Re: Why are inertial and gravitational mass equivalent?

The equivalence of inertial and gravitational mass has a long history. 
(I will probably leave some important people out, but...,
and forgive me if this repeats what you already know.)

The principle that all objects fall at the same acceleration on earth was 
stated by Galileo, presumably after observing this in experiment.

Newton's theory of gravititation "explained" this by postulating 
F=Gmm'/r^2 and F=ma.  The key was that the gravitational mass was 
equivalent to the inertial mass.
That is, that the m in F=Gmm'/r^2 was the same as the m in F=ma.
So this "equivalence of inertial and gravitational mass" goes way back.
It was an assumption by Newton, and still is;  and is still based on 
experiments.

In GR, particles follow geodesics so that all objects must have the same 
acceleration.  Then inertial mass doesn't even enter the equations.  
It is like going back to Galileo and forgetting about Newton.  If you 
wanted to define an inertial mass in GR, it could only be equivalent to 
gravitational mass.  So this equivalence is "a consequence of GR".

However , there still is a key assumption in GR.
The word "equivalence" gets used in two ways here.  
One is the equivalence of gravitational and inertial mass, as above.  
The more profound way, which was Einstein's contribution, is the 
equivalence of acceleration and gravitation.  This "Equivalence Principle" 
is the central assumption of GR, and I believe it necessitates the 
equivalence of gravitational and inertial mass, as well as many other 
things.  But, of course, it still is an assumption that is in accord with 
experiment.  That is the nature of all physical theories.