Let us assume that B is illuminated 0.1 s after A. When the light emitted
from A and B reaches C, C says "A is illuminated first, and B is illuminated
0.1 s after A."
In this experiment, we assume the velocity of light emitted from B to be
600,000 km/s, which is twice the speed of light. Hence, the light emitted
from B reaches C before the light from A does, and hence, according to
C "B is illuminated before A."
If there exists something that can travel faster than the speed of light, which is 300,000 Km/s, the cause-effect relationship will not hold good.
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