Possible exceptions to light's speed limit
People have come up with theoretical and actual examples where things might seem like they have moved faster than light. Often these are called paradoxes. Here is some examples. For more examples and more detailed explanations go here.
Third observer point of view
Imagine standing on earth. A jet moves .6c away from you to your left, and another moves away from you .6c to your right. It seems the relative speed compared to each other must be 1.2c which is impossible.
The Answer: Velocities cannot be added the way that you could in a Newtonian universe instead you must use a relativistic equation for adding velocities found here. This give a speed of .88c as the relative velocity between the two jets.
The Universe's largest pair of Scissors
Sometimes called the superluminal scissors, imagine a pair of scissors with blades one light year long. Now imagine closing them quickly. It seems since the scissors are rigid that the ends (which is miles apart) closes just as fast as the handle, thus going faster than the speed of light.
The Answer: Relativity tells us that no objects are truly inflexible. Thus the act of closing the handle starts a wave that moves down the material of the scissors blades, however this wave moves much slower than the speed of light. See superluminal scissors.
Shadows, and Light Spots
Imagine projecting a shadow of your hand on a wall far away from a lamp that is close by. If you move your hand quickly your shadow can move faster than the speed of light depending on the distance from the light source to the wall. Another hypothetical, imagine shining a laser beam on one edge of the moon from earth. Then quickly shine the laser beam to the other side. The dot of light moves from one side of the moon to the other at a speed much quicker than the speed of light.
The Answer: These things are not physical objects. They have no mass and no substance. Think of the laser for instance as a machine gun sending out a spray of light bullets. Each of these light bullets obey the speed of light, they were just shot in different directions. The area of impact then is not moving faster than the speed of light, each area is a new impact altogether.
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