Imagine a pen or something of proper length L. In 2D (1 space, 1 time), if the pen is osciallating so that, to an observer at rest at x=0, the left end traces out x(t)=Sin(.7t), what will the right end look like? This question goes along with a program that I'm writing that you can find at http://www.people.cornell.edu/pages/mm473/ in Applet form. My first thought was to just apply the length contraction forumla (L/gamma) across the function so the right end would be x_right(t)=x(t)+L*Sqrt(1-x'(t)^2). This is the function you can see on the right. It can't be right because, for one, it goes faster than light at points. If you right-click on the Sine function and click Traverse, the program will animate what it would look like going along the worldline of the left end of the "pen". I expected the right end of the pen to be a constant length away as viewed from this frame, and you can see as it is traversed a constant length is traced out. This however doubles back on itself (impossible). This I now realise is not true because the pen is not an inertial frame. So the length changes as viewed from an outside stationary observer, and from the non-intertial frame of the pen, but still... what does it look like?