Hilbrand Johannes "Hip" Groenewold (1910–1996) was a Dutch

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 experimen ...

who pioneered the largely operator-free formulation of

quantum mechanics 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, ...

phase space In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually ...

known as phase-space quantization.

Biography

Groenewold was born on 29 June 1910 in

Muntendam Muntendam is a village in the municipality of Midden-Groningen, in the Dutch province of Groningen. Until 1990 it was a separate municipality, which boasted the title 'reddest (most socialist) municipality in the Netherlands', with a council of 1 ...

in the province of

Groningen Groningen (; gos, Grunn or ) is the capital city and main municipality of Groningen province in the Netherlands. The ''capital of the north'', Groningen is the largest place as well as the economic and cultural centre of the northern part of t ...

. He graduated from the

University of Groningen The University of Groningen (abbreviated as UG; nl, Rijksuniversiteit Groningen, abbreviated as RUG) is a Public university#Continental Europe, public research university of more than 30,000 students in the city of Groningen (city), Groningen in ...

, with a major in physics and minors in mathematics and mechanics in 1934. After a visit to Cambridge to interact with

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

(1934–5) on the links between classical and quantum mechanics, and a checkered career working with

Frits Zernike Frits Zernike (; 16 July 1888 – 10 March 1966) was a Dutch physicist and winner of the Nobel Prize in Physics in 1953 for his invention of the Phase-contrast microscopy, phase-contrast microscope. Early life and education Frits Zernike was ...

in Groningen, then Leiden, the Hague,

De Bilt De Bilt () is a municipality and town in the province of Utrecht, Netherlands. It had a population of in . De Bilt houses the headquarters of the Royal Netherlands Meteorological Institute (KNMI). It is the ancestral home and namesake for the pro ...

, and several addresses in the North of the Netherlands during World War II, he earned his Ph.D. degree in 1946, under the tutelage of

Léon Rosenfeld Léon Rosenfeld (; 14 August 1904 in Charleroi – 23 March 1974) was a Belgium, Belgian physicist and Marxist. Rosenfeld was born into a Jewish secularism, secular Jews, Jewish family. He was a polyglot who knew eight or nine languages and ...

Utrecht University Utrecht University (UU; nl, Universiteit Utrecht, formerly ''Rijksuniversiteit Utrecht'') is a public research university in Utrecht, Netherlands. Established , it is one of the oldest universities in the Netherlands. In 2018, it had an enrollme ...

. In 1951, he obtained a position in Groningen in theoretical physics, first as a lecturer, then as a senior lecturer, and finally as a professor in 1955. He was the initiator and organizer of the Vosbergen Conference in the Netherlands for over two decades. His 1946 thesis paper laid the foundations of quantum mechanics in phase space, in unwitting parallel with J. E. Moyal. This treatise was the first to achieve full understanding of the

Wigner–Weyl transform In quantum mechanics, the Wigner–Weyl transform or Weyl–Wigner transform (after Hermann Weyl and Eugene Wigner) is the invertible mapping between functions in the quantum phase space formulation and Hilbert space operators in the Schrödin ...

as an invertible transform, rather than as an unsatisfactory quantization rule. Significantly, this work further formulated and first appreciated the all-important star-product, the cornerstone of this formulation of the theory, ironically often also associated with Moyal's name, even though it is not featured in Moyal's papers and was not fully understood by Moyal. Moreover, Groenewold first understood and demonstrated that the

Moyal bracket In physics, the Moyal bracket is the suitably normalized antisymmetrization of the phase-space star product. The Moyal bracket was developed in about 1940 by José Enrique Moyal, but Moyal only succeeded in publishing his work in 1949 after a le ...

is isomorphic to the

quantum In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizati ...

commutator In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Group theory The commutator of two elements, a ...

, and thus that the latter ''cannot be made to faithfully correspond'' to the

Poisson bracket In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. Th ...

, as had been envisioned by

Paul Dirac Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. He was the Lucasian Professor of Mathematics at the Univer ...

. This observation and his counterexamples contrasting Poisson brackets to commutators have been generalized and codified to what is now known as the ''Groenewold– Van Hove theorem''. See Groenewold's theorem for one version. Philosopher

Toby Ord Toby David Godfrey Ord (born July 1979) is an Australian philosopher. He founded Giving What We Can in 2009, an international society whose members pledge to donate at least 10% of their income to effective charities, and is a key figure in the ...

, in his 2020 book '' The Precipice: Existential Risk and the Future of Humanity'', identified a pioneering discussion of general

global catastrophic risk A global catastrophic risk or a doomsday scenario is a hypothetical future event that could damage human well-being on a global scale, even endangering or destroying modern civilization. An event that could cause human extinction or permanen ...

in Groenewold's 1968 paper "Modern Science and Social Responsibility", which Ord described as:

References

External links

Biographical note
from U Groningen memorial conference, 2016.
Alternate open source
of the 1946 article. 1910 births 1996 deaths 20th-century Dutch physicists Mathematical physicists People from Menterwolde University of Groningen alumni Academic staff of the University of Groningen Utrecht University alumni {{physicist-stub