As far as I understand, when a modification of a theory is made it is because some observation required this modifcation. Quantum Mechanics is a nice example of that: observations of microscopic phenomena showed that classical mechanics was giving the wrong predictions, so a new approach was required.
Now, another case is special relativity. It is often said that special relativity was required because newtonian mechanics was inconsistent with Maxwell's electrodynamics.
I must confess though that I've always failed to see what is that inconsistency. What I want here is to find a motivation for the requirement of special relativity. I want to understand what led Lorentz and Einstein to see the need of a new theory of spacetime.
So what is the inconsistency between newtonian mechanics and Maxwell's electrodynamics which led to the development of special relativity?
Best Answer
The obvious difference is that Newton's equations retain their form for all inertial reference frames when Galileo's Principle of Relativity is used, but Maxwell's equations are not invariant under this transformation.
Instead one must use the Lorentz transform, which recognizes that there is a fixed speed for light, $c$. This limit was recognized by Maxwell when he first worked out the form of electro-magnetic waves; the theoretical value matched well with the then best experimental results for the speed of light.
The final result was the theory of Special Relativity, and the modification of Newton's Laws of Motion so as to make them Lorentz invariant.