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.
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

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

that are described by their internal energies $U$ and some quark coefficients $n$. Definition: 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

$\begin{align} \rho_{z} \equiv \frac{ {\Delta}n^{ \mathsf{U}} U^{ \mathsf{u}} - {\Delta}n^{ \mathsf{D}} U^{ \mathsf{d}} }{ k_{\sf{F}} } \end{align}$

where $k_{\sf{F}}$ is a positive constant. An ordered set of these three numbers 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 associative propertiesXlink.png of addition and subtraction

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

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

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

Definition: if P is described by a chain of events $\Psi$ where each cycle $\sf{\Omega}$ has the same radius vector, then we say that P is rigid. This condition is obtained if there are no changes to the quark content of P.

achromatic.jpgBangladeshi.GIFSwedish.gifodd.jpg
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.
Right.png Next step: making room for quark models.
Summary
Noun Definition
Magnetic Radius $\begin{align} \rho_{ m} \equiv \frac{ {\Delta}n^{ \mathsf{A}} U^{ \mathsf{a}} - {\Delta}n^{ \mathsf{M}} U^{ \mathsf{m}} }{ k_{\sf{F}} } \end{align}$ 5-1
Noun Definition
Electric Radius $\begin{align} \rho_{e} \equiv \frac{ {\Delta}n^{ \mathsf{G}} U^{ \mathsf{g}} - {\Delta}n^{ \mathsf{E}} U^{ \mathsf{e}} }{ k_{\sf{F}} } \end{align}$ 5-2
Noun Definition
Polar Radius $\begin{align} \rho_{z} \equiv \frac{ {\Delta}n^{ \mathsf{U}} U^{ \mathsf{u}} - {\Delta}n^{ \mathsf{D}} U^{ \mathsf{d}} }{ k_{\sf{F}} } \end{align}$ 5-3
Noun Definition
Radius Vector $\overline{\rho} \equiv \left( \rho_{ m}, \rho_{e}, \rho_{ z} \right)$ 5-4
Noun Definition
Rigid $\overline{\rho} \ \ {\sf\text{has the same value for all events} }$ 5-5
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