A Rotini Model of an Atom Principia Philosophiae by Rene Descartes, page 271 (detail). Amsterdam 1644. Click on the image above for photographs of the full text well-posted by the European Cultural Heritage Online project, and the Max Planck Institute for the History of Science. 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 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 This rotating cylinder model smooths out some rough edges, but it is still amiss 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 . 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}
where $\lambda$ is the wavelength of $\mathbf{A}$. When moving, the rotini model looks a lot like a machine called the . Humans have been thinking about screw conveyor mechanisms like this for thousands of years. They were reportedly used to irrigate the as early as 600 BC. This atomic model is good for understanding the Euclidean metric of the ordinary spaces in our laboratories and classrooms.

page revision: 175, last edited: 20 Oct 2019 20:00