## Failure of the Galilean Transformation

Anyone carrying a light source would emit light that traveled faster in their direction of travel, and slower to a stationary observer behind the.

Repeated experiments showed however, that the speed of light was a fixed number

\[c=299792458\]

m/s, whatever speed of source and observer. Light, and in fact all electromagnetic radiation did not obey the Galilean transformation.In addition there was the puzzling form of the Lorentz Force

\[\mathbf{F}=q \mathbf{E}+q \mathbf{v} \times \mathbf{B}\]

.The Lorentz law implied a force that depended on speed. Because the speed changes under the Galilean Transformation, so should the force, then using

\[\mathbf{F}=m \mathbf{a}\]

, so should the acceleration. This directly contradicts the Galilean transformation, which implies forces and accelerations are unchanged by the Galilean Transformation.