Galileo's Genius: The Experiment That Never Was.

Stolen from Clueless Fundatma.

Many of us have this mental picture of Galileo standing on top of the Leaning Tower of Pisa and dropping a feather and stone to watch them fall on the ground simultaneously, thus upsetting the Aristotelian assertion that "heavier objects fall faster".

Of course, we know Galileo couldn't possibly have done that experiment, because if he actually had, the presence of air would have reaffirmed the Aristotelian world-view, and the feather would have fallen later.

So what exactly did Galileo do?

I haven't read his original work, but my PhD advisor - Ron Larson - told us this charming story during a class I took with him, and its stuck with me since.

Apparently Galileo did a thought experiment.

He used the idea of "reductio ad absurdum", which begins by assuming something that we wish to prove as false, and hitting a contradiction.

The proof is beautiful, and here is a rough outline.

Consider two objects, with the heavier object of mass M, and the lighter object of mass m. Let us assume that "heavier objects fall faster" - which is opposite of what we wish to prove.

Further consider a really tall tower. If you can think of an infinitely tall tower, that is even better.

Now we've assumed that mass M falls faster than mass m. Here's the beautiful construction: Consider tying the two masses with a piece of string - to create a new object of mass M + m, as shown below.

Let us drop this composite object from the top of our tall tower, and think about what may happen. Because of what we've assumed, the mass M is going to fall faster than m, and in a short while the composite object (that is still falling, remember) will have adopted a configuration that looks more like the following.

Let us now consider the tension inside the string (red line in my diagram). The big mass tugs on the small mass, while the small mass tugs back.

Thus, the small mass slows the big mass down.

Consequently, the composite object of mass (M+m) falls slower than the unfettered object of mass M. But the composite object is heavier, and should fall faster.

Reductio ad absurdum!