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| Is Objectivity Really an ObjectiveConcept? |
| Nicolas Van Goethem |
| (Universidade de Lisboa, Faculdade de Ci?encias, Departamento de Matem′atica,
CMAFcIO, Alameda da Universidade, C6, 1749-016 Lisboa, Portugal) |
| DOI： |
| Abstract: |
| Objectivity is the name given to covariance with respect to changes
in observers by the action of the Euclidean group and is a central concept for
mathematical modelling in Physics and Continuum mechanics. However, this
notion is delicate and therefore hard to understand by both mechanicians and
mathematicians, precisely because it resides at the junction of the two disciplines and hence appeals to knowledge and notions from both fields to become
clear. In a first part (”behind objectivity”) some classical notions of objectivity
and frame-dependence are presented, discussed and critically revisited with the
purpose to introduce in a second part (”beyond objectivity”) a novel modelling
approach in incompatible elasticity, based on intrinsic and geometric concepts,
related but distinct from conventional objectivity. This contribution is primarily
conceived to assist students, academics and researchers, mathematicians in particular, to find their way through some difficult and often ill-understood concepts
of Physics and Continuum mechanics, since objectivity still remains nowadays
a profound concept that deserves our attention. |
| Key words: Frame indifference, objectivity, elasticity, incompatibility. |