Deficiencies of Newtonian Mechanics

Relativistic Quantum Chemistry. Markus Reiher and Alexander Wolf 

However, it has been verified in numerous experiments that all observers in all inertial frames, independently of their state of motion, will always measure the same speed of light, 

The first high-precision experiment of this kind was performed by Michelson and Morley in 1887 using their famous interferometer for velocities n w 30 km/s. This experiment has been repeated again and again by Michelson and Miller between 1902 and 1904 with much higher accuracy but the very same result the speed of light is constant in all inertial frames of reference. 

Another formal deficiency of Newtonian mechanics and therefore of the Galilei transformations is the existence of Maxwell s equations (2.94)-(2.97), which contain the speed of light c as a parameter. Maxwell s equations directly yield the wave equation (2.121), which states that the propagation of electromagnetic fields in vacuum occurs with speed c. Either Maxwell s equations are not valid in all inertial frames of reference or the Galilei transformations cannot be the correct coordinate transformations between inertial frames. Experimentally one finds that the Maxwell equations are valid for any inertial system. 

There is an overwhelming plethora of further experimental evidence that proves the inadequacy of Newtonian mechanics and the Galilean transformations (at least for very high relative velocities). For example, the velocity of 

---