Building Quark Models
 Ajat basket, Penan people. Borneo 20th century, 20 (cm) diameter by 35 (cm) height. Hornbill motif. From the Teo Family collection, Kuching. Photograph by D Dunlop.

Consider a particle P characterized by some repetitive chain of events

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

where each orbital cycle is a bundle of quarks

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

described by some quark coefficients $n$ and their internal energies $U$. Recall that $H_{chem}$ notes the enthalpy of the chemical quarks in P. The constant $k_{\sf{F}}$ has a positive value, with the units of a force. These quantities are used to define the following radii that describe the form and location of P. The chemical radius is

\begin{align} \rho_{chem} \equiv \frac{H_{chem}}{k_{\sf{F}}} \end{align}

The magnetic radius of P is

\begin{align} \rho_{m} \equiv \frac{ {\Delta}n^{ \mathsf{A}} U^{ \mathsf{A}} - {\Delta}n^{ \mathsf{M}} U^{ \mathsf{M}} }{ k_{\sf{F}} } \end{align}

the electric radius is given by

\begin{align} \rho_{e} \equiv \frac{ {\Delta}n^{ \mathsf{G}} U^{ \mathsf{G}} - {\Delta}n^{ \mathsf{E}} U^{ \mathsf{E}} }{ k_{\sf{F}} } \end{align}

the polar radius of P is defined as

\begin{align} \rho_{z} \equiv \, \rho_{chem} + \frac{{\Delta}n^{\mathsf{U}} U^{\mathsf{U}} - {\Delta}n^{\mathsf{D}} U^{\mathsf{D}}}{k_{\sf{F}}} \end{align}

An ordered set defines the radius vector of particle P as

$\overline{\rho} \equiv \left( \rho_{ m}, \rho_{e}, \rho_{ z} \right)$

Components of $\overline{\rho}$ are conserved because they are defined from sums and differences of quark coefficients, and quarks are indestructible. So if some generic particles $\mathbb{X}$, $\mathbb{Y}$ and $\mathbb{Z}$ interact like $\mathbb{ X } + \mathbb{ Y } \leftrightarrow \mathbb{ Z }$ then by the of addition and subtraction

$\overline{\rho}^{ \mathbb{X}} + \overline{\rho}^{\mathbb{Y}} = \overline{\rho}^{\mathbb{Z}}$

Also $\rm{\Delta} \it{n} ^{\sf{Z}} \left( \sf{P} \right) = - \rm{\Delta} \it{n}^{\sf{Z}} \left( \sf{\bar{P}} \right)$ so particles and anti-particles have symmetrically opposed radius vectors

$\overline{\rho} \left( \sf{P} \right) = - \overline{\rho} \left( \sf{\overline{P}} \right)$

We use the foregoing radii to describe particle shape. If P has the same radius vector for every cycle then we call it a rigid particle. But some particles are not very solid or exactly located. Then we may use the following radii to describe their range. The inner radius is

\begin{align} \rho_{\LARGE{\bullet}} \equiv \frac{ \left| \Delta n^{\sf{D}} \right| }{8} \sqrt{ \frac{hc}{ 2 \pi k_{\sf{F}}} \vphantom{\frac{hc}{2 \pi k_{\sf{F}}}^2} } \end{align}

And the outer radius of P is

\begin{align} \rho_{\LARGE{\circ}} \equiv \frac{N^{\sf{D}}}{8} \sqrt{ \frac{hc}{ 2 \pi k_{\sf{F}}} \vphantom{\frac{hc}{2 \pi k_{\sf{F}}}^2} } \end{align}

We say that a particle is free when $\left| \Delta n^{\sf{D}} \right| ≳ 8$ and $N^{\sf{D}} \! \to ∞$. That is, when the inner radius is close to zero, and the outer radius is big.

Sensory Interpretation: In these formulae $\Delta n$ means that contributions from sensations on the right side are cancelled by sensations felt on the left. The radius vector depends on their net magnitude. Coefficients of baryonic quarks do not appear in these definitions, only dynamic quarks. So the radius does not depend on thermal sensation, only somatic and visual sensations. Also the null value for energy is referred to down-quarks which are objectified from black sensations. So overall the radius vector is interpreted as a description of the magnitude of somatic and visual sensations, relative to black sensations, net right from left.
 Next step: making room for quark models.
 Summary
 Noun Definition Chemical Radius \begin{align} \rho_{\sf{chem}} \equiv \frac{H_{\sf{chem}}}{k_{\sf{F}}} \end{align} 5-2
 Noun Definition Magnetic Radius \begin{align} \rho_{ m} \equiv \frac{ {\Delta}n^{ \mathsf{A}} U^{ \mathsf{A}} - {\Delta}n^{ \mathsf{M}} U^{ \mathsf{M}} }{ k_{\sf{F}} } \end{align} 5-3
 Noun Definition Electric Radius \begin{align} \rho_{e} \equiv \frac{ {\Delta}n^{ \mathsf{G}} U^{ \mathsf{G}} - {\Delta}n^{ \mathsf{E}} U^{ \mathsf{E}} }{ k_{\sf{F}} } \end{align} 5-4
 Noun Definition Polar Radius \begin{align} \rho_{z} \equiv \, \rho_{\sf{chem}} + \frac{{\Delta}n^{\mathsf{U}} U^{\mathsf{U}} - {\Delta}n^{\mathsf{D}} U^{\mathsf{D}}}{k_{\sf{F}}} \end{align} 5-5
 Noun Definition Inner Radius \begin{align} \rho_{\LARGE{\bullet}} \equiv \frac{ \lvert \Delta n^{\sf{D}} \rvert }{8} \sqrt{ \frac{hc}{ 2 \pi k_{\sf{F}}} \vphantom{\frac{hc}{ k_{\sf{F}}}^2} } \end{align} 5-6
 Noun Definition Outer Radius \begin{align} \rho_{\LARGE{\circ}} \equiv \frac{N^{\sf{D}}}{8} \sqrt{ \frac{hc}{ 2 \pi k_{\sf{F}}} \vphantom{\frac{hc}{2 \pi k_{\sf{F}}}^2} } \end{align} 5-7
 Noun Definition Radius Vector $\overline{\rho} \equiv \left( \rho_{ m}, \rho_{e}, \rho_{ z} \right)$ 5-8
 Noun Definition Rigid Particle $\overline{\rho} \ \ {\sf\text{has the same value for all events} }$ 5-9
 Noun Definition Free Particle $\lvert \Delta n^{\sf{D}} \rvert ≳ 8 \ \ \ \ \ {\sf{\text{and}}} \ \ \ \ \ N^{\sf{D}} \! \to ∞$ 5-10
page revision: 148, last edited: 05 Nov 2019 03:33
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