After a theory is born, it would be continually checked for accuracy and generality against old and new experimental results and when anomalies are detected, it prompts the berth of new theories. The Newton and Einstein theories are no different. The special theory of relativity for example is said to generalize the theories of Newton about momentum to include a correction increasing with the energy of a particle. The general theory of relativity attempts to derive the gravity force from simpler physical principles rather than have it empirical as it was then. The end result is a correction to the predictions of Newton and a wider scope of understanding of physics.
A vivid example of a theory cannot die easily, is that of Newton about light being made of small corpuscles. Then Huygens theory came to claim it was waves instead. Then Einstein came back to show that it is photons.. very much like corpuscles, then QM came to suggest that it is both a corpuscle and a wave, and this is our final theory up to now. This is because the original theories did satisfy what was observed at the time and that cannot be proved wrong.
I myself did some work to show that the wave behavior can in fact come from the corpuscles themselves. This is so if these are point material points obeying the conservation of momentum, moving at c. This resulted in an inverse square relation and the latter can be shown to lead to a spring force when the displacement is small and the umber of interacting particles is large. In other words both views are correct.
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