Sidney Dancoff
Encyclopedia
Sidney Michael Dancoff was an American
theoretical physicist
best known for the Tamm–Dancoff approximation method and for nearly developing a renormalization
method for solving quantum electrodynamics
(QED).
While Dancoff was at the University of California at Berkeley, Robert Oppenheimer
suggested that he work on the calculation of the scattering of a relativistic
electron
by an electric field
. Such QED calculations typically gave infinite answers. Following earlier perturbation-theory
work by Oppenheimer and Felix Bloch
, he found that he could deal in various ways with the infinities that arose, sometimes by canceling a positive infinity with a negative one. However, some infinities remained uncanceled and the method (later called renormalization) did not give finite results. He published a general description of this work in 1939.
In 1948, Sin-Itiro Tomonaga
and his students revisited this paper. Using improved calculational methods, they found that Dancoff had omitted one term or two terms. Once they repaired this omission, Dancoff's method worked, and they built on it to produce a theory of QED, for which Tomonaga shared the Nobel Prize
in 1965. (At the same time, American physicists discovered Dancoff's error and solved QED, relying less directly on Dancoff.)
During the Second World War, Dancoff worked on the theory of the newly invented nuclear reactor
s. To take into account how fuel rods could "shadow" other rods by absorbing neutrons headed toward the other rods, he and M. Gainsburg developed the Dancoff factor, still used in reactor calculations.
After the war, Dancoff was on the faculty of the University of Illinois at Urbana-Champaign
. In 1950 he published an approximation method for many-body theory
that has been used in nuclear
and solid-state physics
. Igor Tamm
had found it in 1945, and the method is now named after both.
In the late 1940s, Dancoff began a collaboration with the Viennese-refugee physician and radiologist Henry Quastler in the new field of cybernetics
and information theory
. Their work led to the publication of what is now commonly called Dancoff's Law. A non-mathematical statement of this law is, "the greatest growth occurs when the greatest number of mistakes are made consistent with survival".
Dancoff died in 1951.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
theoretical physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
best known for the Tamm–Dancoff approximation method and for nearly developing a renormalization
Renormalization
In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....
method for solving quantum electrodynamics
Quantum electrodynamics
Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...
(QED).
While Dancoff was at the University of California at Berkeley, Robert Oppenheimer
Robert Oppenheimer
Julius Robert Oppenheimer was an American theoretical physicist and professor of physics at the University of California, Berkeley. Along with Enrico Fermi, he is often called the "father of the atomic bomb" for his role in the Manhattan Project, the World War II project that developed the first...
suggested that he work on the calculation of the scattering of a relativistic
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
by an electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
. Such QED calculations typically gave infinite answers. Following earlier perturbation-theory
Perturbation theory (quantum mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an...
work by Oppenheimer and Felix Bloch
Felix Bloch
Felix Bloch was a Swiss physicist, working mainly in the U.S.-Life and work:Bloch was born in Zürich, Switzerland to Jewish parents Gustav and Agnes Bloch. He was educated there and at the Eidgenössische Technische Hochschule, also in Zürich. Initially studying engineering he soon changed to physics...
, he found that he could deal in various ways with the infinities that arose, sometimes by canceling a positive infinity with a negative one. However, some infinities remained uncanceled and the method (later called renormalization) did not give finite results. He published a general description of this work in 1939.
In 1948, Sin-Itiro Tomonaga
Sin-Itiro Tomonaga
was a Japanese physicist, influential in the development of quantum electrodynamics, work for which he was jointly awarded the Nobel Prize in Physics in 1965 along with Richard Feynman and Julian Schwinger.-Biography:...
and his students revisited this paper. Using improved calculational methods, they found that Dancoff had omitted one term or two terms. Once they repaired this omission, Dancoff's method worked, and they built on it to produce a theory of QED, for which Tomonaga shared the Nobel Prize
Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...
in 1965. (At the same time, American physicists discovered Dancoff's error and solved QED, relying less directly on Dancoff.)
During the Second World War, Dancoff worked on the theory of the newly invented nuclear reactor
Nuclear reactor
A nuclear reactor is a device to initiate and control a sustained nuclear chain reaction. Most commonly they are used for generating electricity and for the propulsion of ships. Usually heat from nuclear fission is passed to a working fluid , which runs through turbines that power either ship's...
s. To take into account how fuel rods could "shadow" other rods by absorbing neutrons headed toward the other rods, he and M. Gainsburg developed the Dancoff factor, still used in reactor calculations.
After the war, Dancoff was on the faculty of the University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
The University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
. In 1950 he published an approximation method for many-body theory
Many-body theory
The many-body theory is an area of physics which provides the framework for understanding the collective behavior of vast assemblies of interacting particles. In general terms, the many-body theory deals with effects that manifest themselves only in systems containing large numbers of constituents...
that has been used in nuclear
Nuclear physics
Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...
and solid-state physics
Solid-state physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from...
. Igor Tamm
Igor Tamm
Igor Yevgenyevich Tamm was a Soviet physicist and Nobel laureate who received most prestigious Nobel Prize in Physics, jointly with Pavel Alekseyevich Cherenkov and Ilya Frank, for the discovery of Cherenkov radiation, made in 1934.-Biography:Tamm was born in Vladivostok, Russian Empire , in a...
had found it in 1945, and the method is now named after both.
In the late 1940s, Dancoff began a collaboration with the Viennese-refugee physician and radiologist Henry Quastler in the new field of cybernetics
Cybernetics
Cybernetics is the interdisciplinary study of the structure of regulatory systems. Cybernetics is closely related to information theory, control theory and systems theory, at least in its first-order form...
and information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
. Their work led to the publication of what is now commonly called Dancoff's Law. A non-mathematical statement of this law is, "the greatest growth occurs when the greatest number of mistakes are made consistent with survival".
Dancoff died in 1951.