Перетворення Лоренца в освіті учнів фізико-математичного профілю навчання

Abstract

Запропоновано елементарне виведення перетворень Лоренца. Метод може бути використаний при вивченні елементів спеціальної теорії відносності і розгляді її найпростіших наслідків в старших класах профільної середньої школи, гуртковій роботі та на факультативних заняттях з фізики. In the context of improving the content of natural and mathematical education, more attention is paid in the educational literature to the study of the fundamental principles of natural science, among which the principles of relativity occupy a leading place in the development of the modern worldview of the young man, which causes the development of new didactic and methodological requirements for textbooks and manuals. Thus, the textbook on physics, as an element of the system of physical education, constantly feels the stimulating effect of fundamental principles. The most important of them, the principle of relativity, prescribes the invariance of all the laws of physics in the transition from one inertial frame of reference to another, which is formally, in the language of mathematics, understood as the invariance of all the equations of physics with respect to Lorentz transformations and is the basic paradigm of relativistic physics. Thus, the available derivation of Lorentz transformations and the simple presentation of the main corollaries that follow from them is one of the attributes of the modern educational standard for students of physics, and the possession of this material is the main sign of the student's physical competence. An in-depth study of the section "Relativistic mechanics" in the modern school is carried out in the popular textbooks T. Zasekina, M. Golovko and T. Zasekina, D. Zasekin, and also in the textbook, ed. A. Pinsky, O. Kabardin. However, the Lorentz transformation is given in its final form and is not used to derive the kinematic consequences of SRT. In the well-known manual G. Myakishev, B. Bukhovtsev, V. Charugin, the study of SRT generally does without Lorentz transformations. At present, Lorentz transformations are absent in the curricula of the "standard" level and the academic level for the 10-11 grades of general education schools. They appear only in the curriculum of the profile level. This raises the question of how to apply Lorentz transformations in this case. The complete derivation of Lorentz transformations is contained in modern textbooks for high schools on theoretical physics and electrodynamics, which is built on the basis of the symmetry properties of space and time. Approaches contained in physics courses for higher technical and pedagogical institutions A. Detlaf, B. Yavorsky and I. I. Kucheruk, І. Gorbachuk, P. Lutsik, too, can not be called elementary. The problems of the method of in-depth study of the kinematic consequences of relativistic mechanics in high school are thoroughly examined in the article by V. Buryak, O. Konoval. However, even here, the authors circumvent the issues of the derivation of the Lorentz transformations. The purpose of this article is to give an elementary derivation of the Lorentz transformations, which corresponds to the physical and mathematical level of knowledge of students in the upper grades of the profile level of education and has a meaningful content at such a level. The proposed conclusion is accessible and is expedient for use in other forms of studying the special theory of relativity - in particular, in particular, in elective groups and circle work in physics. The method is based on the idea of correcting the standard Galilean transformation by some additional corrective transformation. The form of this transformation is found by means of simple operations of elementary algebra using the requirement of the constancy of the speed of light. The desired transformation is constructed as a sequence of two transformations: the Galileo transformations and the required corrective transformation, which eventually lead to the Lorentz transformation.