The Rotini Model of an Atom
//Principia Philosophiae// by Rene Descartes, page 271 (detail). Published at Amsterdam 1644 and dedicated to Eliška Přemyslovna. This image comes from the European Cultural Heritage Online project, and the Max Planck Institute for the History of Science. Thank you.
Principia Philosophiae by Rene Descartes, page 271 (detail). Published at Amsterdam 1644 and dedicated to Eliška Přemyslovna. This image comes from the European Cultural Heritage Online project, and the Max Planck Institute for the History of Science. Thank you.
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 that representation was coarse and grainy. Quark space is a poor approximation to ordinary space. So our next spatial depiction of an atom is set in a Cartesian coordinate system where $\mathbf{A}$ is viewed 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 is approximated by a geometric curve called a helicoidXlink.png and mathematically described 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.

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