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Quantum Mechanics: Knocking at the Gates of Mathematical Foundations

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Romanian Studies in Philosophy of Science

Part of the book series: Boston Studies in the Philosophy and History of Science ((BSPS,volume 313))

Abstract

Quantum characteristics like superposition, entanglement, wave-particle duality, nonlocality, contextuality are difficult to reconcile with our everyday intuition. I survey some aspects of quantum foundations and discuss intriguing connections with the foundations of mathematics.

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Notes

  1. 1.

    I’m grateful to Prof. I. Pârvu for bringing to my attention Mac Lane’s article (Mac Lane, 1981) which shares a similar view of mathematical concepts.

  2. 2.

    Kochen’s distinction between intrinsic and extrinsic properties is different from the more well-known one discussed in Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/intrinsic-extrinsic/.

  3. 3.

    Due to the finite experimental precision, the outcome of a measurement is always a rational number. However, it is generally assumed that the underlying physical property is continuous and takes values in a subset of \(\mathbb{R}\).

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Acknowledgements

I am grateful to Ilie Pârvu, Cristi Stoica and Iulian Toader for discussions and critical comments of the manuscript.

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Correspondence to Radu Ionicioiu .

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Ionicioiu, R. (2015). Quantum Mechanics: Knocking at the Gates of Mathematical Foundations. In: Pȃrvu, I., Sandu, G., Toader, I. (eds) Romanian Studies in Philosophy of Science. Boston Studies in the Philosophy and History of Science, vol 313. Springer, Cham. https://doi.org/10.1007/978-3-319-16655-1_11

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