Starting with something small:
I’m in a circular room 100 feet across. I’m standing at the center with a laser, shining it on the wall 50 feet (more or less) away.
I spin around 360° in one second. My hand-held laser has traveled maybe five or six feet, as it whirls around with me (I’m holding it some small distance from my body).
The spot on the wall would seem to have traveled 314 or so feet in that same second, as it moves across the wall.
Is that accurate? If so, then, how about this:
Let’s say, I’m in a big, big room circular (apparently the walls and floor are made of unobtainium).
It’s big: 372,000 miles across.
I’m at the center and also have a really good laser that I’m pointing at the wall. It’s so good that it makes a spot on the wall 186,000 miles away.
Ok, holding the laser, I turn around really quickly in this room, 360° in one second. At first glance, it would appear that the spot would then travel around the wall (over 1M miles) in less than one second. An illusion of moving faster than the speed of light. But I don’t think that’s what would happen, would it? Would the spot’s motion max out at the speed of light?
I’m thinking that if we were looking at it from far above, there would be about a 1 second delay (as the walls are 186K miles away) before the change in position of the laser was indicated on the wall. That is, the spot cannot change instantaneously with respect to the laser source, right?
But once it does start moving, how fast does it move? Would it actually travel around across the 1M mile perimeter in about one second? I know that nothing is actually “moving” past the speed of light, that the spot is not anything physical, only a reflection of light that still has to obey the laws of physics, but it seems as though there is some ‘gotcha ya’ that I’m missing?