I don't know how one would guess the size of atoms from crystal structure, but I'd be surprised if there weren't some way to make a reasonable guess. At the opposite extreme, if all scales made equal physical sense, then there would be no way for nature to choose some scale. Also, Occam's Razor would probably complain that that isn't the simplest physical model that fits the evidence. (Not conclusive of course, but suggestive.) On the third hand, I wouldn't be at all surprised if as more is learned about physics, it becomes increasingly clear that there is some kind of structure at scales that are arbitrarily small. Or not. --Dan On 2013-02-08, at 9:05 PM, James Propp wrote:
I just watched George Hart's video https://simonsfoundation.org/multimedia/attesting-to-atoms/ and was left with a vexing disquiet about the fact that the macroscopic structure of crystals seems to imply the existence of atoms and yet gives us no information about how big atoms are. If the observed structure of macroscopic crystals is compatible with an infinite range of models of reality, each positing the existence of atoms but at ever-smaller scales, could there be some sort of projective limit of these theories, with "cubes all the way down" but no bottom level? I'm not saying it's a believable physical theory, but it seems like it would give an example of a universe with crystals but without atoms. Or is this idea incoherent in some way?
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