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- Title
ON DIMENSIONAL INVARIANCE
- Authors
Osborne, D.K.
- Abstract
This article presents information regarding dimensional invariance which is a law or indeed any mathematical relation between measurable variables. This paper, without attempting a general definition of physical laws, offers two supports for the third argument. Both are undoubtedly known to many workers in the field but one of them has never to the authors' knowledge been published. If they are somewhat pedestrian and commonsensical they nevertheless go beyond mere assertion, and enable to see more clearly the implicit assumptions on which the otherwise argument is based. One support applies in the case of the empirical, and the other in the case of the numerical, interpretation of laws. If they are correct they push the problem back to a more fundamental level and thus reduce the puzzle by another small increment. In the numerical interpretation a law is a relation between numbers. The numbers are of two kinds, "dimensional" and "dimensionless," but this distinction is only a shorthand way of keeping track of which numbers are measures and which are not, all the numbers are in fact real or complex. Two kinds of mapping occur properties into numbers and numbers into numbers. Once the numbers come into the picture they take over, as it were, operations on them are in no way restricted by operations permitted on properties.
- Subjects
BIO-bibliography; PUBLISHING; STENOGRAPHERS; LAW; WRITING; SYMMETRY (Physics)
- Publication
Quality & Quantity, 1978, Vol 12, Issue 1, p75
- ISSN
0033-5177
- Publication type
Article
- DOI
10.1007/BF00138660