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Indeterministic finite-precision physics and intuitionistic mathematics

van der Lugt, Tein (2020) Indeterministic finite-precision physics and intuitionistic mathematics. [Preprint]

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Abstract

In recent publications in physics and mathematics, concerns have been raised about the use of real numbers to describe quantities in physics, and in particular about the usual assumption that physical quantities are infinitely precise. In this thesis, we discuss some motivations for dropping this assumption, which we believe partly arises from the usual point-based approach to the mathematical continuum. We focus on the case of classical mechanics specifically, but the ideas could be extended to other theories as well. We analyse the alternative theory of classical mechanics presented by Gisin and Del Santo, which suggests that physical quantities can equivalently be thought of as being only determined up to finite precision at each point in time, and that doing so naturally leads to indeterminism. Next, we investigate whether we can use intuitionistic mathematics to mathematically express the idea of finite precision of quantities, arriving at the cautious conclusion that, as far as we can see, such attempts are thwarted by conceptual contradictions. Finally, we outline another approach to formalising finite-precision quantities in classical mechanics, which is inspired by the intuitionistic approach to the continuum but uses classical mathematics.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
van der Lugt, Teinteinvdlugt@gmail.com0000-0003-3648-8055
Additional Information: Completed in July 2020 in partial fulfillment of the requirements for Bachelor of Science in Physics and in Mathematics at Radboud University Nijmegen.
Keywords: Indeterminism; Intuitionistic mathematics; Information in physics
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Physics > Classical Physics
General Issues > Determinism/Indeterminism
General Issues > Laws of Nature
Depositing User: Mr Tein van der Lugt
Date Deposited: 15 Aug 2021 16:23
Last Modified: 15 Aug 2021 16:23
Item ID: 19438
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Physics > Classical Physics
General Issues > Determinism/Indeterminism
General Issues > Laws of Nature
Date: 31 July 2020
URI: http://philsci-archive.pitt.edu/id/eprint/19438

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