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Spatial Extension

Let some particle P be described by its mechanical energy  E, and its angular momentum quantum number \textsl{\textsf{J}}. The orbital radius of P is defined by

R \equiv \dfrac{hc}{2\pi} \dfrac{ \sqrt{\textsl{\textsf{J}} \; }}{E}

where h,  c and  \pi are all constants. Since  E and \textsl{\textsf{J}} 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 no orbital radius because \textsl{\textsf{J}}=0 when N^{\mathsf{U}}=N^{\mathsf{D}}. So particles that are shaped like points or lines are mathematically described by saying R=0.

For photons, the angular momentum \textsl{\textsf{J}} is always one. And the wavelength  \lambda is related to the energy by  \lambda = h c \! / \! E. So the orbital radius of a photon can be written as

R \left( \gamma \right) = \dfrac{\lambda}{2\pi}

Then a circular perimeter of 2 \pi R is the same as one wavelength.

Spatial extension starts small as suggested by this German engraving of radiolarians.
Ernst Haeckel, Discoidea, Kunstformen der Natur. Chromolithograph 32 x 40 cm. Verlag des Bibliographischen Instituts, Leipzig 1899. Photograph by D Dunlop.