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The mathematics and physics of quantum mechanics

Narasimhaiengar Mukunda

Published Jan 1, 1987• 0 citations
OpenAlex

Abstract

A short history of the development of the mathematics of quantum mechanics, with some comments on the strangeness of the conventional physical interpretation.

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Paul Benioff was a physicist and mathematician working as a research scientist at the Argonne National Laboratory. He published two papers on Everett interpretation shortly after this letter: Benioff (1977)["Finite and infinite measurement in quantum mechanics and randomness: The Everett interpretation," Journal of Mathematical Physics 18(12), 2289] and Benioff (1978) ["A Note on the Everett Interpretation of Quantum Mechanics," Foundations of Physics 8(9/10), 709]. In both cases, Benioff was interested in the role of infinite sequences of measurements in the Everett interpretation. In this letter, Wheeler asks Everett to comment on Benioff's argument.
In this thesis I argue that many problems in the philosophy of science and mathematics (in particular, the unreasonable effectiveness of mathematics in physics) can only be addressed within a broader metaphysical framework which provides a coherent world view. I attempt to develop such a framework and draw out its consequences. The attempt is in two parts: first, I develop a speculative framework based on an analogy to set theory; then I combine elements of the framework with ideas from Leibnizian monadology and consistent histories quantum theory to introduce (what I call) quantum monadology. The two parts focus on different aspects of the problem and should be viewed as stages on the way to a final formulation. The inspiration for the thesis came from Plato’s Timaeus and Wigner’s comments on quantum mechanics. As it turned out, Leibniz’s Monadology became a third key source.