"Is it not possible to present quantum mechanics as a self-sufficient discipline, without first learning the incorrect principles of classical mechanics only to throw them away again after sharpening our mathematical tools in solving exercises? As prerequisite to thermodynamics we do not set a course in caloric theory, simply because it served as a "springboard" for energetics or because problems of heat conduction illustrate techniques of manipulation. The answer to this question is simple: Like any physical theory, classical mechanics predicts correctly only a certain range of observable phenomena, but this range is so enormous, so far greater than that describable by any other branch of physics, that any person who wishes to understand the world about him must learn classical mechanicsfor its own sake. The writers on quantum mechanics recognize this fact when they invariably derive the classical equations as an approximation. There are eminent physicists who believe that quantum mechanics may require certain ultimate revisions; that Newtonian mechanics must again be somehow included, is unquestioned. Goldstein expresses his contempt for macroscopic phenomena {e.g., page 15), butit is only macroscopic phenomena that classical mechanics adequately describes.

Macroscopic phenomena do indeed occur in nature, and their inherent interest to physicists is recognized by the existence of member societies of the Institute and divisions of the Physical Society whose field is wholly or partially classical. The fault in the older treatments of mechanics lies not in their failure to be similar enough to quantum mechanics, but in their being too similar to it—they begin (as does the author) with the Newtonian laws for a mass-point, literally a mathematical point occupying no volume at all, while in fact modern physics has taught us that the classical laws become a poorer and poorer approximation to observed phenomena the smaller is the body. Since classical mechanics yields a correct description of the motions only of rather large bodies, its basic concepts and equations should therefore be put in terms of large bodies, so that the more nearly the physical body approximates the mathematical concept the more accurately the mathematical equation describes its behavior. Theconceptof mass-point may be altogether abandoned. The familiar mass-pointequations, nonetheless, are satisfied by the centers of mass of large bodies, and the classical mass-point structure thus reappears as an approximation valid when the motions of large bodies relative to their centers of mass are negligible."

# о преподавании механики

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