Unsolved Problem in Classical Mechanics

Abstract

The critical analysis of the foundations of classical mechanics is proposed.Methodological basis of the analysis is the unity of formal logic and rationaldialectics. The main results of the analysis of concepts “force”, “work” and “work offorce” are the following statements: (1) the standard concept “work of force”contradicts to dialectics (practice) and formal logic because the concept “force” is ageneral abstract concept. The concept “force of interaction of material objects” is ageneral concrete concept because this concept expresses the property (feature, sign,quality) of the interaction of material objects. But the property does not perform thework because the property is not a material object. Work is performed by acontrollable (operated) material object. Consequently, the standard mathematicaldefinition of work is an incorrect relationship; (2) the concept “force of interaction ofmaterial objects” can only be defined in a genetic way: one should measure the forceof interaction with the help of a dynamometer. The dynamometer reading representsthe value of the measured quantity (force). If the measured quantity (force) is avariable quantity, then a change of this quantity (force) is called the movement ofthis quantity (force). But if the force is a constant quantity, then the movement of theforce does not exist. Consequently, the standard mathematical definition of work isan incorrect relationship; (3) the position of the force in the coordinate system cannotbe determined because a force is not a material object, and the quantity of the forcedoes not have the dimension (measure) “meter”. This signifies that: (a) a force doesnot exist in the material coordinate system; (b) a force does not exist on the materialpath; the path length (distance) for force does not exist. Consequently, force cannotmove over a distance that has the dimension “meter”. This signifies that thestandard mathematical definition of work is an incorrect relationship; (4) in point ofview of dialectics; work and energy are nonidentity concepts. Work is the activity ofman, a robot, a controllable machine created by man. Work represents a rational,reasonable, well-directed, purposeful, purposive activity which manifested in theinformational and material change of reality. This activity is the impossible ifintellectual, informational, energy, and material resources do not exist. Thus, thestandard mathematical definition of the work of force is a formal-logical, dialectical(practical), and physical errors