TO THE METHOD OF STUDYING THE BASICS OF SPECIAL THEORY OF RELATIVITY

Y. Krasnobokyi, Ihor Tkachenko, Kateryna Ilnitska
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Abstract

Special Theory of Relativity (STR) is a fundamental physical theory that underlies modern physics andhas enormous worldview potential. At the same time, in the process of teaching (studying) the elementsof STR in school and higher education institutions face a number of problems. These problems areprimarily related to the complex mathematical apparatus that describes it; consideration of imaginarymodel representations that do not really exist in nature; formation of the concept of “event” anddistinguishing under different initial conditions of the concepts of “relative”, “portable” and“absolute” movements, etc. In this regard, it is important to find ways to improve the methodology ofstudying the elements of STR, which is what this article is about.The article offers one of the tested options for studying the main provisions of the special theory ofrelativity in the general course of physics, which is taught in the programs of physical andmathematical specialties of pedagogical universities. The main approaches on which the proposedmethodology is based are the reference to the principle of conformity in the transformation of physicaltheories from their partial cases to more general ones. In this regard, the limits of application ofclassical Galilean-Newton mechanics in the plane of absolutization by this theory of categories of spaceand time, the simultaneity of events in a different frame of reference, the instantaneous transmission ofinteractions between bodies at a distance, etc. are analyzed.The physical meaning of Einstein’s postulates, which underlie the theory of relativity, regarding thespecial status of the speed of light propagation as a natural phenomenon is clarified. On the basis ofthese postulates, the formulas of the Lorentz coordinate and time transformations are deduced. Aconsistent, detailed derivation of the formula for the transition coefficient from the Galilean coordinateand time transformations (for the transition from one inertial frame of reference to another) to theLorentz coordinate and time transformations, which reflects their relativistic content, is given. Theestablishment of these formulas is based on the mathematical apparatus, which corresponds to the levelof school mathematical training of participants in the educational process. Based on the obtainedresults on the formulas of Lorentz transformations, the relativity of the concepts of “duration ofevents”, “time intervals”, “changes in size and shape of bodies”, etc. is demonstrated mathematically,if they are considered in reference systems that are in motion relative to each other. Keywords: classical mechanics; reference system; the principle of relativity; space-time invariant;coordinate and time conversion.
研究狭义相对论基础的方法
狭义相对论(STR)是现代物理学的基础物理理论,具有巨大的世界观潜力。与此同时,中小学和高等院校在教学(学习)过程中也面临着诸多问题。这些问题主要与描述它的复杂数学装置有关;考虑在自然界中并不真正存在的假想模型表示;“事件”概念的形成以及在不同初始条件下对“相对”、“可移动”、“绝对”运动等概念的区分。在这方面,重要的是要找到方法来改进研究STR要素的方法,这也是本文的内容。本文为高等师范院校物理、数学专业物理普通课程中关于狭义相对论主要内容的研究提供了一种测试选项。所提出的方法论所依据的主要途径是在将物理理论从局部情况转变为更一般的情况时参考一致性原则。在此基础上,分析了经典伽利略-牛顿力学在时空范畴绝对化平面、不同参照系中事件的同时性、远距离物体间相互作用的瞬时传递等方面应用的局限性。爱因斯坦的假设的物理意义,作为相对论的基础,关于光速传播作为一种自然现象的特殊地位被澄清。在这些假设的基础上,推导了洛伦兹坐标变换和时间变换的公式。给出了从伽利略坐标和时间变换(从一个惯性参照系到另一个惯性参照系的转换)到洛伦兹坐标和时间变换的过渡系数公式的一致的、详细的推导,反映了它们的相对论性内容。这些公式的建立是建立在数学仪器的基础上的,这与教育过程中参与者的学校数学训练水平相对应。从洛伦兹变换公式得到的结果出发,用数学方法证明了“事件持续时间”、“时间间隔”、“物体大小和形状的变化”等概念在相互相对运动的参照系中的相对性。关键词:经典力学;参考系统;相对性原理;时空不变;坐标和时间转换。
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