Studies on the Motion of Viscous Flows— II 



treating force as primitive and thereby not imposing arbitrary restrictions on 

 what is not understood of it. The interpretation given in the present paper to 

 force as it appears in the propositions of classical mechanics is not presented 

 in Newton's writings, but rather is inferred here from its usage and the way the 

 symbol F is formally treated in his propositions. Froni_the above considera- 

 tions it follows that the global connection designated by F and called force, has 

 the same stature in classical mechanics, as does inertia interpreted according 

 to Mach's principle, according to which inertia is also a manifestation of a 

 global connection between a body and the universe —a connection which however 

 is characterized by a scalar, and is therefore intrinsically endowed with high 

 uniformity. 



What is strictly local in Newton's propositions is the kinematical content on 

 which their dynamical aspect is based. It is this dynamical and local aspect 

 which restricts their covariance to inertial frames and consequently limits their 

 generality. From this it also follows that it is naive to interpret Newton's law 

 of motion as a definition of force, as it is nonsense to define a fundamental as- 

 pect of nature that has unrestricted covariance, in terms of an aspect whose co- 

 variance is limited to inertial frames. We see here again, from this point of 

 view, that force does in fact dominate the laws of classical mechanics. 



These considerations show that in classical mechanics, the presence of a 

 resultant force impressed by the universe on an inertial body which is conse- 

 quently not free, implies a nonsymmetrical and thus nonuniform connection be- 

 tween the body and the universe. When the connection between an inertial body 

 and the universe is symmetrical and thus uniform —in the particular sense that 

 individually impressed forces cancel vectorially —the body is then said to be 

 free according to the established laws of classical mechanics and consequently 

 moves according to Galileo's principle. We shall show in the section titled 

 'Hierarchies of Uniformity' that there in fact exists a hierarchy of free bodies, 

 i.e., bodies which can with meaning be distinguished as being more or less free, 

 but all of which are equivalent and therefore not distinguishable by the estab- 

 lished laws of classical mechanics. 



These and other considerations concerning the nature of force made within 

 the framework of classical mechanics are sufficient to demonstrate that all 

 forces in nature may be conceived of as manifestations of the existence in 

 nature's space-time manifold of nonuniform connections between inertial bodies 

 and the universe. According to this thinking, forces that are revealed in the 

 domain of classical mechanics emerge from the same ultimate and universal 

 processes in nature as do all other forces. Force, thus conceived as the uni- 

 versal manifestation of nonuniformity in the space -time manifold posited to 

 sense-perception and to inertial bodies embedded in this manifold, brings into 

 universal correspondence the various domains of physical theory which we have 

 by convention learned to distinguish as classical and modern. These ideas and 

 considerations are particularly designed to point out the fundamental connection 

 between nonuniformity in nature and in force, and to establish the thesis that 

 force is the universal manifestation of these nonuniformities invoked in sensa- 

 tion and experience. 



463 



