Relativity on Rotated Graph Paper

Abstract

We present visual calculations in special relativity using spacetime diagrams drawn on graph paper that has been rotated by 45 degrees. The rotated lines represent lightlike directions in Minkowski spacetime, and the boxes in the grid (called "light-clock diamonds") represent units of measurement modeled on the ticks of an inertial observer's lightclock. We show that many quantitative results can be read off a spacetime diagram by counting boxes, using a minimal amount of algebra. We use the Doppler Effect, in the spirit of the Bondi k-calculus, to motivate the method.