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The Π-Theorem as a Guide to Quantity Symmetries and the Argument Against Absolutism

Jalloh, Mahmoud (2022) The Π-Theorem as a Guide to Quantity Symmetries and the Argument Against Absolutism. [Preprint]

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Abstract

In this paper a symmetry argument against quantity absolutism is amended. Rather
than arguing against the fundamentality of intrinsic quantities on the basis of transformations of basic quantities, e.g. mass doubling, a class of symmetries defined by the Π-theorem is used. This theorem is a fundamental result of dimensional analysis and shows that all unit-invariant equations which adequately represent physical systems can be put into the form of a function of dimensionless quantities. Quantity transformations that leave those dimensionless quantities invariant are empirical and dynamical symmetries. The proposed symmetries of the original argument fail to be both dynamical and empirical symmetries and are open to counterexamples. The amendment of the original argument requires consideration of the relationships between quantity dimensions. The discussion raises a pertinent issue: what is the modal status of the constants of nature which figure in the laws? Two positions, constant necessitism and constant contingentism, are introduced and their relationships to absolutism and comparativism undergo preliminary investigation. It is argued that the absolutist can only reject the amended symmetry argument by accepting constant necessitism, which has a costly outcome: unit transformations are no longer symmetries.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Jalloh, Mahmoudmahmoudtimbojalloh@gmail.com0000-0001-8511-9294
Keywords: quantity, symmetry, dimensional analysis
Subjects: General Issues > Scientific Metaphysics
General Issues > Laws of Nature
Specific Sciences > Physics
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Mahmoud Jalloh
Date Deposited: 24 Sep 2022 13:11
Last Modified: 24 Sep 2022 13:11
Item ID: 21199
Subjects: General Issues > Scientific Metaphysics
General Issues > Laws of Nature
Specific Sciences > Physics
Specific Sciences > Physics > Symmetries/Invariances
Date: September 2022
URI: http://philsci-archive.pitt.edu/id/eprint/21199

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