On criticism of the nature of objectivity in classical continuum physics

Murdoch (J. Elasticity 60, 233-242, 2000) showed that restrictions imposed upon response functions by material frame-indifference are the consequences of five distinct aspects of observer agreement (that is, of objectivity) and involve only proper orthogonal tensors. Accordingly it is unnecessary to invoke the principle of invariance under superposed rigid motions (in the sense of one observer, two motions), which imposes a restriction upon nature. Liu (Continuum Mech. Thermodyn. 16, 177-183, 2003, and Continuum Mech. Thermodyn. 17, 125-133, 2005) has challenged, misinterpreted and misrepresented the content of both Murdochs work and this work. Here all criticisms of Liu are answered, his counter-examples are used to amplify the tenets of Murdochs work, and a key modelling issue in the controversy is indicated. Further, the response function restrictions for a given observer, derived on the basis of considering other observers, are shown to be independent of possible differences in the scales of mass, length, and time employed by other observers.