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The Relativity on Rotated Graph Paper Model displays Minkowski spacetime diagrams on rotated graph paper. The worldlines of three inertial observers carrying horizontal light clocks and the resulting clock ticks are drawn. Each clock consists of two mirrors a constant distance d away from an observer. The world lines of the clock's light rays form causal diamonds that can be used to count the clock ticks for each observer. A second window shows the causal diamonds in a second (other) reference frame.
The causal diamond construction (described in detail by Salgado) exploits the following geometrical facts: (1) a rectangle in the grid (with its lightlike sides) has an area proportional to the square-interval8 of its timelike-diagonal, and (2) a Lorentz boost transforms a rectangle in the grid into another rectangle in the grid with a different shape but equal area. These geometrical facts encode properties of the invariant hyperbolas of Minkowski spacetime.
The Relativity on Rotated Graph Paper Model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_sr_RelativityOnRotatedGraphPaper.jar file will run the program if Java is installed. You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.
Last Modified October 2, 2013
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The source code zip archive contains an EJS-XML representation of the Relativity on Rotated Graph Paper Model. Unzip this archive in your EJS workspace to compile and run this model using EJS.
Last Modified November 12, 2011