First, forget the term light speed. Light is just one of the many things that travels at this speed. The term is the speed of causality or the fastest any information can move though space.
As you move faster through space, you move slower through time. At the speed of light, you don’t experience time at all. To something moving at light speed, it arrives at its destination instantly. You cannot move faster than instantly. It is only to the viewer that it seems to move at a slower rate of time. A stationary viewer sees it as 300k km per second because you experience a different second. At the speed of causality, there is no movement through time and so you cannot go faster.
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