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Infinite Scale Scepticism: Probing the Epistemology of the Limit of Infinite Degrees of Freedom and Hilbert Space Non-Uniqueness

Fraser, James D. (2023) Infinite Scale Scepticism: Probing the Epistemology of the Limit of Infinite Degrees of Freedom and Hilbert Space Non-Uniqueness. [Preprint]

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Abstract

There has been much debate about how the semantic content of quantum theories with infinitely many degrees of freedom ought to be understood. This paper focuses instead on the epistemological status of the limit of infinite degrees of freedom. Do we have strong grounds to believe that the actual world is an infinite quantum system? I consider two types of argument for thinking that we do: indispensability arguments, which appeal to the role that unitarily inequivalent Hilbert space representations play in accounting for physical phenomena like spontaneous symmetry breaking, and what I call extrapolation arguments, which support the physical significance of the limit of infinite degrees of freedom by pointing to infinite volume cosmological models. Neither of these strategies turn out to be conclusive as they stand leaving the relevance of novel features of infinite quantum systems to real-world physics murky. I go on to discuss ways of motivating foundational work on infinite quantum systems which do not turn on the representational veracity of these features, and point out that when it comes to the question of the epistemological status of unitarily inequivalent Hilbert space representations other sources of non-uniqueness than the limit of infinite degrees of freedom must also be considered.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Fraser, James D.jamesf09@hotmail.co.uk
Keywords: Scientific Realism, Confirmation, Quantum Mechanics, Quantum Field Theory, General Relativity, Infinity, Scale, Inequivalent Representations
Subjects: Specific Sciences > Physics > Cosmology
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
General Issues > Realism/Anti-realism
Depositing User: Mr James Fraser
Date Deposited: 04 Sep 2023 18:42
Last Modified: 04 Sep 2023 18:42
Item ID: 22503
Official URL: https://www.journals.uchicago.edu/doi/abs/10.1086/...
DOI or Unique Handle: https://doi.org/10.1086/727426
Subjects: Specific Sciences > Physics > Cosmology
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
General Issues > Realism/Anti-realism
Date: August 2023
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/22503

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