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Reconciling Quantum Physics with Math

By Chris Edwards
Communications of the ACM, September 2016, Vol. 59 No. 9, Pages 11-13
10.1145/2967975
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From left, Nikhil Srivastava, Adam Marcus, and Daniel Spielman shortly after completing the proof of the Kadison-Singer problem.

Credit: Nikhil Srivastava

A solution to a problem in mathematics that lingered unsolved for more than 50 years could help deliver faster computer algorithms to many problems in physics and signal processing. However, it may take years for mathematicians to fully digest the result, which was first published online three years ago.

The roots of the problem defined by Richard Kadison and Isadore Singer in the late 1950s lie in attempts to give the physics of quantum mechanics a footing in abstract mathematics. The concept it deals with traces back to Werner Heisenberg's initial work on quantum mechanics. Heisenberg used matrix mathematics to develop his model of the quantum world that says it is not possible to accurately measure simultaneously different properties of a physical system at the microscopic level.

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