Planck's little 1905 Dover book which resolved the "ultraviolet catastrophe" of black body radiation remains (to me) one of the outstanding triumphs of pure thought. Planck extends Maxwell & Boltzmann to the point where energy _has_ to be quantized. (I don't have my copy in front of me just now, but I think this is the correct book. I highly recommend it.) http://www.amazon.com/Theory-Radiation-Dover-Books-Physics/dp/0486668118/ Maxwell's & Boltzmann's own approaches aren't to be sneezed at. Once I read Planck's book, I could no longer accept any physical theory based on real numbers & calculus. I'm still amazed at how far physics has gotten with the absurd notions of real numbers (& therefore complex numbers) & calculus, and a complete disrespect for bits and information. The field of quantum computation seems to have gotten completely stuck, because the computer scientists have allowed the field to be taken over by physicists instead of providing the physicists an alternate paradigm. A revolution in physics is coming, very much akin to the quantum revolution, wherein real numbers & calculus are finally replaced with an inherently discrete mathematics. You can't seriously believe that a quantum state is represented by _all_ of the complex numbers, no matter how many bits of information would be required to describe that complex number. At 09:36 PM 2/8/2013, 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?
Jim Propp