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A Massive Mystery

How faster would it get over time when you drop a random ball? Well — some AP Physics 1 level easy piece of cake. You have Newton's laws of motion, F=maF=ma, and the force of the acting body due to gravity is F=GMmr2F={GMm \over r^2}, so a=g=GMr2a=g={GM \over r^2}. Easy peasy.

But is it? The first mm in F=maF=ma is the inertial mass, and the second mm in F=GMmr2F={GMm \over r^2} is the gravitational mass. Einstein later expanded that these two masses are equal and stated it as a precondition to transforming general relativity to special relativity, known as the Einstein Equivalence Principle. While we empirically know that these two mms are equal, there's no direct proof.

Scientists believe that Einstein is correct, based on many experiments conducted at ultra-microscopic-quantum levels. But it is yet to be discovered why those two mm must be equal, if: