# Special Relativity - Twisted contradiction?

#### dseppala

Can anyone explain how relativity works in the following scenario?

There are two inertial reference frames, the rest frame F0 and the moving frame F1. They have a velocity V along the x-axis. In the rest frame F0 there is a long cylinder of length L along the x-axis. Let's call the top of the cylinder zero degrees and the bottom of the cylinder 180 degrees. There is a red line that starts at one end of the cylinder at the zero degrees position. That red line follows a spiral path in a clockwise direction (like on an old time barbershop pole), spiraling N times around the cylinder ending at the other end of the cylinder at the zero degree position of the cylinder. On this same cylinder there is a blue line that starts at the same zero degree position as the red line and spirals around the cylinder N times ending at the zero degree position at the other end, but this blue line spirals in the counter-clockwise direction.

Now the rest frame and the moving frame measure that at any distance x or x' from the end of the cylinder if the red line is at angle alpha then the blue line is at 360 degrees - alpha. So for example if the red line at x = X meters from the end of the cylinder is at 10 degrees, the blue line is at 350 degrees. This is true at any and every point along the length of the cylinder.

Now we let the moving frame simultaneously start rotating all points of this cylinder that is at rest in the rest frame at some constant rpm along the longitudinal axis of the cylinder, with the rotation rate and starting time at every point on the cylinder being identical. The rotation direction is perpendicular to the x-axis. From the rest frame's point of view, per Einstein's theory, one end of the cylinder started rotating before the other end started rotating as measured in the rest frame. This causes the red spiral in this scenario to increase the number of times it spirals around the cylinder and the blue spiral to decrease the number of times it spirals around the cylinder (or vice versa depending on the direction of rotation).

So if the moving frame or the rest frame look at the angle of the red line at x = X meters from the end of the cylinder when the red line is at 10 degrees, the moving frame discovers that the angle of the blue line at x = X meters is no longer at 350 degrees as it was before the moving frame simultaneously started all points of the cylinder rotating in the identical fashion. So the moving frame must conclude that all points of the cylinder did not start rotating at the same time and speed, even though the moving frame started the rotation of every point of the cylinder simultaneously and in an identical manner with identical speed.

How do the moving frame observers explain why all points of the cylinder started rotating simultaneously and in an identical fashion, but the red and blue lines did not rotate in the identical fashion?

Thanks,
David Seppala
Bastrop TX

#### dseppala

There is no contradiction. I tried to simplify an analogous problem that involved more physics than math and in doing so I screwed up this problem that is posted here.
David Seppala
Bastrop TX