This is another one of those questions along the lines of “if you’re driving at the speed of light, and you turn on the headlights…”
Let’s say, hypothetically, an object is flying between a source of light (sun?) and, say, the earth… and that object is flying at 3/4 the speed of light… and it’s closer to the sun than to the earth…
What happens to its shadow? Is it moving at more than the speed of light? I know it’s basically the same idea as that scissors post I saw earlier, but I just wanted some opinions…
Glenoled
I think you may need to specify… it’s shadow as cast by which light source? The sun? Something else? (Sounds stupid on my part, but consider all the cases)
the shadow from the sun, cast upon the earth.
the shadow would be sent forward at the speed of light, and would seem the same to all observing the shadow’s motion (this assumes there is some way of observing the shadow, such as a series of walls made from all-but-a-fraction transparent paper) and would be apperently moving, to the shadow-caster, at slightly under one fourth of the speed of light, slowing down marginally as the shadow streaked away (due to response time limitations; when the shadow is ten seconds away, it is going to take 7.5 seconds for you to realize where it is).
{that was a long sentence!}
If you’re asking if a shadow can travel across the surface of the Earth at faster than the speed of light, then yeah. So, this is different than the scissors paradox, in which the answer is no. The shadow thing doesn’t violate Relativity or anything like that.
Another way that it’s proposed is to look at it like this. Suppose you’re in the center of a circular room that’s two light-seconds in circumference and you shine a light on one wall. You spin the light source around once a second. The light on the wall is then moving at twice the speed of light, even though your flashlight or laser or whatever is moving relatively slowly, and the walls aren’t moving at all.
But nothing can travel faster than light, right? Well, the spot of light on the wall isn’t really a thing, because the photons that make it up one instant are not the same photons that make it up the next instant.
In the same way, a shadow is not a thing. This is going to sound really dumb, but the photons that do not make up a shadow at one instant are not the same photons that do not make it up the next instant, so nothing is really moving faster than light in your example.
Another question… if an object is moving at the speed of light, directly away from a light source, does it cast a shadow on itself? 
Glenoled
