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 this inquiry constitute the basis of a proposal that relies on a Minkowskian geometrical formulation for teaching special relativity in upper secondary education.
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…
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
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…
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.
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.
While Newtonian gravity is an adequate model for current geophysical exploration, Einsteinian gravity, based on the connection between free fall and warped time, has superseded Newtonian gravity as our best understanding of the universe. Einsteinian gravity is fundamental to GPS navigation and is a useful tool for geodesy. The Einstein-First Project is pioneering new curriculum material that seeks to teach students, from ages 11 upwards, the Einsteinian paradigm for gravity. By developing models, analogies and classroom activity based learning, we have found that students are fascinated and ea…
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…
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…
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…
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…
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…
Real Time Relativity is a computer program that lets students fly at relativistic speeds though a simulated world populated with planets, clocks, and buildings. The counterintuitive and spectacular optical effects of relativity are prominent, while systematic exploration of the simulation allows the user to discover relativistic effects such as length contraction and the relativity of simultaneity. We report on the physics and technology underpinning the simulation, and our experience using it for teaching special relativity to first year university students.
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…
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 …
Distance education has expanded significantly over the last decade, but the natural sciences have lagged in the implementation of this instructional mode. The abrupt onset of the COVID-19 pandemic left educational institutions scrambling to adapt curricula to distance modalities. With projected effects lasting through the 2020--21 academic year, this problem will not go away soon. Analysis of the literature has elucidated the costs and benefits of, as well as obstacles to, the implementation of e-learning, with a focus on undergraduate physics education. Physics faculty report that a lack of t…
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…
Captain Einstein is a virtual reality (VR) movie that takes you on a boat trip in a world with a slow speed of light. This allows for a direct experience of the theory of special relativity, much in the same spirit as in the Mr. Tompkins adventure by George Gamow (1939). In this paper we go through the different relativistic effects (e.g. length contraction, time dilation, Doppler shift, light aberration) that show up during the boat trip and we explain how these effects were implemented in the 360 video production process. We also provide exercise questions that can be used - in combination w…
The importance of a teaching a clear definition of the ``observer'' in special relativity is highlighted using a simple astrophysical example from the exciting current research area of ``Gamma-Ray Burst'' astrophysics. The example shows that a source moving relativistically toward a single observer at rest exhibits a time ``contraction'' rather than a ``dilation'' because the light travel time between the source and observer decreases with time. Astrophysical applications of special relativity complement idealized examples with real applications and very effectively exemplify the role of a fin…
This work gives a brief summary of major formulations of the third law of thermodynamics and their implications, including the impossibility of perpetual motion of the third kind. The last sections of this work review more advanced applications of the third law to systems with negative temperatures and negative heat capacities. The relevance of the third law to protecting the arrow of time in general relativity is also discussed. Additional information, which may useful in analysis of the third law, is given in the Appendices. This short review is written to assist lecturers in selecting a str…
Barriers to women's education and employment in Europe and the U.S. in the nineteenth century made it unlikely that any women would be among the few physicists whose ideas are taught in high school and college courses. This paper explores the social settings in which three influential physicists worked--James Clerk Maxwell, Robert Millikan, and Albert Einstein--to better understand the limited opportunities available to women. By acknowledging and explaining why there weren't more women among these founding physicists, instructors may help students understand the barriers that still exist and …
