CONSTRUCTION OF A MODEL OF AN ELECTROMAGNETIC FIELD FROM THE STANDPOINT OF RATIONAL MECHANICS
Zhilin P. A.
Saint Petersburg State Polytechnical University, http://www.spbstu.ru/
195251 St.Petersburg, Russian Federation
Represented by a Academician of RANS V.I. Erofeev 08.04.2013
Mechanics before Newton had been remaining by a collection of many important, but separated facts. Newton was the first, who set up a problem of construction of mechanics, as a science of the first principles. As the first principles Newton pointed out the three Laws of Motion, but he did not consider them as a sufficient base for full construction of mechanics. The Newton idea about construction of mechanics on the base of the first principles had played a huge stimulating role. Euler carried out the realization of this program. During period between 1732 and 1755 Euler has developed the concept, which now is accepted as Newtonian mechanics. In this concept the translation of mechanics on the language of differential equations was main, what had been made by Euler. The stage of the construction of Newtonian mechanics in the fundamental plan was finished by the memoir of Euler “Discovery of a new principle of mechanics”, published in 1752. In that time Euler was considering, that the principle, opened by him, may be accepted as a unique base of mechanics and other sciences, which treat about movement of any bodies. Unfortunately, this point of view dominated in science down to 1925, when it finally had failed, and Newtonian mechanics had lost the status of fundamental science, for Newtonian mechanics was not able to describe the important physical phenomena. Probably, for the first time this problem had arisen in the investigations of J. Maxwell, when he tried to describe true, i.e. not induced, magnetism, but it was not possible. Finally, this period was finished by the creation of quantum mechanics. For example, it is impossible to explain the Plank formula E=ħν from the point of view of Newtonian mechanics — the mechanical meaning of this formula will be shown in the report body. Between that, in 1771 L.Euler not only clearly had realized an incompleteness of Newtonian mechanics, but also had indicated the path of its extension. In Newtonian mechanics there is only one form of movement, namely translation movement that is describing the displacement of a body-point in space. However, so-called spinor movements play the main role in many natural processes in microworld. In such a movement the body-point does not change the position in space, but has own rotation. The spinor movements are the main way of accumulation and preservation of energy in the Nature. Not surprised therefore, that Newtonian mechanics has appeared powerless at the level of the microworld, where the spinor movements in essence cannot be ignored. In 1776 Euler had published memoir “New method of determination of movement of solids”, where two independent Laws of Dynamics are stated for the first time: the equation of balance of momentum and equation of balance of kinetic moment (or moment of momentum in accepted, but unsuccessful, terms). This work opens new era in mechanics. Under an appropriate development of ideas of this work modern physics would look completely differently then it looks now. Unfortunately, the recognition of ideas by Euler has taken place only at the last quarter of XX century. At the end of XVIII century only J. Lagrange had realized significance of Euler’s work, but he had not agreed with its main conclusions. In essence problem was reduced to a possibility or impossibility of the proof of the Archimedes law of the lever. Lagrange, as opposed to Euler, considered that the lever law is a corollary of the Newton laws. A large part of extensive introduction to the treatise “Analytical mechanics” Lagrange devotes to the proof of the law of the lever. Obviously, the Lagrange proof contains an important error, which was not trivial for that time. The Lagrange method of description of mechanics has made a great impression on scientific community. The stable, but faulty, point of view had established that Lagrange mechanics is quite able to replace by itself Newtonian mechanics. Actually mechanics of Lagrange is a rather poor subclass of Newtonian mechanics and it can not be considered as self-sufficient science about natural phenomena. It follows, for example, from the fact that the fundamental concepts like space, time, forces, moments, energy and etc., are not discussed and can not be introduced into consideration in Lagrange mechanics, where all these concepts are used, but are not determined. Unfortunately, many theorists with a mathematical kind of thinking obviously underestimate importance and complexity of originating here problems. Besides, mechanics of Lagrange is not suitable for the description of open systems, what all real systems are. All said is quite valid with respect to mechanics of Hamilton that has mathematical merits, but is very poor from a physical point of view. The Lagrange-Hamilton mechanics is the beautiful clothes for small part of mechanics, but not more. Namely inapprehension of this fact has allowed to M. Plank to say the following words: “Today we must recognize that... frameworks of classical dynamics (that means mechanics of Hamilton in its primitive form, P. Zh.)... have appeared too narrow to envelop all those physical phenomena that do not lend to direct observation by our rough organs of sense... The proof of this conclusion is given to us by the crying contradiction, that come to light in the universal laws of heat radiation, between the classical theory and experience.” This point of view had become conventional in physics. Mechanics had avoided from a discussion of these hard questions and continued researches on the important applied problems. The situation existing in a mechanics and physics within the last century can be called paradoxical. On the one hand, there are actual phenomena, which can not be described within the framework of Newtonian mechanics from the point of view of the first principles. On the other hand, nobody has shown an inaccuracy of these principles. From this it follows, that the principles of Newtonian mechanics are necessary, but not sufficient, for the full description of the known experimental facts. This means, that Newtonian mechanics should be extended by adding of new principles. Namely this way was pointed out by Euler. In fact, we need more general mechanics then Eulerian mechanics. The statement of these new principles should emanate from intuitive understanding of a nature of those phenomena, which can not be described by methods of Newtonian mechanics. Certainly, this very complex problem can not be solved by simple means and requires special researches. If the mechanics does not realize necessity of the indicated researches and will limit by the analysis traditional (let even very important) problems, then its future has not any perspectives. If someone doubts of this, he should pay attention to the quick vanishing of mechanics in the educational and research programs now. If we do not want mechanics to be out of the problems of modern physics, then we, at least, have to understand the electrical and magnetic phenomena from the point of view of the principles of mechanics. But how to achieve to this purpose? The answer on this question is the main aim of given report. The analysis of the known facts has shown, that the spinor movements, absent in Newtonian mechanics, are necessary for a description of the electromagnetic phenomena. More over, the full description of electromagnetism could not be executed in the frameworks of Eulerian mechanics. For this it is necessary to develop so called mechanics of multi-spin particles. In the report we want to show that the construction of mechanics of multi-spin particles is the main direction of the development of mechanics in XXI century.
: continuum mechanics, Cosserat continuum, multi-spin particle, electrodynamics, Maxwell’s equations
PACS: 41.20.-q, 46.05.+b, 46.25.Cc, 46.90.+s, 61.30.-v
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