Natural units via linear algebra
作者:
Alexander Maksymowicz,
期刊:
American Journal of Physics
(AIP Available online 1976)
卷期:
Volume 44,
issue 3
页码: 295-297
ISSN:0002-9505
年代: 1976
DOI:10.1119/1.10470
出版商: American Association of Physics Teachers
数据来源: AIP
摘要:
A systematic procedure is presented for introducing natural units, in which physical constants such as the speed of light in vacuum, Planck’s constant, and the mass of the electron are set equal to unity. The dimensions of physical quantities are represented by vectors in an abstract linear vector space, referred to as thedimensionspace. The quantities chosen as basic units play the role of basis vectors in this space. Conversion from one system of basic units to another corresponds to a different choice of basis vectors. Such a conversion is equivalent to a linear transformation on the dimension space and may be implemented by matrix multiplication. A detailed treatment is given of the transformation from mass–length–time units to a system of natural units appropriate to the atomic domain. The broader applicability of linear algebra techniques to dimensional analysis is briefly indicated by way of conclusion.
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