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A Seed-Aggregate Model
An electron can be mathematically represented using the repetitive chain of events
$\Psi \left( \sf{e^{-}} \right) = \left( \sf{\Omega}_{1} , \sf{\Omega}_{2} , \sf{\Omega}_{3} \; \ldots \; \right)$
where each repeated cycle $\sf{\Omega}$ is a bundle of 40 Anaxagorean sensations; 8 right-side and 12 left-side somatic sensations; 2 burning, 2 freezing, 2 warm and 2 cool thermal sensations; 4 yellow, 4 blue and 4 white visual sensations. The chain of events $\Psi$ is called a history of the electron. Each Anaxagorean sensation may be objectified to define a seed and so here is a model of the electron as an aggregation of seeds
$\sf{\Omega} \left( \sf{e^{-}} \right) \leftrightarrow \mathrm{4}\sf{U} + \mathrm{2}\sf{B} + \mathrm{2}\sf{T} + \mathrm{2}\sf{S } + \mathrm{2}\sf{C} + \mathrm{4}\sf{G} + \mathrm{4}\sf{E} + \mathrm{8}\sf{O} + \mathrm{12}\overline{\sf{O}}$
A Quark Model of the Electron
The quark hypothesis asserts that seeds are all bound together in quarks. So the seed-aggregate model of the electron is developed further by associating seeds in these pairs
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so that an electron consists of twenty quarks. And here is a visual representation of the electron made by combining quark icons. The back row of quarks is the same as the front row.
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$\begin{align} \sf{\Omega} \left( \sf{e^{-}} \right) \leftrightarrow \mathrm{4}\bar{\sf{u}} &+ \mathrm{2}\bar{\sf{b}} + \mathrm{2}\sf{t} + \mathrm{2}\bar{\sf{s}} + \mathrm{2}\sf{c} + \mathrm{4}\bar{\sf{g}}+ \mathrm{4}\sf{e} \end{align}$ |
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Using these quarks, the mass of the electron is calculated to be 0.5109989280 (MeV/c2). This is exactly the same as the experimentally observed value because adjustable parameters like quark energies have been carefully chosen1 to get this result. For more mathematical detail, please see these spreadsheets.
A Ground-State Electron Model
Quark coefficients are all integer multiples of two, and so the image above is drawn with the back row of quarks the same as the front. But we cannot have two identical quarks in the same bundle and still satisfy Pauli's exclusion principle. So the quark model is developed further with an additional requirement that the quarks in the front and back rows are out of phase with each other. That is, we suppose there is a difference in their relationship with the frame of reference that allows us to distinguish between them. This satisfies the definition for being in a ground-state and so the new arrangement is called a ground-state model of the electron. It can be expressed mathematically as
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| Click on this image for a short movie about the ground-state of an electron. The frame of reference is shown by shading in the background. |
$\sf{\Omega} \left( \sf{e^{-}} \right) = \left\{ \mathcal{S}_{\LARGE{\circ}}, \mathcal{S}_{\LARGE{\bullet}} \right\}$
where
$\mathcal{S}_{\LARGE{\circ}} = \mathcal{S}_{\LARGE{\bullet}} \leftrightarrow \mathrm{2}\bar{\sf{u}} + \bar{\sf{b}} + \sf{t} + \bar{\sf{s}} + \sf{c} + \mathrm{2}\bar{\sf{g}}+ \mathrm{2}\sf{e}$
And recall that $\delta_{\theta}$ notes the phase so that
$\delta_{\theta} \left( \mathcal{S}_{\LARGE{\circ}} \right) =- \delta_{\theta} \left( \mathcal{S} _{\LARGE{\bullet}} \right) = \pm 1$
To illustrate this model, we show quarks with a background that is dark or bright depending on their phase. Then the image above is made into a movie that uses shadows, horizons and background brightness to suggest a quark's relationship with the frame-of-reference.
Here is a link to the most recent version of this content, including the full text.
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The Electron |
