If a visible laser on the earth is shone on the moon and the beam is moved along the
surface, could the beam spot on the moon be made to travel faster than the speed of
Yes, the spot could move from point A on the surface of the moon to point B on the surface of the moon faster than a photon emitted at point A could get to point B.
'But I thought nothing could move faster than the speed of light!' Yes, that would be the rational objection, but let's think about what's actually moving here. Specifically, relativity prohibits particles and information from traveling faster than the speed of light. What is actually moving faster than light in this case? The point where a laser beam is striking the moon.
First, it's fairly simple to see that there aren't any particles traveling faster than the speed of light, just an instance of an event - a point under consideration, if you will. The moon isn't doing the moving, and the photons coming from the earth are moving exactly at the speed of light, but in a completely different direction than the motion of the point. So nothing physical is moving here, what is moving is a small set of coordinates on the moon which we are 'considering' by hitting it with a laser.
So now as long as we can't use this point to send information from point A to point B, we aren't violating relativity in any way (and while being very interesting to think about, it becomes a slightly less 'cool' situation). An astronaut sitting at point A can't affect the point of light without sending a message to the Earth, which would take considerably longer than just sending a message to point B with say a flashlight. And since neither astronaut can affect this superluminal point of light, it seems to me the best that they can do is to use it as a coordination signal, no different than if they both had a watch. They could both agree to do something when they saw the light, but they wouldn't be able to get any information about what had actually happened at the other point unless one of them could affect the signal in some way, which (as noted) would take longer than sending a message between them at the speed of light.
This type of problem has actually been considered before, and usually goes by the name 'superluminal scissors,' i.e. a pair of really really long (no, longer than that) scissors, so long that as you closed them the point where the two blades touched would move out towards the end of the scissors faster than the speed of light.
Oh, and what would it look like? I imagine it would just look like a little point of light moving really really fast. Actually, although there aren't any laws of physics that _prohibit_ you from seeing this spot, it would probably be there and gone so fast that there wouldn't be enough photons reflected off its path for your eye to register.
Gregory Ogin, Physics Undergraduate Student, UST, St. Paul, MN
A spot of light can appear to travel at any speed. The Special Theory of Relativity sets c (the speed of light in a vacuum) as the speed limit for any physical object or packet of energy.
Your example does not violate Relativity principles because any single photon does not exceed c. Imagine throwing tennis balls along a wall, with each ball hitting some distance to the right of the previous one. The apparent path of each hit against the wall moves at a rate that depends only on the distance between them and how frequently the balls are thrown. The speed of the balls is not important. The 'beam spot' example just replaces tennis balls with photons.
Paul Walorski, B.A., Part-time Physics Instructor
'There is no inductive method which could lead to the fundamental concepts of physics. Failure to understand this fact constituted the basic philosophical error of so many investigators of the nineteenth century.'