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Why do Galilean transformations fail to preserve the constant speed of light?

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Brian Greene sits in a living room, holding a pen, with handwritten equations m = E/c^2 and E = mc^2 on a whiteboard beside him, highlighting c^2 as the speed of light. — relativity Brian Greene kicking off his *Your Daily Equation* video series with Albert Einstein's famous equation E = mc².

Galilean transformations fail to preserve the constant speed of light because they are based on the assumption that space and time are absolute and independent of the observer's motion. Under these classical transformations, if an object moves at velocity $v$ relative to one frame, its velocity in another frame moving at velocity $u$ is simply additive, implying that the speed of light would necessarily change depending on the observer's inertial frame.123

This contradicts the fundamental principle of electromagnetism established by James Clerk Maxwell, which dictates that the speed of light is constant in empty space. Experimental evidence, such as the Michelson-Morley experiment, confirmed that the velocity of light does not change with the observer's motion.32

To resolve this, Albert Einstein rejected the Galilean assumption of absolute time and replaced it with Lorentz transformations. These transformations account for the relativity of simultaneity and ensure that the laws of physics—and the speed of light—remain invariant across all inertial frames of reference.23