Further remarks on Euclidean objectivity and the principle of material frame-indifference

摘要

Murdoch [1] claimed that purely objective considerations imply the restrictions imposed upon response functions by the principle of invariance under superposed rigid body motions. In response to the criticism raised by Liu [2], Murdoch failed to recognize the mathematical implication of the condition of objectivity, as pointed out by Liu, that if a response function for an observer is given, the corresponding one for any other observer can be defined uniquely. Consequently his criticism against Lius counter-example, based on the assumption of observer agreement concerning response functions of different observers, cannot be taken as a valid argument. Furthermore, regarding "objective considerations" as playing the central role in continuum physics, besides our disagreement, especially on the assumption that it is possible to contemplate arbitrary relative motions between two given observers, it is impractical, because, it cannot be stated unambiguously in mathematical terms, and some physical intuitions need to be purposely conceived for occasional cases. Therefore, it runs against the rational spirit deeply cherished in Modern Continuum Mechanics.