Originally Posted by

**xyzt**
Originally Posted by

**SpeedFreek**
is not the angle between the rods, it is the angle between a rod and the axis of motion in the rest frame of the rod. Length contraction does not care what the angle of the other rod is, it is only concerned with the angle relative to the axis of motion.

You don't get it, do you? The transformation

holds for

**any** angle , between

**any** two

**arbitrary** directions. I have

shown this early in the thread. The wiki link is just a particular case of my general proof.

I have been contacted by a member here who doesn't post in the forum any more, but who has read through this thread and he has confirmed to me that my diagrams with the blue and red rods are in fact correct for my gedank. This is a variation of the "meter stick and the hole" paradox, and the principle does apply to your OP, just as I thought.

Your rod hits the floor of the train at an angle, as viewed from the embankment, just as Janus said.

The member who contacted me is the author of a website that hosts a java applet that can illustrate all this.

You can find the java applet here (I have tested it and it is safe (on my system at least!) but it is quite large and takes a while to load)

Newtonian and Relativistic Simulations
Or you can just read through the tutorial for the app here -

http://www.relativitysimulation.com/...ckAndHole.html which illustrates the meter stick and the hole paradox and shows how the angles are different from each frame of reference.

The only difference between the "meter stick and the hole" paradox and your gedank is that in yours there is no hole. And if you don't believe the author of that website, google for the meter stick and the hole paradox to find other equivalent treatments.

__The meter stick and the hole__

We have a meter stick aligned with the x-axis, moving at 0.866c. We have a panel moving in the y-axis, sitting perpendicular to the y-axis, with a hole in it that is just larger than half a meter. Because the panel is perpendicular to its axis of motion, there is no contraction in the length of the hole. From the frame of the panel, the meter stick is parallel, but approaching at an angle. When they intersect, the meter stick passes through the hole because, in the frame of the panel, the meter stick is length contracted to half its rest length.

But what happens from the view of the meter stick? In its own frame it is a meter long, and we know the hole in the panel is only just over half a meter long in its rest frame. The answer is that they

**don't** meet parallel. From the frame of the meter stick, the panel makes an angle, allowing the meter long stick to pass through the hole.