Objectivity in classical continuum physics: A rationale for discarding the 'principle of invariance under superposed rigid body motions' in favour of purely objective considerations

Abstract

Individual aspects of observer consensus are discussed in the context of classical continuum physics. These are shown to be sufficient to mandate standard restrictions upon response functions employed in constitutive relations by any given observer. No a priori assumption is made that observers should employ the same response functions, and restrictions are shown to involve only proper orthogonal tensors. Since the 'principle of material invariance under superposed rigid motions' (interpreted in the sense of 'one observer, two motions') is not needed to establish such restrictions, and imposes a requirement upon Nature that kinetic theory has shown to be questionable, this 'principle' serves no useful purpose and should be discarded.