Dumitru N. Vulcanov, Gabriela Ciobanu
We present some Maple procedures using the GrTensorII package for teaching purposes in the study of the canonical version of the general relativity based on the ADM formalism
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The article presents some aspects on the use of computer in teaching general relativity for undergraduate students with some experience in computer manipulation. The article presents some simple algebraic programming (in REDUCE+EXCALC package) procedures for obtaining and the study of some exact solutions of the Einstein equations in order to convince a dedicated student in general relativity about the utility of a computer algebra system.
GRTensorJ - Books is an active interface to a small part of the computer algebra systems GRTensorII (for Maple) and GRTensorM (for Mathematica) with the specific intent of providing students of General Relativity with an advanced programmable calculator-style tool. All standard functions associated with a classical tensor approach to the subject are available thus reducing these to "elementary functions". This is not a traditional database. The database entries are spacetimes and calculations are done in real time. All spacetimes are referenced directly by equation number in ten current (and c…
This work analyzes the difficulties in learning and teaching Einstein's theory of special relativity. An extensive bibliographic review has been performed, considering articles published in the most relevant journals on science education, which were selected taking into account the following impact factors: JCR, SJR, IN-RECS and ICDS. The typical thinking of students and teachers is discussed pointing out that, occasionally, it does not befit the proper scientific perspective. Different educational proposals are examined and particular didactic implications are inferred. The conclusions of thi…
The Einstein-First project aims to change the paradigm of school science teaching through the introduction of modern Einsteinian concepts of space and time, gravity and quanta at an early age. These concepts are rarely taught to school students despite their central importance to modern science and technology. The key to implementing the Einstein-First curriculum is the development of appropriate models and analogies. This paper is the first part of a three-paper series. It presents the conceptual foundation of our approach, based on simple physical models and analogies, followed by a detailed…
This paper presents some ideas which might assist teachers incorporating special relativity into an introductory physics curriculum. One can define the proper-time/velocity pair, as well as the coordinate-time/velocity pair, of a traveler using only distances measured with respect to a single ``map'' frame. When this is done, the relativistic equations for momentum, energy, constant acceleration, and force take on forms strikingly similar to their Newtonian counterparts. Thus high-school and college students not ready for Lorentz transforms may solve relativistic versions of any single-frame N…
Teaching the general theory of relativity to high school or undergraduate students must be based on an approach that is conceptual rather than mathematical. In this paper we present such an approach that requires no more than elementary mathematics. The central idea of this introduction to general relativity is the use of so-called sector models. Sector models describe curved spaces the Regge calculus way by subdivision into blocks with euclidean geometry. This procedure is similar to the approximation of a curved surface by flat triangles. We outline a workshop for high school and undergradua…
The AstroCamp is an academic excellence program in the field of astronomy and physics for students in the last 3 years of pre-university education, which often includes a course (or a significant part thereof) on Relativity. After an introduction to the principles, goals and structure of the camp, I describe the approach followed by camp lecturers (myself and others) for teaching Special and General Relativity, and some lessons learned and feedback from the students. I also provide some thoughts on the differences between the physics and mathematics secondary school curricula in Portugal and i…
Sector models are tools that make it possible to teach the basic principles of the general theory of relativity without going beyond elementary mathematics. This contribution shows how sector models can be used to determine geodesics. We outline a workshop for high school and undergraduate students that addresses gravitational light deflection by means of the construction of geodesics on sector models. Geodesics close to a black hole are used by way of example. The contribution also describes a simplified calculation of sector models that students can carry out on their own. The accuracy of th…
Sector models permit a model-based approach to the general theory of relativity. The approach has its focus on the geometric concepts and uses no more than elementary mathematics. This contribution shows how to construct the paths of light and free particles on a spacetime sector model. Radial paths close to a black hole are used by way of example. We outline two workshops on gravitational redshift and on vertical free fall, respectively, that we teach for undergraduate students. The contribution also describes a simplified calculation of the spacetime sector model that students can carry out …
V-SeMo: a digital learning environment for teaching general relativity with sector models
本文介绍了数字学习环境 V-SeMo，它将扇形模型引入交互式 Web 应用，让学习者通过构造测地线和评估曲率探索相对论时空，并在中学生评估中证明了其高学习有效性。
Teaching special relativity in elementary physics or upper high school courses
本文面向基础物理与高中高年级教学，利用零持续时间闪光交换的思想实验推导狭义相对论运动学效应，并结合模拟、实验证据及能量动量守恒解释多普勒效应。
This review presents an overview and analysis of the body of research on special relativity theory (SRT) education at the secondary and lower undergraduate level. There is currently a growing international interest in implementing SRT in pre-university education as an introduction to modern physics. For this reason, insights into learning opportunities and challenges in SRT education are needed. The field of research in SRT education is still at an early stage, especially at the level of secondary education, and there is a shortage of empirical evaluation of learning outcomes. In order to guid…
Special relativity is no longer a new revolutionary theory but a firmly established cornerstone of modern physics. The teaching of special relativity, however, still follows its presentation as it unfolded historically, trying to convince the audience of this teaching that Newtonian physics is natural but incorrect and special relativity is its paradoxical but correct amendment. I argue in this article in favor of logical instead of historical trend in teaching of relativity and that special relativity is neither paradoxical nor correct (in the absolute sense of the nineteenth century) but the…
We present an investigation of game-like simulations for physics teaching. We report on the effectiveness of the interactive simulation "Real Time Relativity" for learning special relativity. We argue that the simulation not only enhances traditional learning, but also enables new types of learning that challenge the traditional curriculum. The lessons drawn from this work are being applied to the development of a simulation for enhancing the learning of quantum mechanics.
Visualizations that adopt a first-person point of view allow observation and, in the case of interactive simulations, experimentation with relativistic scenes. This paper gives examples of three types of first-person visualizations: watching objects that move at nearly the speed of light, being a high-speed observer looking at a static environment and having a look-around near a compact object. I illustrate and explain the main aspects of the visual observations, outline their use in teaching relativity and report on teaching experiences. For teaching purposes, our visualization work is availa…
Cosmology and general relativity (GR) in upper secondary school through new targeted teaching materials: a study on student learning and motivation
本研究针对高中难以开展广义相对论与宇宙学教学的问题，开发了结合概念理解、适配高中数学的主动学习课程教材，经前后测验证能显著提升非专业高中生的学习效果与动机，证明该教学整合可行。
We discuss pedagogical problems associated with the conventional approach in teaching relativity and the potential value of "Lorentzian route to relativity" for addressing these pedagogical problems. We think that Lorentzian approach may be valuable part of an introduction to relativity but the historical route should be followed up to its end. It must namely include Einstein's application of Occam's razor in reinterpreting Lorentz transformations kinematically and the discussion of the central role of the evolution from Lorentz's "local time" to relativity of simultaneity. We discuss also wha…
This review presents an overview of various kinds of models -- physical, abstract, mathematical, visual -- that can be used to present the concepts and applications of Einstein's general theory of relativity at the level of undergraduate and even high-school teaching. After a general introduction dealing with various kinds of models and their properties, specific areas of general relativity are addressed: the elastic sheet model and other models for the fundamental geometric properties of gravity, models for black holes including the river model, cosmological models for an expanding universe, …
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