Special relativity as a simple geometry problem

Canadian Journal of Physics, 2004

A century after its formulation by Einstein, it is time to incorporate special relativity early in the physics curriculum. The approach advocated here employs a simple algebraic extension of vector formalism that generates Minkowski spacetime, displays covariant symmetries, and enables calculations of boosts and spatial rotations without matrices or tensors. The approach is part of a comprehensive geometric algebra with applications in many areas of physics, but only an intuitive subset is needed at the introductory level. The approach and some of its extensions are given here and illustrated with insights into the geometry of spacetime. PACS Nos.: 03.30.+p, 01.40.Gm, 03.50.De, 02.10.Hh

Aimed at both physics students and non-science majors, this unique book explains Einstein's Special Theory of Relativity pictorially, using diagrams rather than equations. The diagrams guide the reader, step-by-step, from the basics of relativity to advanced topics including the addition of velocities, Lorentz contraction, time dilation, twin paradox, Doppler shift, and Einstein's famous equation E = mc 2 . The distinctive figures throughout the book enable the reader to visualize the theory in a way that cannot be fully conveyed through equations alone.

American Journal of Educational Research, 2014

In this paper a pedagogical, but rigorous introduction to the key concepts of relativity is presented. Starting by the notions of space and time, of fundamental importance for the evolution for the global knowledge of children already in the primary school, we arrive to indications about the teaching of relativity in high school and university. Interesting considerations related to fascinating topics, like the evolution of the concept of space-time and the unusual amazing peculiarities emerging by the extensions of relativity, will be done.

2011

Keywords: neo-Lorentzian interpretation relativity simultaneity didactic teaching education Kennedy Thorndike Trouton Noble experiment

The wide availability of information has led to the fact that students are well aware of the difficulties of existing physical theories. In this article we analyze some logical paradoxes of the special relativity theory (SRT), concerning the time dilation and length contraction. The Lorentz transformations and the relativistic law for velocity addition are considered in detail. The notion of relativity and the transverse Doppler effect are discussed. The whole complex of numerous paradoxes in the special theory of relativity worries us by further complications.

The mathematical treatment and graphical representation of Special Relativity (SR) are well established, yet carry deep implications that remain hard to visualize. This paper presents a new graphical interpretation of the geometry of SR that may, by complementing the standard works, aid the understanding of SR and its fundamental principles in a more intuitive way. From the axiom that the velocity of light remains constant to any inertial observer, the geodesic is presented as a line of constant angle on the complex plane across a set of diverging reference frames. The resultant curve is a logarithmic spiral, and this view of the geodesic is extended to illustrate the relativistic Doppler effect, time dilation, length contraction, the twin paradox, and relativistic radar distance in an original way, whilst retaining the essential mathematical relationships of SR. Using a computer-generated graphical representation of photon trajectories allows a visual comparison between the relativistic relationships and their classical counterparts, to visualize the consequences of SR as velocities become relativistic. The model may readily be extended to other situations, and may be found useful in presenting a fresh understanding of SR through geometric visualization.

International Journal of Physics and Chemistry Education

In this work, we present a possible didactic sequence for the study of basic aspects of special relativity in high school. The sequence re-signifies the role of classical kinematics and Galileo´s relativity principle. It has been implemented in four courses of two secondary schools in Argentina in 2014-2015 and in Colombia in 2016, with students aged 15-16, during 20 school hours, being the teacher a member of our research team.

Five topics: A rigid body does not exist in the special theory of relativity; distant simultaneity defined with respect to a given frame of reference without any reference to synchronized clocks; challenges on Einstein's connection of synchronization and contraction; a theory of relativity without light, composition of relative velocities and space of relative velocities

2018

In this stroll about the Special Relativity Theory, I analyze Einstein’s insights about the actual meaning of his Relativity Theory. This analysis clarifies us about the way that the Special Relativity Theory should be understood, and help us to see if one really needs to be a genius for fully understanding it. It is found that the Special Relativity Theory is consisting of two independent concepts, of which the basics are unveiled and put in the right context of physics. The experiments that are claimed to prove the Special Relativity Theory are scrutinized in the context of the findings.

2007

This paper has pedagogical motivation. It is not uncommon that students have great difficulty in accepting the new concepts of standard special relativity, since these seem contrary to common sense. Experience shows that geometrical or graphically exposition of the basic ideas of relativity theory improves student's understanding of the algebraic expressions of the theory. What we suggest here may complement standard textbook approaches. * The exact speed of light, in vacuum, is 2.99792458 x 10 8 km/s.