On the moon, you and a feather fall equal distances in identical times. The most recent confirmation, more accurate than dropping dissimilar objects from the Leaning Tower of Piza, was conducted aboard a spacecraft called MICROSCOPE. The aim of the project is to achieve an accuracy in parts per quadrillion, and some scientists have proposed launching satellites for conducting experiments accurate to one part per sextillion. If that isn’t splitting the hair enough for you, there’s even a proposal to launch Bose-Einstein condensates to test the equivalence principle on a level of single quantum waves.* How’s that for distinguishing between a feather and a hammer in free fall?
Galileo would be astonished, of course. So would Newton. Einstein would rejoice in further confirmation of his work; and you, well, you are probably saying that’s it’s all a bit too much refinement of knowledge. “What’s next?” you might ask. “I don’t live my life on that level of refinement.”
You’re right. You don’t. You’re also wrong. You sometimes do. Have you noticed that you use one level of refinement when you deal with yourself and another level when you deal with others? Dropping a feather and a hammer from somewhat bulky spacesuit gloves and eyeing their fall is sufficient refinement when we consider our own stumbles and falls. But when others trip, we get very scientific. As they fall, we seek refinements of information; we become very particular. We examine; we reexamine. We analyze. We overanalyze. You see your falls in terms of one part per one part; their falls in parts per million. “Of course, she stumbled. What do you expect? Look at her history, her manner, her company, her vices, her….”
It seems that when we compare our own falls to those of others, we don’t see an equivalence. In judging the falls of others and making comparisons, we apply a Principle of Nonequivalence.
* https://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html
** http://www.sciencemag.org/news/2017/11/galileos-400-year-old-theory-free-falling-objects-passes-space-test