed remarkable ability for mathematics, enchanting himself with geometry, which had a strong influence on his works. Schenberg 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 experime ...

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 said, Astrophysics "seeks to ascertain the nature of the h ...

, particularly the theory of nuclear processes in the formation of

supernova A supernova is a powerful and luminous explosion of a star. It has the plural form supernovae or supernovas, and is abbreviated SN or SNe. This transient astronomical event occurs during the last evolutionary stages of a massive star or whe ...

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 ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...

and then re-emitting a

beta particle A beta particle, also called beta ray or beta radiation (symbol β), is a high-energy, high-speed electron or positron emitted by the radioactive decay of an atomic nucleus during the process of beta decay. There are two forms of beta decay, � ...

plus a

neutrino A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...

-antineutrino pair, leading to the loss of internal supporting pressure and consequent collapse and explosion in the form of a supernova.

George Gamow George Gamow (March 4, 1904 – August 19, 1968), born Georgiy Antonovich Gamov ( uk, Георгій Антонович Гамов, russian: Георгий Антонович Гамов), was a Russian-born Soviet and American polymath, theoret ...

(1904–1968) was inspired to name the process Urca after the name of a

casino A casino is a facility for certain types of gambling. Casinos are often built near or combined with hotels, resorts, restaurants, retail shopping, cruise ships, and other tourist attractions. Some casinos are also known for hosting live enterta ...

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 Subrahmanyan Chandrasekhar (; ) (19 October 1910 – 21 August 1995) was an Indian-American theoretical physicist who spent his professional life in the United States. He shared the 1983 Nobel Prize for Physics with William A. Fowler for " ...

(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 Gravitational collapse is the contraction of an astronomical object due to the influence of its own gravity, which tends to draw matter inward toward the center of gravity. Gravitational collapse is a fundamental mechanism for structure formatio ...

, once the core

hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...

is exhausted.

Quantum physics and geometric algebra

In the

University of São Paulo The University of São Paulo ( pt, Universidade de São Paulo, USP) is a public university in the Brazilian state of São Paulo. It is the largest Brazilian public university and the country's most prestigious educational institution, the bes ...

had Schönberg interacted closely with

David Bohm David Joseph Bohm (; 20 December 1917 – 27 October 1992) was an American-Brazilian-British scientist who has been described as one of the most significant theoretical physicists of the 20th centuryPeat 1997, pp. 316-317 and who contributed ...

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 The de Broglie–Bohm theory, also known as the ''pilot wave theory'', Bohmian mechanics, Bohm's interpretation, and the causal interpretation, is an Interpretations of quantum mechanics, interpretation of quantum mechanics. In addition to the wa ...

. He wrote a series of publications of 1957/1958 on

geometric algebra In mathematics, a geometric algebra (also known as a real Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the ...

s that stand in relation to

quantum physics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qua ...

and

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...

. He pointed out that those algebras can be described in terms of extensions of the commutative and the anti-commutative

Grassmann algebra In mathematics, the exterior algebra, or Grassmann algebra, named after Hermann Grassmann, is an algebra that uses the exterior product or wedge product as its multiplication. In mathematics, the exterior product or wedge product of vectors is a ...

s which have the same structure as the ''boson algebra'' and the ''fermion algebra'' of

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

. 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. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hyperco ...

, 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 In mathematics, the Heisenberg group H, named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form ::\begin 1 & a & c\\ 0 & 1 & b\\ 0 & 0 & 1\\ \end under the operation of matrix multiplication. Elements ...

, and this suggestion was taken up and expanded upon in the 1980s by

Basil Hiley Basil J. Hiley (born 1935), is a British quantum physicist and professor emeritus of the University of London. Long-time colleague of David Bohm, Hiley is known for his work with Bohm on implicate orders and for his work on algebraic description ...

and his co-workers in their work on algebraic formulations of quantum mechanics; this work was performed at

Birkbeck College , mottoeng = Advice comes over nightTranslation used by Birkbeck. , established = , type = Public research university , endowment = £4.3 m (2014) , budget = £10 ...

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 also a member of the

Brazilian Communist Party The Brazilian Communist Party ( pt-BR, Partido Comunista Brasileiro), originally the Communist Party of Brazil (), is a communist party in Brazil founded on 25 March 1922 which makes the disputed claim of being the oldest political party sti ...

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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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 Brazilian communists University of São Paulo alumni University of São Paulo faculty 20th-century Brazilian scientists 20th-century Brazilian people Presidents of the Brazilian Physical Society