The Proton
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A Seed-Aggregate Model

WikiMechanics describes the proton by starting with the archetypal chain of events

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

where each repeated cycle $\sf{\Omega}$ is a bundle of 24 Anaxagorean sensations; four somatic perceptions on the right-side, eight on the left, four hot thermal feelings, four freezing, and finally four black visual sensations. The chain of events $\Psi$ is called a history of the proton. Each Anaxagorean sensation may be objectified to define a seed. And AristotleXlink.png refers to the primordial atomic mass as a πανσπερμία or seed-aggregate1. So to make a seed-aggregate model for the proton we express $\sf{\Omega}$ as a bundle of seeds

$\sf{\Omega} \left( \sf{p^{+}} \right) \leftrightarrow \mathrm{4}\sf{D} + \mathrm{4}\sf{B} + \mathrm{4}\sf{T} + \mathrm{4}\sf{O} + \mathrm{8}\overline{\sf{O}}$

A Quark Model of the Proton

Quarks are defined by pairs of seeds. So the seed-aggregate model of the proton is further developed by associating seeds as

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Then a proton is represented by a bundle of twelve quarks. And here is an iconic image of a proton where the back row of six quarks is the same as the front row.

$\sf{\Omega} \left( \sf{p^{+}} \right) \leftrightarrow \mathrm{4}\bar{\sf{d}} + \mathrm{4}\sf{b} + \mathrm{4}\bar{ \sf{t} }$ proton1.png

Using these quarks, the mass of the proton is calculated to be 938.2720460 (MeV/c2). This is exactly the same as the experimentally observed value because adjustable parameters like quark energies have been carefully chosen2 to get this result. For more mathematical detail, here are some spreadsheets.

A Ground-State Proton 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 proton. It can be expressed mathematically as

Click on this image for a short movie of the ground-state model of a proton. The frame of reference is shown by shading in the background.
Click on this image for a short movie of the ground-state model of a proton. The frame of reference is shown by shading in the background.

$\sf{\Omega} \left( \sf{p^{+}} \right) = \left\{ \mathcal{S}_{\LARGE{\circ}}, \mathcal{S}_{\LARGE{\bullet}} \right\}$

where

$\mathcal{S}_{\LARGE{\circ}} = \mathcal{S}_{\LARGE{\bullet}} \leftrightarrow \mathrm{2}\bar{\sf{d}} + \mathrm{2}\sf{b} + \mathrm{2}\bar{ \sf{t} }$

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.

Proton Stability

The thermodynamic temperature of a proton in its ground state is easily calculated from the quark average

$\begin{align} \it{T} \left( \sf{p^{+}} \right) &= \frac{1}{N} \sum T ^{\sf{q}} \\ &\ \\ &= \frac{1}{12} \left( 4 T ^{\sf{d}} + 4 T ^{\sf{b}} + 4 T ^{\sf{t}} \right) \\ &\ \\ &= \mathrm{2.7254885} \, \sf{(K)} \end{align}$

This is within experimental uncertainty of the observed3 value of 2.72548 ± 0.00057 (K) for the thermal black body spectrum of the microwave backgroundXlink.png radiation. It is common to describe this background radiation as 'cosmic', and to assert that it comes from a 'big-bang'. But seeing bare naked protons could offer another explanation. The proton temperature corresponds to a calculated mean life of 1.71 X 1055 seconds, which is consistent with the observed4 lower bound of 6.6 X 1036 seconds. So the proton is an extremely stable particle. This gives it a starring role in narratives connecting cause and effect.
Right.png Next step: the electron.
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