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In his classic 1932 treatise Mathematical Foundations of Quantum Mechanics, John von Neumann noted that projections on a Hilbert space can be viewed as propositions about physical observables; that is, as potential yes-or-no questions an observer might ask about the state of a physical system, questions that could be settled by some measurement. [2]
The field of quantum logic was subsequently inaugurated in a 1936 paper by von Neumann and Garrett Birkhoff, the first to introduce quantum logics, [237] wherein von Neumann and Birkhoff first proved that quantum mechanics requires a propositional calculus substantially different from all classical logics and rigorously isolated a new algebraic ...
Mathematical Foundations of Quantum Mechanics (German: Mathematische Grundlagen der Quantenmechanik) is a quantum mechanics book written by John von Neumann in 1932. It is an important early work in the development of the mathematical formulation of quantum mechanics. [1]
John von Neumann (1903–1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He had perhaps the widest coverage of any mathematician of his time, integrating pure and applied sciences and making major contributions to many fields, including mathematics, physics, economics, computing, and statistics.
The von Neumann description of quantum measurement of an observable A, when the system is prepared in a pure state ψ is the following (note, however, that von Neumann's description dates back to the 1930s and is based on experiments as performed during that time – more specifically the Compton–Simon experiment; it is not applicable to most ...
In his 1932 book The Mathematical Foundations of Quantum Mechanics, John von Neumann argued that the mathematics of quantum mechanics allows the collapse of the wave function to be placed at any position in the causal chain from the measurement device to the "subjective perception" of the human observer.
His first book, Quantum Logic in Algebraic Approach, is an overview of quantum logic catering to physicists with a philosophical interest in the mathematics underpinning it. His second book, John von Neumann: Selected Letters , is the first substantial collection of letters from the influential mathematician covering the wide range of ...
John von Neumann in his 1932 book Mathematical Foundations of Quantum Mechanics had presented a proof that there could be no "hidden parameters" in quantum mechanics. The validity of von Neumann's proof was questioned by Grete Hermann in 1935, who found a flaw in the proof. The critical issue concerned averages over ensembles.