Studies on the Motion of Viscous Flows — II 



II— Aspects of the Principle of 



Maximum Uniformity: A New and 



Fundamental Principle of Mechanics 



'■■ ■ ' Paul Lieber . 



- . ' University of California 



Berkeley, California 



INTRODUCTION v :;■:. v ■ ^ a r 



A comparative study of the principles of classical mechanics has revealed 

 that they are only conditionally equivalent, and that questions concerning their 

 equivalence and completeness cannot be put with meaning, without naturally 

 evoking a new concept pertaining to the existence in nature of categories of in- 

 formation (1). The emergence of this concept in this study, shows that the 

 equivalence or nonequivalence of the principles of mechanics, considered as 

 propositions about the world of mechanical experience, should be decided ac- 

 cording to the nature of the information which they do and can render explicit 

 about it. 



The observations and conclusions noted above, were developed by focusing 

 attention on the principles of Newton, Gauss, and Hertz. In so doing, it was 

 demonstrated that general and fundamental global information on the distribution 

 of internal forces in many -body systems, which is rendered explicit and without 

 integration by using the principles of Gauss and Hertz, at present appears inac- 

 cessible in terms of the principles of Newton (2). This information is obtained 

 within the edifice of the principles of Gauss (3) and Hertz (4), by reintroducing 

 and underlining therein the concept force, which they sought to eliminate as a 

 primitive notion, by its geometrization in terms of geometrical constraints. 

 This was done for a nontrivial class of mechanical systems which included the 

 gas model used by Maxwell, by first establishing and then using a fundamental 

 connection between nonholonomic, unilateral, geometrical constraints and the 

 impenetrability of matter (Refs. 5 through 11). In so doing it was found that the 

 primitive role ascribed by Newton to the concept force is linked with the primi- 

 tive concept of the impenetrability of matter, conceived here as the physical 

 basis for the geometrization of force in terms of the geometrical constraints as 

 used by Gauss and Hertz. That is, the ultimate ontological, geometrical prop- 

 erty by which matter evokes its being and thus its existence in space -time, is 

 local impenetrability, and it is this property of matter and evidently only this 

 property which can account for the existence in nature of stringent geometrical 

 constraints. Impenetrability of matter is accordingly envisaged here as an 



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