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The Ninth Marcel Grossmann Meeting

A glimpse to Feynman’s contributions to the debate on the foundations of quantum mechanics

Mario Di Mauro, Salvatore Esposito, Adele Naddeo

Published Jan 24, 2023• 2 citations
Publisher
DOI
10.1142/9789811269776_0302

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The broad debate on foundational issues in quantum mechanics, which took place at the famous 1957 Chapel Hill conference on \textit{The Role of Gravitation in Physics}, is here critically analyzed with an emphasis on Richard Feynman's contributions. One of the most debated questions at Chapel Hill was whether the gravitational field had to be quantized and its possible role in wave function collapse. Feynman's arguments in favor of the quantization of the gravitational field, based essentially on a series of gedanken experiments, are here discussed. Then the related problem of the wave function collapse, for which Feynman hints to decoherence as a possible solution, is discussed. Finally, another topic is analyzed, concerning the role of the observer in a closed Universe. In this respect, Feynman's many-worlds characterization of Everett's approach at Chapel Hill is discussed, together with later contributions of his, including a kind of Schrödinger's cat paradox, which are scattered throughout the 1962-63 Lectures on Gravitation. Philosophical implications of Feynman's ideas in relation to foundational issues are also discussed.

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Inter-relation between quantum and classical probability models is one of the most fundamental problems of quantum foundations. Nowadays this problem also plays an important role in quantum technologies, in quantum cryptography and the theory of quantum random generators. In this letter, we compare the viewpoint of Richard Feynman that the behavior of quantum particles cannot be described by classical probability theory with the viewpoint that quantum–classical inter-relation is more complicated (cf, in particular, with the tomographic model of quantum mechanics developed in detail by Vladimir Man'ko). As a basic example, we consider the two-slit experiment, which played a crucial role in quantum foundational debates at the beginning of quantum mechanics (QM). In particular, its analysis led Niels Bohr to the formulation of the principle of complementarity. First, we demonstrate that in complete accordance with Feynman's viewpoint, the probabilities for the two-slit experiment have the non-Kolmogorovian structure, since they violate one of basic laws of classical probability theory, the law of total probability (the heart of the Bayesian analysis). However, then we show that these probabilities can be embedded in a natural way into the classical (Kolmogorov, 1933) probability model. To do this, one has to take into account the randomness of selection of different experimental contexts, the joint consideration of which led Feynman to a conclusion about the non-classicality of quantum probability. We compare this embedding of non-Kolmogorovian quantum probabilities into the Kolmogorov model with well-known embeddings of non-Euclidean geometries into Euclidean space (e.g., the Poincaré disk model for the Lobachvesky plane).

Physica Scripta•Jun 1, 2015•8 citations
The broad debate on foundational issues in quantum mechanics, which took place at the famous 1957 Chapel Hill conference on \textit{The Role of Gravitation in Physics}, is here critically analyzed with an emphasis on Richard Feynman's contributions. One of the most debated questions at Chapel Hill was whether the gravitational field had to be quantized and its possible role in wave function collapse. Feynman's arguments in favor of the quantization of the gravitational field, based essentially on a series of gedanken experiments, are here discussed. Then the related problem of the wave function collapse, for which Feynman hints to decoherence as a possible solution, is discussed. Finally, another topic is analyzed, concerning the role of the observer in a closed Universe. In this respect, Feynman's many-worlds characterization of Everett's approach at Chapel Hill is discussed, together with later contributions of his, including a kind of Schrödinger's cat paradox, which are scattered throughout the 1962-63 Lectures on Gravitation. Philosophical implications of Feynman's ideas in relation to foundational issues are also discussed.
Inter-relation between quantum and classical probability models is one of the most fundamental problems of quantum foundations. Nowadays this problem also plays an important role in quantum technologies, in quantum cryptography and the theory of quantum random generators. In this letter, we compare the viewpoint of Richard Feynman that the behavior of quantum particles cannot be described by classical probability theory with the viewpoint that quantum–classical inter-relation is more complicated (cf, in particular, with the tomographic model of quantum mechanics developed in detail by Vladimir Man'ko). As a basic example, we consider the two-slit experiment, which played a crucial role in quantum foundational debates at the beginning of quantum mechanics (QM). In particular, its analysis led Niels Bohr to the formulation of the principle of complementarity. First, we demonstrate that in complete accordance with Feynman's viewpoint, the probabilities for the two-slit experiment have the non-Kolmogorovian structure, since they violate one of basic laws of classical probability theory, the law of total probability (the heart of the Bayesian analysis). However, then we show that these probabilities can be embedded in a natural way into the classical (Kolmogorov, 1933) probability model. To do this, one has to take into account the randomness of selection of different experimental contexts, the joint consideration of which led Feynman to a conclusion about the non-classicality of quantum probability. We compare this embedding of non-Kolmogorovian quantum probabilities into the Kolmogorov model with well-known embeddings of non-Euclidean geometries into Euclidean space (e.g., the Poincaré disk model for the Lobachvesky plane).