Mário Schenberg#Quantum physics and geometric algebra

{{Short description|Brazilian electrical engineer, physicist, art critic and writer}}

{{Infobox scientist

|name = Mário Schenberg

|image = Schenberg.jpg

|image_size = 220px

|caption =

|birth_name = Mayer Schönberg

|birth_date = {{birth date|1914|7|2|mf=y}}

|birth_place = Recife, Pernambuco, Brazil

|death_date = {{death date and age|1990|11|10|1914|7|2|mf=y}}

|death_place = São Paulo, Brazil

|residence =

|fields = Theoretical physics

|workplaces =

|alma_mater = University of São Paulo

|doctoral_students = José Leite Lopes

|notable_students =

|known_for = Schönberg-Chandrasekhar limit
Urca process

|footnotes = Brazilian physicist of the 'heroic era' (1900–1945), together with José Leite Lopes, Cesar Lattes, Jayme Tiomno, and Joaquim da Costa Ribeiro.

}}

Mário Schenberg (born Mayer Schönberg [var. Mário Schönberg, Mario Schonberg, Mário Schoenberg]; 2 July 1914 – 10 November 1990) was a Brazilian electrical engineer, physicist, art critic and writer.

Early life

Schenberg was born in Recife, Brazil as Mayer Schönberg. His parents were Russian Jews of German origin.{{clarify|date=April 2024}} 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 physicists, Schenberg is best remembered for his contributions to astrophysics, particularly the theory of nuclear processes in the formation of supernova 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 and then re-emitting a beta particle plus a neutrino-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 casino 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 is exhausted.

= Quantum physics and geometric algebra =

In the University of São Paulo had Schönberg interacted closely with David Bohm during the final years of Bohm's exile in Brazil,[http://www.aip.org/history/ohilist/33822.html Interview with Basil Hiley] {{Webarchive|url=https://web.archive.org/web/20121015004915/http://www.aip.org/history/ohilist/33822.html |date=October 15, 2012 }} 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.{{cite journal | doi = 10.1007/BF02820368 | first = M. | last = Schönberg | title = On the hydrodynamical model of the quantum mechanics | journal = Il Nuovo Cimento | year = 1954 | volume= 12 | pages = 103–133 |bibcode =1954NCim...12..103S | issue = 1 | s2cid = 123655548 }} ([https://doi.org/10.1007%2FBF02820368 abstract])

He wrote a series of publications of 1957/1958 on geometric algebras that stand in relation to quantum physics and quantum field theory. 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. These algebras, in turn, are related to the symplectic algebra and Clifford algebra, respectively.F. A. M. Frescura, B. J. Hiley: [http://www.bbk.ac.uk/tpru/BasilHiley/P12FrescandHiley3.pdf 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 to the Heisenberg algebra,M. Schönberg, Quantum mechanics and geometry, An. Acad. Brasil. Cien., 30, pp. 1–20, 1958. Cited after: F. A. M. Frescura, B. J. Hiley: [http://www.bbk.ac.uk/tpru/BasilHiley/P12FrescandHiley3.pdf 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) 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;B. J. Hiley: [http://www.bbk.ac.uk/tpru/BasilHiley/IdpsinEEHA5.pdf A note on the role of idempotents in the extended Heisenberg algebra], "Implications", Scientific Aspects of ANPA 22, pp. 107–121, Cambridge, UK, 2001. 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.M.C.B. Fernandes, J.D.M. Vianna: On the generalized phase space approach to Duffin–Kemmer–Petiau particles, Foundations of Physics, vol 29, no. 2, pp. 201–219 (1999), {{doi|10.1023/A:1018869505031}} ([https://doi.org/10.1023%2FA%3A1018869505031 abstract]), therein p. 201

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.Artibani Micali, Roger Boudet, Jacques Helmstetter (edds.): Clifford Algebras and their Applications in Mathematical Physics. Workshop Proceedings: 2nd (Fundamental Theories of Physics), Kluwer, 1989, {{ISBN|0-7923-1623-1}}, [https://books.google.com/books?id=FhU9QpPIscoC&pg=PP13 Foreword] (in French language)

Politics and life

Schenberg was a member of the Brazilian Communist Party{{cite book | title=The Utopian Impulse in Latin America | publisher=Palgrave Macmillan |author1=Beauchesne, Kim |author2=Santos, Alessandra | isbn=9780230339613 | year=2011 | page=[https://books.google.com/books?id=fePHAAAAQBAJ&pg=PA177 177]}}{{cite journal| author =Barros, Alberto Luiz da Rocha | year=1991 | title=Schenberg: nada que é humano lhe era estranho | journal = Estudos Avançados | volume = 5 | issue = 11 | pages =197–198 | publisher=University of São Paulo | doi=10.1590/S0103-40141991000100011 | issn=0103-4014 | url=http://www.scielo.br/pdf/ea/v5n11/v5n11a11.pdf | language=pt | access-date=December 7, 2015 | doi-access=free }} and professor of the University of São Paulo.

Articles

His articles include:

M. Schönberg: Quantum kinematics and geometry, Il Nuovo Cimento (1955–1965), vol. 6, Supplement 1, pp. 356–380, 1957, {{doi|10.1007/BF02724793}} ([https://doi.org/10.1007%2FBF02724793 preview])
M. Schönberg, S. Chandrasekhar: On the Evolution of the Main-Sequence Stars, Astrophysical Journal, vol. 96, no. p. 161 ff., 1942, [http://adsabs.harvard.edu/full/1942ApJ....96..161S fulltext]