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Ни о какой безапелляционности в моих высказываниях не может быть и речи! [entries|archive|friends|userinfo]
Anatoly Vorobey

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о преподавании механики [сент. 4, 2014|02:38 pm]
Anatoly Vorobey
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Американский физик и математик Клиффорд Трусделл (Clifford Truesdell) написал отрицательную рецензию на знаменитый учебник Голдстейна "Классическая механика", когда он впервые вышел в свет в 1950 году. Трусделлу не понравилось, что Голдстейн подходит к классической механике снова и снова как бы желая побыстрее разделаться с ней и перейти к квантовой механике. Вот длинная цитата, которая мне показалась интересной:

"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 mechanics for 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), but it 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. The concept of mass-point may be altogether abandoned. The familiar mass-point equations, 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."
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Comments:
From: inhm
2014-09-04 12:13 pm
"Трусделлу не понравилось, что Голдстейн подходит к классической механике снова и снова как бы желая побыстрее разделаться с ней и перейти к квантовой механике."

как это понимать - вроде "подходить снова и снова" и "побыстрее разделаться" - противоположные вещи.

(с научным английским не дружу, потому цитату осилить не смог)
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[User Picture]From: avva
2014-09-04 12:20 pm
Голдстейн написал учебник классической механики, не квантовой. Трусделл пишет, что учебник создает такое впечатление, что классическая механика - это что-то такое в целом неинтересное, что нужно изучить и побыстрее отбросить в сторону и перейти к квантовой механике; но раз уж нужно изучить, то в процессе изучения следует все излагать, пользуясь подходами, терминологией, ипроч. ипроч. которые потом пригодятся в квантовой механике. И даже вопрос о том, что излагать, а что опустить (учебник не может говорить обо всем на свете) следует решать исходя из того, что потом полезно для квантовой механики, а не что полезно для лучшего понимания классической механики.

Все это Трусделлу не нравится и он это ругает. Так примерно.
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[User Picture]From: mtsyr
2014-09-04 01:22 pm
А где можно почитать рецензию целиком? Из приведенных отрывков совершенно непонятно, что же конкретно предлагается изучать для лучшего понимания классической механики, а что опустить, о каких "подходах, терминологии и проч. проч." идет речь и т. п.
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[User Picture]From: avva
2014-09-04 01:41 pm
Вот полный текст. Рецензия опубликована в его книге "An idiot fugitive's essays on science", сборнике эссе, рецензий и исторических статей разных лет.

GOLDSTEIN'S CLASSICAL MECHANICS
(1950)

This book is intended as an advanced text on classical mechanics for the student whose sole desire is to learn quantum mechanics. The author defends teaching mechanics to a physicist despite the fact that "it introduces no new physical concepts ... nor does it aid him ... in solving the practical mechanics problems he encounters in the laboratory." He states that "classical mechanics remains an indispensable part of the physicist's education" because it "serves as the springboard for the various branches of modern physics" and "affords the student an opportunity to master many of the mathematical techniques necessary for quantum mechanics. ..." After reading this preamble we are not surprised to learn that Goldstein finds "the traditional treatment... no longer adequate" and that at the same time the basic concepts of mechanics "will not be analyzed critically...." His treatment of what is ordinarily called mechanics is little else than formal manipulation; his frequent remarks concerning physics almost invariably fall outside the classical framework and deal with the behavior of small particles. He observes that in some special cases classical principles remain valid even today, and he quotes as illustrations the neutron pile and the V-2 rocket. There are frequent promises of better things to come when the student reaches quantum mechanics.

The following subjects are treated: vectorial mechanics of a system of mass-points, Lagrange's equations and Hamilton's principle, the two-body central force problem, the motion of rigid bodies, special relativity, transformation theory, Hamilton-Jacobi theory, small oscillations, the LAGRANGEan and HAMiLTONian formulations for continuous systems. The book differs from the traditional treatment not only in attitude but also in detail. First, numerous topics are omitted, an example being the entire theory of orbits and their stability. Second, the following unusual topics (many of them to be found as incidental or introductory material in books on quantum mechanics) are included: frequent examples of the motion of particles subject to electromagnetic forces, scattering in a central force field, vibrations of a triatomic molecule. Goldstein states that "mathematical techniques usually associated with quantum mechanics have been introduced wherever they result in increased elegance and compactness." An example may be found in his treatment of rigid bodies, where in order to introduce linear transformations, matrices, spinors, eigenvalues, dyadics, and tensors in rapid succession he uses sixty-four pages to reach "the so-called Euler equations" by surely the longest derivation in the literature. After all this preparation there are only nineteen pages on the actual motion of a rigid body, containing mostly material found in intermediate texts. Goldstein makes a point of introducing at length the Cayley-Klein parameters but does not ever employ them.

[cont'd]
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[User Picture]From: avva
2014-09-04 01:41 pm
[cont'd]

The mathematical level of the book may be judged from the fact that Goldstein avoids elliptic functions, claiming that "such a treatment is not very illuminating". The explanations of some elementary mathematical topics are clear, as for example in the unusually straightforward statement of the formal problem of the calculus of variations and in the discussion of nonholonomic constraints. At the ends of the chapters are problems, largely concerned with applications to modern physics. "Pedantic museum pieces have been studiously avoided." Goldstein also fills pages with candid evaluations of his competitors. Of Whittaker's Analytical Dynamics he says "the development is marred, regrettably, by an apparent dislike of diagrams .. . and of vector notation, and by a fondness for the type of pedantic mechanics problems made famous by the Cambridge Tripos examinations." The Theorie des Kreisels, he says "... has all the external appearances of the typical stolid and turgid German 'Handbuch'. Appearances are deceiving, however, for it is remarkably readable, despite the handicap of being written in the German language."

As far as style is concerned, Goldstein himself inhabits a glass rather than an ivory tower; infinitives are split and participles suspended as if by rule, and were it not for Goldstein's repeated disparagement ofGerman we should suspect Teutonic influence in his exclamation points, his isolation of lonely words by commas, his use of "so-called" in the attribution of names, and his hyphenated word-marriages.

In reading this book I have learnt how to solve some problems I failed to find in the classical works which Goldstein banishes to pedantic museums, but his apologetic attitude toward his subject at every page raised the question, why study classical mechanics at all? The rise of modern particle physics has certainly necessitated a
revision of our concepts. 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?

[дальше идет цитата из записи и заканчивается потом так]

This truly physical approach to the subject was presented long ago by Hamel and is summarized in his article on the axioms of mechanics in the (perhaps stolid, German, and turgid) Handbuch der Physik.

I can heartily agree with Goldstein in wishing a more modern and more physical treatment of mechanics, but I cannot help regretting that his refusal to re-examine the fundamental concepts of his subject prevented him from giving us a confident and substantial book.
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[User Picture]From: mtsyr
2014-09-04 03:43 pm
Спасибо, интересно, хотя понял я не намного больше. После чтения некоторых его текстов складывается впечатление, что Трусдейл а) считает, что механику надо выводить из аксиом сплошной среды; б) крайне фрустрирован ролью теории сплошной среды в современной ему физике, особенно по сравнению с квантовой механикой, ядерной физикой и т. д.
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[User Picture]From: buddha239
2014-09-04 04:22 pm
Интересно, у физиков эллиптические функции - то же, что и у математиков?:)
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From: inhm
2014-09-04 04:34 pm
Понятно. Ну, тогда я на стороне Трусделла, ибо, насколько я могу судить, во-первых, квантовая механика не созрела до законченной полноценной науки (вместо ответов на "почему?", большей частью дает ответы на "как?"), а во-вторых, в изложении дисциплины по дедукции всегда есть вероятность того, что какой-то важный содержательный момент был упущен в угоду формализму.
В этом плане мне всегда не нравилось изложение механики в варианте Ландау-Лившица, когда вместо законов Ньютона и проч, сразу все начиналось плясать от принципа наименьшего действия. Вроде все получается просто, но в то же время теряется физическая интуиция.
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From: migmit
2014-09-04 09:04 pm
Физика никогда не даёт ответа на вопрос "почему?". Она всегда говорит лишь о "как?".
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From: inhm
2014-09-05 11:06 am
Ну что за глупости. Яблоко падает на землю ПОТОМУ ЧТО между телами существует взаимное притяжение. А КАК оно падает - это описание процесса: v = g t, z = z0 - g t^2/2

Edited at 2014-09-05 11:07 (UTC)
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(Удалённый комментарий)
From: dmpogo
2014-09-04 05:10 pm
Бээ ..
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[User Picture]From: avva
2014-09-04 06:09 pm
Что?
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From: dmpogo
2014-09-04 06:10 pm
Да дурные аргументы, совсем не интересные
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[User Picture]From: gruimed
2014-09-05 05:48 am
Если мне ничего не изменяет, мы учились по этому текстбуку и он никому не нравился - в библиотеке первым делом расхватывали Ландау, а Голдстейна брали опоздавшие.
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