We derive the addition of velocities in special relativity from the Minkowski’s space-time diagram. We only need to draw some world lines on the diagram, measure the lengths and divide the two lengths for obtaining t...We derive the addition of velocities in special relativity from the Minkowski’s space-time diagram. We only need to draw some world lines on the diagram, measure the lengths and divide the two lengths for obtaining the velocity. We also give the theoretical background for this method. This method is so simple that it is worth for undergraduate students to acquire the addition of velocities in special relativity.展开更多
In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyp...In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyperbolic space, which are the analogues of the geometric construction of inversions with respect to a circle on the complex plane. These results are then applied to Lorentz transformation and Einstein velocity addition to obtain geometric illustrations. We gain new insights into the relationship between special relativity and hyperbolic geometry.展开更多
文摘We derive the addition of velocities in special relativity from the Minkowski’s space-time diagram. We only need to draw some world lines on the diagram, measure the lengths and divide the two lengths for obtaining the velocity. We also give the theoretical background for this method. This method is so simple that it is worth for undergraduate students to acquire the addition of velocities in special relativity.
文摘In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyperbolic space, which are the analogues of the geometric construction of inversions with respect to a circle on the complex plane. These results are then applied to Lorentz transformation and Einstein velocity addition to obtain geometric illustrations. We gain new insights into the relationship between special relativity and hyperbolic geometry.
