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Higher Theory and the Three Problems of Physics

Veilahti, Antti (2017) Higher Theory and the Three Problems of Physics. [Preprint]

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Abstract

According to the Butterfield–Isham proposal, to understand quantum gravity we must revise the way we view the universe of mathematics. However, this paper demonstrates that the current elaborations of this programme neglect quantum interactions. The paper then introduces the Faddeev–Mickelsson anomaly which obstructs the renormalization of Yang–Mills theory, suggesting that to theorise on many-particle systems requires a many-topos view of mathematics itself: higher theory. As our main contribution, the topos theoretic framework is used to conceptualise the fact that there are principally three different quantisation problems, the differences of which have been ignored not just by topos physicists but by most philosophers of science. We further argue that if higher theory proves out to be necessary for understanding quantum gravity, its implications to philosophy will be foundational: higher theory challenges the propositional concept of truth and thus the very meaning of theorising in science.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Veilahti, Antti
Keywords: Topos quantum physics, category theory, higher theory, quantum interaction, quantum gravity, Yang–Mills theory
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics > Ontology
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Mr. Antti Veilahti
Date Deposited: 01 Jan 2018 20:24
Last Modified: 01 Jan 2018 20:24
Item ID: 14242
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics > Ontology
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Symmetries/Invariances
Date: 26 December 2017
URI: http://philsci-archive.pitt.edu/id/eprint/14242

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