More Minkowski for Free
Here's a nice relativistic analysis of an experiment, building on the framework in the last blog (at http://weblogs.asp.net/brianbec), calculations courtesy of Geometry Expressions once again. Think of laser ranging to the moon. The astronauts left mirrors on the moon, and every day pulses are shot at the mirrors, which are actually corner reflectors, so the pulses bounce straight back. The moon is about 1.5 light-seconds away, so the round trips take about 3 seconds. The moon is moving about 2300 miles per hour, which is about 3e-6 times the speed of light, so the pulses are lengthened by (at most) microseconds, which is very easy to measure with modern equipment, so relativity is spectacularly verified every day in experiments like this.
As before, the blue axes are our non-moving lab frame, and the red axes are a frame of reference moving at velocity v in the x direction. The pulse begins at event A and ends at event J in our blue frame. The red (moon) frame sees the pulse beginning at event Q and ending at event B. The line CB is a line of constant position -- say, the position of the mirror -- in the red moon frame. When we get the pulse back on Earth, it has been stretch to duration RK. This is relativistic Doppler shifting of light.
Here's a slightly prettier picture.