- Person
- John von Neumann
- Lived
- 1903–1957
- Field
- Mathematics & computing
- From
- Hungarian-American
The story
By the late 1920s physicists had two working versions of quantum mechanics, Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave mechanics. Both worked, but the mathematics underneath them was loose, and nobody had shown precisely how they fitted together. Paul Dirac had offered a unifying formalism, but it relied on mathematical devices that were not rigorous.
John von Neumann, a young mathematician who had worked with David Hilbert at Göttingen, set out to fix that. He realised in 1926 that the state of a quantum system could be represented as a point in an abstract, possibly infinite-dimensional space, now called a Hilbert space, and that measurable quantities such as position or momentum could be represented by operators acting on it. In this language Heisenberg's uncertainty principle becomes the fact that two operators do not commute. The framework included both earlier versions as special cases.
He published it in 1932 in German as Mathematical Foundations of Quantum Mechanics, his last book in German. It also contained a deep analysis of the measurement problem, describing how a measured system differs from one left alone, and the first proposal of a quantum logic, which he developed further with Garrett Birkhoff in 1936. The book was later translated into French, Spanish, English and Russian, and a new English edition appeared in 2018.
The framework, often called the Dirac–von Neumann axioms, remains the standard mathematical language of quantum theory. The mathematical physicist Arthur Wightman called it perhaps the most important axiomatisation of a physical theory to date, and with it quantum mechanics became a mature theory with a precise mathematical form. His analysis of hidden variables also began a line of research that led, through Bell's theorem and the experiments of Alain Aspect in 1982, to the demonstration that quantum physics requires a notion of reality very different from that of classical physics.
Discussions of how to interpret quantum mechanics are still largely conducted on its shared foundations.
Why it matters
Von Neumann's framework underpins every branch of quantum science, including the quantum computers and sensors now being built.
About John von Neumann
Budapest-born mathematician whose 1945 EDVAC report set out the stored-program design behind almost every computer, and who helped found game theory and modern quantum mechanics.
More about John von Neumann
- Von Neumann warned of CO2 warming in 1955In 1955 John von Neumann noted that carbon dioxide from burning coal and oil might already have changed the atmosphere enough to cause general warming.
- Von Neumann's ergodic theorem earned 'immortality'John von Neumann's 1932 papers on ergodic theory were so important that Paul Halmos said they alone would have guaranteed him mathematical immortality.
- Von Neumann launched computer weather forecastingIn 1950 John von Neumann and Jule Charney used ENIAC to make the first numerical weather forecasts; in 1955 routine computer forecasting began in the US.
- John von Neumann founded game theoryJohn von Neumann proved the minimax theorem in 1928 and, with Oskar Morgenstern, published Theory of Games and Economic Behavior in 1944, founding game theory.
- Von Neumann's IAS computer was copied worldwideThe IAS machine John von Neumann built in Princeton from 1946 became the blueprint for early computers worldwide, and its design shaped IBM's first scientific computers.
- John von Neumann invented merge sort in 1945In 1945 John von Neumann invented merge sort, one of the most widely used methods for putting data in order, in what Donald Knuth called his first computer program.
- Von Neumann helped create the Monte Carlo methodWith Stanislaw Ulam, John von Neumann helped develop the Monte Carlo method, using random numbers on computers to solve problems too complex for direct calculation.
- Von Neumann designed a machine that copies itselfIn the late 1940s John von Neumann designed a self-reproducing 'universal constructor' and, with Stanislaw Ulam, created the field of cellular automata.
- John von Neumann wrote the blueprint for modern computersJohn von Neumann's 1945 report on the EDVAC gave the first published description of the stored-program computer, the design behind almost every computer since.
Sources
- John von Neumann Wikipedia
- Mathematical Foundations of Quantum Mechanics Wikipedia
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