Where does Einstein need Quantum Mechanics?

    It took Newton 20 years to extend
    his gravity law to extended objects.


    J. S. Bell's view of the electron orbit
    in the hydrogen atom.
It took Isaac Newton 20 years to extend his gravity law to extended objects such as the sun and earth.

When Einstein invented his special relativity 1905, he must have thought about Lorentz-boosting extended objects. However, there were no physical processes where this effect could be observed. Even for point particles, the time dilation and space contraction were not experimentally established until mesons were discovered from cosmic rays.

Of course, like Newton, people have investigated the possibility of rigid spherical balls, and there are some published papers on this subject. I once checked those papers, but I am not able to present a comprehensive review at this time.