Dimensions

In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. London, UK: Routledge (2022)
  Copy   BIBTEX

Abstract

This chapter concerns dimensions as the term is used in the physical sciences today. Some key points made are: Quantities of the same kind have the same dimension; but that two quantities have the same dimension does not necessarily mean they are of the same kind. The dimension of a quantity is not determined for a single quantity in isolation, but relative to a system of quantities and the relations that hold between them. Dimensions, units, and quantities are distinct notions. In this article, I explain how dimensions, units, and quantities are involved in the design of coherent systems of units; the account involves the equations of physics. When the use of a coherent system of units can be presumed, dimensional analysis is a powerful logico-mathematical method for deriving equations and relations in physics, and for parameterizing equations in terms of dimensionless parameters, which allows identifying physically similar systems. The source of the information yielded by dimensional analysis is not yet well understood in philosophy of physics. This chapter aims to reveal the role of dimensions not only in applications of dimensional analysis to obtain information by involving the principle of dimensional homogeneity, but to the role of dimensions in encoding information about physical relationships in the language of dimensions, specifically via the feature of coherence of a system of units. Philosophers of mathematics and philosophers of science have been concerned to address the question of the effectiveness of mathematics in science. It is argued here that no philosophical analysis of the question of the applicability of mathematics to science is complete without including dimensions and dimensional analysis in the picture.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,593

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Relations Between Units and Relations Between Quantities.S. G. Sterrett - 2019 - In Nadine De Courtenay, Olivier Darrigol & Oliver Schlaudt (eds.), The Reform of the International System of Units (SI) Philosophical, Historical and Sociological Issues. London: Routledge. pp. 99-124.
How dimensional analysis can explain.Mark Pexton - 2014 - Synthese 191 (10):2333-2351.
Vector-spinor space and field equations.Nathan Rosen & Gerald E. Tauber - 1987 - Foundations of Physics 17 (1):63-99.
Similar systems and dimensionally invariant laws.R. Duncan Luce - 1971 - Philosophy of Science 38 (2):157-169.
Aesthetic fields—Null theory.M. Muraskin - 1980 - Foundations of Physics 10 (11-12):887-903.
Dimensions of mind.Richard Menary - 2010 - Phenomenology and the Cognitive Sciences 9 (4):561-578.
Eight Dimensions for the Emotions.Tom Cochrane - 2009 - Social Science Information 48 (3):379-420.
Cosmological special relativity.M. Carmeli - 1996 - Foundations of Physics 26 (3):413-416.

Analytics

Added to PP
2017-11-07

Downloads
23 (#584,438)

6 months
8 (#157,827)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Susan G. Sterrett
Wichita State University

Citations of this work

In Defence of Dimensions.Caspar Jacobs - forthcoming - British Journal for the Philosophy of Science.

Add more citations

References found in this work

On the explanatory role of mathematics in empirical science.Robert W. Batterman - 2010 - British Journal for the Philosophy of Science 61 (1):1-25.
Experimentation on Analogue Models.Susan G. Sterrett - 2017 - In Springer handbook of model-based science (2017). Springer. pp. 857-878.
Physically Similar Systems: a history of the concept.Susan G. Sterrett - 2017 - In Magnani Lorenzo & Bertolotti Tommaso Wayne (eds.), Springer Handbook of Model-Based Science. Springer. pp. 377-412.

View all 10 references / Add more references