Final answer:
The Galilean law for the addition of velocities cannot be true because it would allow different observers to see light traveling at different speeds, violating the constancy of the speed of light proven by Maxwell's equations and the theory of special relativity.
Step-by-step explanation:
The Galilean law for the addition of velocities is incompatible with the constancy of the speed of light because it predicts that velocities add together as simple vectors, which can lead to a resulting speed greater than the speed of light, c. However, this contradicts the principles of special relativity and Maxwell's equations, which assert that the speed of light in a vacuum is a constant c, regardless of the motion of the source or observer. If Galilean velocity addition were correct, then observers moving at different speeds would observe light at speeds other than c, which is not supported by experimental evidence. Instead, the theory of relativistic velocity addition developed by Einstein corrects this by ensuring that the speed of light remains constant at c in all inertial frames of reference.
For example, if we imagine a car moving at night and emitting light from its headlights, classical velocity addition would suggest that the light approaches an observer on the sidewalk at a speed of u = v + c. But in reality, whether from the perspective of the driver or an observer on the sidewalk, light always moves at the constant speed c, thus maintaining the principle of constancy of the speed of light in all reference frames.