There can't be a continuum down there, simply because we can't have enough information to specify it. Information density is limited by the Beckenstein limit on black holes. As Henry points out, the idea that a single real number has an infinite information content means that real numbers are only a smoothed approximation to discrete physical observables. My favorite speculation for structure at the Planck scale is a 4-D crystal with dislocations in the crystal structure giving rise to observable particles. Past is represented with a solidified structure, present is the phase boundary, and quantum weirdness and interference is the attempt to extend the phase boundary in a consistent way. We observe the net growth of the crystal, but it is an epiphenomenon -- a result of the crystal growth. I don't expect anyone else to take this seriously, since there is no experimental support. Can we classify 4-D crystal dislocation types and align them with the known particle spectrum? On Feb 9, 2013, at 12:36 AM, Rowan Hamilton wrote:
Rutherford scattering should give the effective size of the nucleus. (Though note that "size" is a squishy term in quantum mechanics.) Quantum electro-dynamics predicts the orbital structure of the electrons, which should give an effective size to any given atom.
As to arbitrarily small structures, the Planck scale seems to give the bottom, if you believe quantum gravitation theories. I have always found this idea interesting, since if you quantize gravity then space-time becomes quantized, which means (at least to this naive observer) that the universe is countable. How cool is that?
Rowan.
On Fri, Feb 8, 2013 at 9:17 PM, Dan Asimov <dasimov@earthlink.net> wrote:
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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