The Equivalence Principle of General Relativity

Bodies of different mass fall the same way.

The pillars of modern physics are quantum mechanics and Einstein's General Theory of Relativity GR, which is based on the following Equivalence Principle EP:

• inertial mass = gravitational mass.                          

In Newtonian Mechanics NM including Newton's Law of Gravitation, EP is not an assumption but instead a necessary consequence of the fact that in NM, as experimentally verified by Galileo dropping different objects from the tower of Pisa while supplying also a theoretical justfication: 

• all bodies independent of mass accelerate the same way in proportion to gravitational force.  

More precisely, with A acceleration and F gravitational force per unit mass, in NM we have 

• A = F

which we can write 

• MA = MF

where M is mass, as an expression of Newton's 2nd Law: mass x acceleration = force. We see that $M$ appears on both sides as an expression of EP. 

Summary: EP is automatically satisfied in NM. It does not make sense in NM to introduce EP as an assumption. On the other hand, EP is an assumption of GR. EP is self-evident in NM but not so in GR, where (P) is made into assumption as if it is possible that inertial mass is different from gravitational mass. This makes GR into a strange perturbation of NM with the following question: What makes GR different from NM when they share the same EP?