The Rotini Model of an Atom
//Principia Philosophiae// by Rene Descartes, page 271 (detail). Amsterdam 1644. From the European Cultural Heritage Online project, and the Max Planck Institute for the History of Science.
Principia Philosophiae by Rene Descartes, page 271 (detail). Amsterdam 1644. From the European Cultural Heritage Online project, and the Max Planck Institute for the History of Science.
atom.png
Consider an atom $\mathbf{A}$ described by a repetitive chain of space-time events with time coordinates $t$. Our first spatial conception of such an atom was as a compound quark in quark space. But to implement the hypothesis of spatial isotropy our next view is set in a Cartesian coordinate system where $\mathbf{A}$ is represented as a rotating atomic clock with a phase-angle $\theta$ given by

$\theta \left(t\right) = \theta_{0} +\omega t$

such that $\mathbf{A}$ is whirling about its polar axis with an angular frequency of $\omega$. The rotation supposedly blurs variations in the electric and magnetic radii leaving an effective orbital radius $R$ that is then used to represent the atom as a rotating cylinder. This rotating cylinder model smooths out some rough edges, but it is still incomplete because the electromagnetic part of the quark metric is larger than the other non-polar components. So one radial direction is predominant and the atom is shaped more like a piece of rotini pasta than a solid cylinder. This corkscrew spiral can be approximated by a geometric curve called a helicoidXlink.png. It is described mathematically by radii of
$\rho_{x} = R \cos{\! 2 \theta}$ and $\rho_{y} = R \sin{\! 2 \theta }$ and $\begin{align} \rho_{z} = \frac{ \lambda \theta}{2 \pi} \end{align}$
Archimedes.gif
where $\lambda$ is the wavelength of $\mathbf{A}$. When moving, the rotini model looks a lot like a machine called the Archimedean screwXlink.png. Humans have been thinking about screw conveyor mechanisms like this for thousands of years. They were reportedly used to irrigate the Hanging Gardens of BabylonXlink.png as early as 600 BC. This atomic model is good for understanding the Euclidean metric of the ordinary spaces in our laboratories and classrooms.

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