On Fri, Jul 18, 2014 at 7:34 PM, Orionworks - Steven Vincent Johnson < orionwo...@charter.net> wrote:
I'm curious about one thing. What is it about Mills' orbitspheres that you > don't like. Keep in mind I don't understand the math involved. My difficulties start with the shape. I understand an orbitsphere to be a sphere of negative charge of negligible thickness made up of an infinite series of current loops. By contrast, (standard) quantum mechanics, even in the context of a hydrogen atom with a single electron, talks about spherical harmonics: http://en.citizendium.org/images/thumb/e/ec/Spherical_harmonics.png/700px-Spherical_harmonics.png Spherical harmonics are 3-dimensional, in contrast to the orbitsphere, which is a two-dimensional shell (if I have gotten a detail wrong, I hope someone will correct me). The three dimensions allow you to say things like "the electron will have a nontrivial probability of being in the nucleus part of the time." Presumably an orbitsphere will not -- there's no obvious reason that the "electron" would ever leave the confines of the 2-dimensional spherical shell. Spherical harmonics are seen once again in the nucleus in trying to understand the energy levels of the constituent protons and neutrons (i.e., as seen in the energies of gamma photons emitted from an exited nucleus). In atoms more complex than the hydrogen atom, the shapes of the shells have various implications. Here is an image in which the charge density is being understood in terms of 3d electron orbitals of non-spherical shape: http://d22izw7byeupn1.cloudfront.net//33e0f36f-eb35-407f-9650-4bd7afcf125b/PhysRevB.90.041105.png There are different approaches we can take to harmonize the cognitive dissonance that the Mills orbitsphere and the spherical harmonic descriptions give rise to: - We can assume that the two descriptions of the single electron in the hydrogen atom are dual. This is what Stefan Israelsson Tampe has suggested in a separate thread. I personally do not see how this could be the case, unless we take the Mills description to be more abstract. - We can say that for the hydrogen atom, below the ground state, there are orbitspheres, and above the ground state (e.g., excited Rydberg levels), there are spherical harmonics. But why the abrupt switch from one model to another? - We can say that when it comes to electrons in any atom, there are no spherical harmonics, only orbitspheres, even for levels above the lowest (non-redundant) one. But if that's the case, do we do the same for the nuclear shells? And what do we tell the poor physicists who have been coming up with incorrect charge density maps for solids by making incorrect assumptions about the electron orbital shapes? These are only the first questions that come to mind. This is a thread that, once pulled, takes you into an alternative universe where everything you've learned must be recast using new explanations. And so far we've only talked about the shape of the electron orbital. Eric
