Suppose you've just established the existence of time dilation using Einstein's 1905 postulates and the light clock. Is there any nice, easy way to go on and prove length contraction? Here are a couple of incorrect arguments that I've been guilty of using in the past: Symmetry: The Lorentz transformation treats time and space the same, so we must have length contraction by the same gamma factor. Wrong because the analogy ruler:distance::clock:time is wrong -- a clock's world-line is a line, a ruler's a strip. Also wrong because taking v<1 (c=1) introduces an asymmetry (interchange of x and t makes v>1). We can also tell it's wrong because the resulting effects should be in opposite directions (moving clock reads too low, contracted ruler measures things to be to big) and don't behave the same in terms of permanence. Constancy of c: Under a Lorentz transformation, we must have [itex]c=x/t\rightarrow (\gamma x)/(\gamma t)[/itex] so that c stays the same. Wrong because [itex]\gamma[/itex]'s interpretation as length contraction and time dilation refers to a rest frame, which doesn't exist for light; the actual factor of interest for something moving at c is the Doppler shift factor. The Feynman Lectures have an argument in 15-5 based on the null result of the Michelson-Morley experiment. I'm sure this is fine logically, but the presentation is IMO not very good and overly abbreviated, and I think a full presentation of this argument would be rather long and complex. I think people like the light clock because it's a quick wham-bam demonstration of time dilation that works well for students with minimal math, and it doesn't require the full development of the Lorentz transformation. It seems unfortunate to have to follow that with a more complicated argument in which the full machinery of the LT is required. Is there some other approach that is both correct and simple?