Equivalence Principle: Einstein vs Galileo/Newton

General Theory of Relativity is based on Einstein's Equivalence Principle EEP, to be compared with the Galileo/Newton's Equivalence Principle expressing Universality of Free Fall UFF.

UFF means that matter independent of composition reacts the same way in a gravitational field and so shows the same free fall. UFF is a prediction of Newtonian mechanics verified with very high precision starting with Galileo's free fall experiments from the Tower of Pisa. The proof that UFF is a consequence/prediction of Newton's mechanics is given in two lines here. Check it out.

Einstein formulated EEP considering two reference frames, K placed in a uniform gravitational field and K′ uniformly accelerated, as follows:

• As long as we restrict ourselves to pure mechanical processes in the realm where Newton’s mechanics holds sway, we are certain of the equivalence of the systems K and K′. 
• But this view of ours will not have any deeper significance unless the systems K and K′ are equivalent with respect to all physical processes, that is, unless the laws of nature with respect to K are in entire agreement with those with respect to K′. 
• By assuming this to be so, we arrive at a principle which, if it is really true, has great heuristic importance. 
• By theoretical consideration of processes which take place relatively to a system of reference with uniform acceleration, we obtain information as to the career of processes in a homogeneous gravitational field.

Einstein thus acknowledges UFF to be a consequence of Newton's mechanics, but finds a need to extend it beyond Newton's mechanics to all physical processes, and then things get complicated. So complicated that Einstein must leave the safe haven of Newton's mechanics with UFF secured, and resort to assuming EEP to be a postulate, now asking for experimental conformation. But that is virtually impossible, since all physical processes are involved. 

So there we stand today: UFF is secured by Galileo/Newton. EEP is waiting for confirmation. 

PS1 UFF is also referred to as the weak equivalence principle, and EEP as the strong equivalence principle.

PS2 Note that UFF does not exclude internal motion of a body subject to a non-uniform gravitational field (tidal motion). 

PS3 Einstein's bright idea was to ask what may happen to Newton's mechanics if it is extended beyond its realm of mechanics to electromagnetics with material bodies traveling at near the speed of light, however  without connection to reality. There is no reason to question Newton's mechanics, and anyway doing that is stupid.