Galileo, Inertial Mass, Gravity

Leaning Tower of Pisa | tower, Pisa, Italy | Britannica

The idea of inertia is not new. It was not invented by Newton, or even by Galileo.

Galileo did make a fascinating elaboration on it, though.

Let's look at the famous thought experiment in which he talked about dropping balls of different sizes from the Tower of Pisa.

The point of the experiment is that, although there are in principle two ways of measuring mass, they come out to be the same. One can measure mass by inertia, or one can measure it in terms of gravity. If mass (gravity) is the important variable in our thought experiment, then one would expect the heavier ball -- say a cannon ball -- to fall to the ground more quickly than the small one, say, the pebble.

On the other hand, if mass (inertia) in the important variable than one would expect the cannonball to move more slowly than the pebble. Inertial mass holds it back from the free fall the pebble enjoys.

The only way that the cannonball and the pebble fall at the same speed is if intertial mass and gravitic mass are the same.

Newton later formalized this idea and Einstein took it a step further. He offered an explanation for why the two in principle distinct notions of mass come out the same. THEY AREN'T THE SAME, THEY ARE IDENTICAL. We can say that they are so because inertia is gravity. Which is affecting a particular mass at a particular time is a matter of our frame of reference.

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