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Photon Types

a spectrum-like image used as an icon for photons

Consider a photon \boldsymbol{\gamma} described by an out of phase pair of components

\mathsf{\Omega} \left( \boldsymbol{\gamma} \right)  = \left\{ \mathcal{A}_{\LARGE{\circ}}, \, \mathcal{A}_{\LARGE{\bullet}} \rule{0px}{9px} \right\}

that are almost perfectly anti-symmetric so that

\mathcal{A}_{\LARGE{\circ}} =   \overline{\mathcal{A}_{\LARGE{\bullet}} }

for all quarks except down quarks. Many photon attributes are nil because phase anti-symmetry implies that almost every quark is matched with a corresponding anti-quark somewhere in the photon. So for most types of quark Z, the net number of quarks is zero

\Delta n^{\mathsf{Z}} \equiv n^{\mathsf{\overline{z}}} - n^{\mathsf{z}} = 0  \;   \;   \;   \;   \;   \;   \forall     \;    \mathsf{Z} \ne \mathsf{D}

As for the down-quarks, \Delta n^{\mathsf{D}} is not zero. But recall that by convention, the internal energy of down-quarks is so small that it is usually taken to be zero. Then any imbalance between ordinary down quarks and down anti-quarks can be ignored. Substituting these conditions into the definitions for charge, strangeness, lepton number, baryon number and enthalpy gives

q(\boldsymbol{\gamma})=0

S(\boldsymbol{\gamma})=0

L(\boldsymbol{\gamma})=0

B(\boldsymbol{\gamma})=0

and

H(\boldsymbol{\gamma})=0

Recall that the lepton-number, baryon-number and charge are conserved, so a particle may freely absorb or emit countless photons without altering its own values for these quantum numbers. No work W is required to assemble a photon because the two phase components \mathcal{A}_{\LARGE{\circ}} and \mathcal{A}_{\LARGE{\bullet}} have radius vectors with the same norm, but in opposing directions

\overline{\rho}^{\, \mathcal{A}_{\LARGE{\circ}}} =- \,  \overline{\rho}^{\, \mathcal{A}_{\LARGE{\bullet}}}

so that

\overline{\rho}^{\, \boldsymbol{\gamma}} =   \overline{\rho}^{\, \mathcal{A}_{\LARGE{\circ}}} +  \overline{\rho}^{\, \mathcal{A}_{\LARGE{\bullet}}} = (0, 0, 0)

Then W(\boldsymbol{\gamma}) \equiv k_{\mathsf{F}} \Vert \, \overline{\rho}^{\, \gamma} \Vert =0 too. But not all photon characteristics are null; the outer radius  \rho_{out} and the inner radius  \rho_{in} may be greater than zero. Also consider the wavevector  \overline{ \kappa } which is found from the sum

    \begin{align*} \displaystyle \overline{\kappa} &\equiv \left( \frac{1}{\rho_{in}^{\, 2}} - \frac{1}{\rho_{out}^{\, 2}} \rule{0px}{18px} \right) \sum_{\mathsf{q} \, \in \, {\boldsymbol{\gamma}} } \delta_{\theta}^{\, \mathsf{q}} \; \overline{\rho}^{\, \mathsf{q}}   \\   &= \left( \frac{1}{\rho_{in}^{\, 2}} - \frac{1}{\rho_{out}^{\, 2}} \rule{0px}{18px} \right)   \left[ \; \rule{0px}{22px}   \delta_{\theta}^{\, \mathcal{A}_{\LARGE{\circ}} } \hspace{-6px} \sum_{\mathsf{q} \, \in \, \mathcal{A}_{\LARGE{\circ}} } \hspace{-4px} \overline{\rho}^{\, \mathsf{q}} \ + \  \delta_{\theta}^{\, \mathcal{A}_{\LARGE{\bullet}} } \hspace{-6px} \sum_{\mathsf{q} \, \in \, \mathcal{A}_{\LARGE{\bullet}} }  \overline{\rho}^{\, \mathsf{q}} \; \right] \\ &= \left( \frac{1}{\rho_{in}^{\, 2}} - \frac{1}{\rho_{out}^{\, 2}} \rule{0px}{18px} \right)   \left[ \, \rule{0px}{16px}   \delta_{\theta}^{\, \mathcal{A}_{\LARGE{\circ}} } \, \overline{\rho}^{\, \mathcal{A}_{\LARGE{\circ}} } \; + \;  \delta_{\theta}^{\, \mathcal{A}_{\LARGE{\bullet}} } \, \overline{\rho}^{\, \mathcal{A}_{\LARGE{\bullet}} } \, \right] \end{align*}

But \mathcal{A}_{\LARGE{\circ}} and \mathcal{A}_{\LARGE{\bullet}} are out of phase, so \delta_{\theta}^{\mathcal{A}_{\LARGE{\circ}}} =- \, \delta_{\theta}^{\mathcal{A}_{\LARGE{\bullet}}} = \pm 1. And radius vectors are symmetrically opposed, so \overline{\rho}^{\mathcal{A}_{\LARGE{\circ}}} \! =- \,  \overline{\rho}^{\mathcal{A}_{\LARGE{\bullet}}}. These two negative factors cancel each other such that \delta_{\theta}^{\, \mathcal{A}_{\LARGE{\circ}} } \, \overline{\rho}^{\, \mathcal{A}_{\LARGE{\circ}} } \! =  \delta_{\theta}^{\, \mathcal{A}_{\LARGE{\bullet}} } \, \overline{\rho}^{\, \mathcal{A}_{\LARGE{\bullet}} }. Then we can express the wavevector as

\overline{\kappa} = 2\left( \dfrac{1}{\rho_{in}^{\, 2}} - \dfrac{1}{\rho_{out}^{\, 2}} \rule{0px}{18px} \right)  \delta_{\theta}^{\, \mathcal{A}_{\LARGE{\circ}} } \, \overline{\rho}^{\, \mathcal{A}_{\LARGE{\circ}} }

The wavenumber is given by the norm of the wavevector, so

\kappa = 2\left( \dfrac{1}{\rho_{in}^{\, 2}} - \dfrac{1}{\rho_{out}^{\, 2}} \rule{0px}{18px} \right)   \left\| \, \overline{\rho}^{\, \mathcal{A}} \, \rule{0px}{11px} \right\|

We can drop the subscript on \mathcal{A} because both phase-components have the same norm. And recall that W^{\mathcal{A}} = k_{\mathsf{F}} \Vert \, \overline{\rho}^{\mathcal{A}} \Vert is the work required to build one of these phase-components. So in energetic terms, the photon’s wavenumber can be written as

\kappa = \dfrac{2W^{\mathcal{A}}}{k_{\mathsf{F}}}  \left( \dfrac{1}{\rho_{in}^{\, 2}} - \dfrac{1}{\rho_{out}^{\, 2}} \rule{0px}{18px} \right)

Photon Typeπœ† (m)
a gamma-ray  \lesssim 10^{-12}
an X-ray 10^{-11} \sim 10^{-8}
an ultraviolet photon \sim 10^{-8}
a visible photon \sim 10^{-7}
an infrared photon 10^{-6} \sim 10^{-3}
a microwave 10^{-3} \sim 1
a radio-wave
 1 \sim 10^{8}

Then the wavelength of a photon is

\lambda = \dfrac{2\pi}{\kappa} = \dfrac{\pi k_{\mathsf{F}}}{\rule{0px}{11px} \, W^{\mathcal{A}} \, } \left( \dfrac{1}{\rho_{in}^{\,2}} - \dfrac{1}{\rho_{out}^{\,2}}  \rule{0px}{18px} \right)^{\! -1}

Finally recall that by definition the inner radius  \rho_{in} is constrained such that for all photons

\rho_{in} \! \left( \boldsymbol{\gamma} \right) \ge \sqrt{ \dfrac{hc}{2\pi k_{\mathsf{F}}} \rule{0px}{17px} }

Then if  \boldsymbol{\gamma} is a free particle where  \rho_{out} \to \infty and  \rho_{in} is as small as possible, the wavelength will be

\lambda = \dfrac{hc}{\rule{0px}{11px} \,2 W^{\mathcal{A}} }

Photons are classified by wavelength as noted in accompanying table. A more general treatment considers that a photon’s wavelength may also depend on its surroundings. Then the symbol  \lambda _{\mathsf{o}} is used to indicate a wavelength where any such environmental effects are negligible. And next we mix photons with other substances to consider excited particles.

Photon types are distinguished by somatic and phase relationships, somewhat like this beaded pattern from Indonesia.
Baby Carrier panel, Kayan people. Borneo 20th century, 31 x 27 cm. Photograph by D Dunlop.