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While usual presentations of physical theories emphasize the notion of physical quantity, this book shows that there is much to gain when introducing the notion of physical quality. The usual physical quantities simply appear as coordinates over the manifolds representing the physical qualities. This allows to develop physical theories that have a degree of invariance much deeper than the usual one. It is shown that properly developed physical theories contain logarithms and exponentials of tensors: their conspicuous absence in usual theories suggests, in fact, that the fundamental invariance principle stated in this book is lacking in present-day mathematical physics. The book reviews and extends the theory of Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. As an illustration, two simple theories are studied with somedetail, the theory of heat conduction and the theory of linear elastic media. The equations found differ quantitatively and qualitatively from those usually presented.
List of contents
Geotensors.- Tangent Autoparallel Mappings.- Quantities and Measurable Qualities.- Intrinsic Physical Theories.
About the author
Professor at the University of Paris. Doctor Honoris Causa by the University of Copenhagen. Silver medal of the French National Science Foundation. Author of a well-known book on Inverse Problem Theory.
Summary
While the traditional approach to physical theories emphasizes the notion of physical ‘quantity,’ this refreshing and challenging book shows that there is much to gain from relying rather on the notion of physical ‘quality.’ Tarantola makes the case that the usual physical quantities, which are employed in most postulated, are really just coordinates over the manifolds representing the physical qualities. The alternative approach enables the development of physical theories that have a degree of invariance much deeper than the usual one. While properly developed physical theories contain logarithms and exponentials of tensors, he demonstrates the implications of their conspicuous absence in the usual theories, namely that the fundamental invariance principle examined here is lacking in present-day mathematical physics. The book reviews and extends the theory of Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usualnotion of linear tangent application to the intrinsic point of view proposed for physics. As an illustration, two simple theories are studied with some detail, the theory of heat conduction and the theory of linear elastic media. The resulting equations derived in this manner differ quantitatively and qualitatively from those usually presented.
