What is the speed of the minute hand on a clock?

Actually, relativity comes in here and says that the force the atoms of the hand exert on the atoms farther out cannot propagate faster than a certain rate. This really long minute hand would bend as it tried to accelerate the tip. The hand in your wristwatch also bends, but imperceptably so.

On the other hand, if it were a laser rotating, the spot would move faster than the speed of light across a target placed farther than that distance away. This is because the image of the spot cannot carry any information from one side of the target to the other.

Hang on a second, Mathochist: the spot “moves”, but from one second to the next, the spot is made up of different photons. Each photon in the laser’s beam is moving at the speed of light in a purely radial direction; the rotation (at non-relativistic speeds) of the laser doesn’t impart any circumferential momentum to them.

If you imagine a stationary laser firing a continuous stream of protons (imagine it as a PVC pipe with a long string of ping-pong balls, firing at a giant circular wall lined with bathroom scales, which will be our photon detectors). As you start rotating the dispenser, the ping-pong balls (photons!) that have already left the aperture are not going to rotate with it – they’re going to continue on in their path and hit the scale they were first aimed at. The beam will curve, and maybe even spiral (not sure on this!) so that your “spot” is not longer a spot. Eventually your ping-pong balls get so spread out that they will start “skipping” scales, or so that not enough of them hit each scale to make a detectable difference.

It seems I didn’t explain myself clearly. Yes, if you imagine a laser as a “photon gun” (which is really not quite the case, but close enough for hand waving), and imagine identifying “the” photons released from the laser as they travel outwards, that will trace a curve in space. What I was getting at is that there is no acceleration bending like there is in a solid minute-hand.

Imagine a hemispherical bowl one light-hour in radius (this is about three times as long as the critical distance mentioned before) centered on the laser’s pivot. The laser will turn through the half-circle in 30 seconds. An hour after the experiment starts, the first photon “fired” by the laser will hit one edge of the bowl, followed by the others until 30 seconds later the last photon hits the opposite edge of the bowl. The spot has travelled pi light-hours in 30 seconds, but has not violated causality because there is no information the spot can move around. If one were to try this with a solid rod, the tip would never move faster than the speed of light.