Spatial Extension
//Discoidea,// Ernst Haeckel, Kunstformen der Natur. Chromolithograph 32 x 40 cm, Verlag des Bibliographischen Instituts, Leipzig 1899-1904. Photograph by D Dunlop.
Discoidea, Ernst Haeckel, Kunstformen der Natur. Chromolithograph 32 x 40 cm, Verlag des Bibliographischen Instituts, Leipzig 1899-1904. Photograph by D Dunlop.

Let some particle P be described by its mechanical energy $E$ and spin $\sigma$. Definition: the orbital radius of P is the number

$\begin{align} R \equiv \frac{hc}{2 \pi } \frac{ \sqrt{\sigma }}{E} \end{align}$

where $h$, $c$ and $\pi$ are constants. Since $E$ and $\sigma$ have been defined from tallies of quarks, the orbital radius is thus established from quark counts too. But now we use it to make a rudimentary account of the expanse or extent of P.

Any non-rotating particle has an orbital radius of zero.

For ethereal particles like $\gamma$ a photon, remember that the wavelength in a non-dispersive medium is given by $\lambda_{ \sf{o} } \equiv h c / E$. Then since the spin of a photon is always one

$\begin{align} R \left( \gamma \right) = \frac{ \lambda_{ \sf{o} } }{ 2 \pi } \end{align}$

and the orbital perimeter $2 \pi R$ is the same as one wavelength.

Right.png Next step: spatial axes.
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