So folks have already explained the stick, but you’re actually somewhat close to one of the ways you can sort of bend the rules of FTL, at least when it comes to a group of photons.

Instead of a stick, imagine a laser on earth pointed at one edge of the moon. Now suddenly shift the laser to the other side of the moon. What happens to the laser point on the moon’s surface?

Well, it still takes light speed (1.3 seconds to the moon) for the movement to take effect, but once it starts, the “point” will “travel” to the other side faster than light. It’s not the same photons; and if you could trace the path of the laser, you’d find that the photons space out so much that there are gaps like a dotted line; but if you had a set of sensors on each side of the moon set up to detect the laser, they would find that the time between the first and second sensor detecting the beam would be faster than what light speed would typically allow.

It’s not exactly practical, and it’s such an edge case that I doubt we can find a good way to use it, but yeah; FTL through arc lengths can kind of be a thing. At least if you tilt your head and squint funny at it.

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Can’t wait for all the pictures of these events with half a dozen people standing around looking lost.