The Labyrinth of Quantum Logics

Bas C. van Fraassen

Gary M. Hardegree, Patricia J. Frazer

Thomas A. Brody

Tim Maudlin

Quantum mechanics predicts many surprising phenomena, including the two-slit interference of electrons. It has often been claimed that these phenomena cannot be understood in classical terms. But the meaning of “classical” is often not precisely specified. One might, for example, interpret it as “classical physics” or “classical logic” or “classical probability theory.” Quantum mechanics also suffers from a conceptual difficulty known as the measurement problem. Early in his career, Hilary Putnam believed that modifications of classical logic could both solve the measurement problem and account for the twoslit phenomena. Over 40 years later he had abandoned quantum logic in favor of the investigation of various theories - using classical logic and probability theory - that can accomplish these tasks. The trajectory from Putnam’s earlier views to his later views illustrates the difficulty trying to solve physical problems with alterations of logic or mathematics.

Thomas A. Brody

Rossella Lupacchini

At the roots of quantum physics we find two “specular” principles: a principle of distinguishability, which arranges the “uncertainty” of quantum \nmeasurement, and a principle of continuity, which drives the evolution of quantum systems. The vital link between the two principles was sharply \ncaptured by Leibniz. In his Theodicy, the issue of continuity (and indivisibles) is presented as one of “the two famous labyrinths” in which our \nreason can lose its way; the other concerns “the great question of freedom and necessity.” According to Leibniz, only geometry can provide a \nthread for the labyrinth of continuity. However, escaping from the labyrinth of Fate, Fortune, and Freedom requires a different perspective on nature. Leibniz’s perspective on the mechanism of nature is significantly different from Descartes’ or Newton’s. It reveals notable affinities with the Chinese correlative thinking. Surprisingly, the rationale behind these affinities may find a coherent setting in quantum information.