Sidney Michael Dancoff (September 27, 1913 in

Philadelphia Philadelphia, often called Philly, is the largest city in the Commonwealth of Pennsylvania, the sixth-largest city in the U.S., the second-largest city in both the Northeast megalopolis and Mid-Atlantic regions after New York City. Sinc ...

– August 15, 1951 in

Urbana, Illinois Urbana ( ) is a city in and the county seat of Champaign County, Illinois, United States. As of the 2020 census, Urbana had a population of 38,336. As of the 2010 United States Census, Urbana is the List of municipalities in Illinois, 38th-most pop ...

) was an American theoretical

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 caus ...

best known for the Tamm–Dancoff approximation method and for nearly developing a renormalization method for solving quantum electrodynamics (QED). Dancoff was raised in the

Squirrel Hill Squirrel Hill is a residential neighborhood in the East End of Pittsburgh, Pennsylvania, United States. The city officially divides it into two neighborhoods, Squirrel Hill North and Squirrel Hill South, but it is almost universally treated a ...

neighborhood of

Pittsburgh Pittsburgh ( ) is a city in the Commonwealth (U.S. state), Commonwealth of Pennsylvania, United States, and the county seat of Allegheny County, Pennsylvania, Allegheny County. It is the most populous city in both Allegheny County and Wester ...

. He attended

Carnegie Tech Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania. One of its predecessors was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools; it became the Carnegie Institute of Technology ...

on a private scholarship and received his B.S. in physics in 1934, followed by a master's degree from the

University of Pittsburgh The University of Pittsburgh (Pitt) is a public state-related research university in Pittsburgh, Pennsylvania. The university is composed of 17 undergraduate and graduate schools and colleges at its urban Pittsburgh campus, home to the universit ...

in 1936. He then went to the

University of California at Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant univ ...

where he earned his PhD in 1939 under

Robert Oppenheimer J. Robert Oppenheimer (; April 22, 1904 – February 18, 1967) was an American theoretical physicist. A professor of physics at the University of California, Berkeley, Oppenheimer was the wartime head of the Los Alamos Laboratory and is often ...

. While Dancoff was at Berkeley, Oppenheimer suggested that he work on the calculation of the scattering of a relativistic

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 no kn ...

by an

electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...

. 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 The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfr ...

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 World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

, Dancoff worked on the theory of the newly invented

nuclear reactor A nuclear reactor is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. Heat from nu ...

s. To take into account how fuel rods could "shadow" other rods by absorbing neutrons headed toward the other rods, he and M. Ginsburg 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 The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univ ...

. In 1950 he published an approximation method for many-body theory that has been used in

nuclear Nuclear may refer to: Physics Relating to the nucleus of the atom: * Nuclear engineering *Nuclear physics *Nuclear power *Nuclear reactor *Nuclear weapon *Nuclear medicine *Radiation therapy *Nuclear warfare Mathematics *Nuclear space *Nuclear ...

and

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 l ...

. 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 Henry Quastler (November 11, 1908 – July 4, 1963) was an Austrian physician and radiologist who became a pioneer in the field of information theory applied to biology after emigrating to America. His work with Sidney Dancoff led to the publica ...

in the new field of

cybernetics Cybernetics is a wide-ranging field concerned with circular causality, such as feedback, in regulatory and purposive systems. Cybernetics is named after an example of circular causal feedback, that of steering a ship, where the helmsperson m ...

and

information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...

. 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 of lymphoma in 1951.

References

{{DEFAULTSORT:Dancoff, Sidney 1913 births 1951 deaths University of Pittsburgh alumni Carnegie Mellon University alumni 20th-century American physicists American nuclear physicists Theoretical physicists Fellows of the American Physical Society