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by tsimionescu
267 days ago
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It's also interesting to note that the thought experiment is actually plain wrong, unless you consider general relativity a given. Galileo's argument is that the theory where heavier objects fall faster is inconsistent a priori, because affixing a small stone to a larger stone would cause the composed object to fall faster than the smaller stone was falling when it was free. However, there is no logical contradiction here: what could happen is that the combined object would have an acceleration that is the (weighted) average of the acceleration of the components - slower than the lighter object but faster then the heavier object. In fact, this is exactly what happens in an electric field: if you have two objects with the same mass but different negative charge moving towards a large positive charge, they will accelerate at different rates (the one with the bigger negative charge will "fall" faster). If you then tie the two objects together, you'll get a combined object that has more mass and more charge; the total electric force will increase, but its larger total mass will mean that it accelerates less. Alternatively, you can explain it as the less charged object dragging the heavier object down, such that the combined object moves at an average of their speeds. The fact that this doesn't happen with gravity is a very special property of gravity, that only experiments can prove. A priori, gravitational mass/charge could have been entirely unrelated to intertial mass, just like electrical charge. Only much later, with Einstein's general relativity, did we get an explanation of gravity that makes this more than a coincidence - and it turns out that gravity is not a force at all, at least not one that acts on objects. |
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