Nature of some Conceptual Problems in Geometry and in the Particle Dynamics
The particle dynamics conception (mathematical formalism) changes rather rare in the process of the particle dynamics development. It connected with associative delusions in the existing dynamics conception and with the logical reloading which is a means of the associative delusion overcoming. Influence of associative delusions (AD) onto development of physics and mathematics is investigated. The associative delusion (AD) means a mistake, appearing from incorrect associations, when a property of one object is attributed to another one. Examples of most ancient delusions are: (1) connection of the gravitation field direction with a preferred direction in space (instead of the direction to the Earth center), that had lead to the antipode paradox, (2) statement that the Earth (not the Sun) is a center of the planetary system, that had lead to the Ptolemaic doctrine. Now these ADs have been overcame. In the paper one considers four modern and not yet got over ADs, whose corollaries are false space-time geometry in the microcosm and most of problems and difficulties of the quantum field theory (QFT). One shows that ADs have a series of interesting properties: (1) ADs appear to be long-living delusions, because they are compensated partly by means of introduction of compensating (Ptolemaic) conceptions, (2) ADs influence on scientific investigations, generating a special pragmatic style (P-style) of investigations resembling the experimental trial and error method, (3) ADs act on investigations directly and via P-style, ADs direct the science development into a blind alley. One considers concrete properties of modern ADs and the methods of their over coming. From viewpoint of application the paper is an analysis of mistakes, made in the quantum theory development. One analyses reasons of these mistakes and suggests methods of their correction.
