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, $F=ma$, and the force of the acting body due to gravity is $F={GMm \over r^2}$, so $a=g={GM \over r^2}$. Easy peasy.

But is it? The first $m$ in $F=ma$ is the inertial mass, and the second $m$ in $F={GMm \over r^2}$ 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 $m$s 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 $m$ must be equal, if:

• These two $m$s are the same physical value, and we are observing in two different ways due to some exquisite geometric property of the universe.
• Humans are just not accurate enough to disprove it yet.