While the relativity of Galileo makes sense in our everyday world, certain developments in physics were beginning to raise questions. We have seen earlier that Maxwell's theory of electricity and magnetism ran into problems surrounding the realities of the photoelectric effect and blackbody radiation. But, it was still one of the most accurate theories in physics existing at the start of the 20th century, so its predictions had to be examined carefully.

One of the things Maxwell predicted about the nature of light is that its speed has the same constant value in empty space for all inertial observers. (This speed is usually indicated as c.) Galilean relativity does not agree with this. To understand the difference, let's look at the spacetime diagrams of a light pulse (called a light cone) from the perspective of two inertial observers.

Our stationary observer sees a light cone, and the worldline of the moving observer as:

where the light pulse (yellow lines) travels with the same speed to both left and right, while the moving observer (red line) travels to the left at a speed less than that of light.

Using the Galilean transformations, the moving observer's spacetime diagram of the same events would look like:

According to this observer, our first observer is moving to the right (at a speed equal to that reported for this observer by the first), and the light cone is not symmetrical. This observer would report different speeds for light traveling to the left as compared to the right, or between what light has arrived (past) and what is going out (future) for the same side!

Something is wrong about this! Clearly, the speed of light is not a constant for all inertial observers in Galileo's spacetime.

Einstein, who we know differed with Maxwell's theory in regard to the photoelectric effect, now had to choose between Maxwell electrodynamics and Newton/Galileo mechanics with regard to fundamental principles. He chose to maintain Galileo's principle of relativity without the idea of absolute time. Instead, he proposed that the speed of light must be uniform and the same for all inertial observers. The result of his change is his theory of special relativity. No physical experiment (mechanical, electromagnetic, optical---or any physical law whatsoever) can distinguish between a state of "absolute" rest and a state of constant velocity.