Bead Panel, Ngaju people. Borneo 20th century, 33 x 26 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop. |

Let particle P be characterized by some repetitive chain of events

$\Psi ^{\sf{P}} = \left( \sf{\Omega}_{\sf{1}}, \sf{\Omega}_{\sf{2}}, \sf{\Omega}_{\sf{3}} \ \ldots \ \right)$

where each orbital cycle is a bundle of quarks

$\sf{\Omega}^{\sf{P}} = \left\{ \sf{q}_{\sf{1}}, \sf{q}_{\sf{2}}, \sf{q}_{\sf{3}} \ \ldots \ \right\}$

and each quark is described by its phase $\, \delta_{\theta}$. Use this phase to sort quarks into a pair of sets, $\mathcal{A}_{\LARGE{\circ}}$ and $\mathcal{A}_{\LARGE{\bullet}}$, so that all quarks of the same phase are in the same set. Then $\mathcal{A}_{\LARGE{\circ}}$ and $\mathcal{A}_{\LARGE{\bullet}}$ are called *phase-components* of P, and they are out of phase with each other. We write

$\sf{\Omega}^{\sf{P}} =\left\{\mathcal{A}_{\LARGE{\circ}} ,\mathcal{A}_{\LARGE{\bullet}} \vphantom{\left( \mathcal{A}_{\LARGE{\circ}} \right)} \right\}$ | and | $\delta_{\theta} \left( \mathcal{A}_{\LARGE{\circ}} \right) =- \, \delta_{\theta} \left( \mathcal{A}_{\LARGE{\bullet}} \right)$ |

Now let P be an almost perfectly phase anti-symmetric particle so that $\mathcal{A}_{\LARGE{\circ}} = \overline{\mathcal{A}_{\LARGE{\bullet}}}$ for all types of quarks except down quarks. Then we define a **photon** $\large{\gamma} \,$ as a particle like P, that also satisfies the conditions

$N^{\mathsf{D}} = N^{\mathsf{U}} \! \pm 8$ | and | $\left| {\Delta}n^{\sf{Z}} \right| = \begin{cases} \ \ 0 \ &\sf{\text{if}} \ &{\sf{Z \ne D}} \\ \ge 8 \ &\sf{\text{if}} \ &{\sf{Z = D}} \end{cases}$ |

These constrain the spin $\, \sigma \,$ and the inner radius $\, \rho_{\LARGE{\bullet}} \,$ so that, for all photons

$\sigma \left( \large{\gamma} \right) = 1$ | and | $\begin{align} \rho_{\LARGE{\bullet}} \left( \large{\gamma} \right) \ge \sqrt{ \frac{hc}{ k_{\sf{F}}} \vphantom{\frac{hc}{ k_{\sf{F}}}^2} } \end{align}$ |

## Anti-Photons

For WikiMechanics anti-photons are just like other anti particles. So $\overline{\gamma}$ is defined from $\gamma$ by exchanging ordinary-quarks with anti-quarks of the same type, while leaving the phase and other relationships unchanged. In a photon, $\Delta n = 0$ for all quarks except down-quarks. So photons and anti-photons have mostly the same intrinsic characteristics as each other

$\sigma \left( \large{\gamma} \right) = \sigma \left( \overline{ \large{\gamma}} \right)$ | and | $\rho_{\LARGE{\bullet}} \left( \large{\gamma} \right) = \rho_{\LARGE{\bullet}} \left( \overline{ \large{\gamma}} \right)$ |

But $\Delta n^{\sf{D}} \left( \gamma \right) = - \Delta n^{\sf{D}} \left( \overline{ \gamma} \right)$. And photons also have relative characteristics which may differ between $\gamma$ and $\overline{\gamma}$ depending on their juxtaposition with a frame of reference. For example, the wavevector $\overline{\kappa}$ depends on the phase so that

$\overline{\kappa} \left( \large{\gamma} \right) = - \, \overline{\kappa} \left( \overline{ \large{\gamma}} \right)$

and the two photons have symmetrically opposed wavevectors. They are mostly the same as each other, but moving in opposite directions.

Related WikiMechanics articles.