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?(adsbygoogle = window.adsbygoogle || []).push({});

This question goes along with a program that I'm writing that you can find at http://www.people.cornell.edu/pages/mm473/" [Broken] 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Length under Acceleration

**Physics Forums | Science Articles, Homework Help, Discussion**