WikiMechanics

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; eight somatic perceptions on the right-side, four on the left, four burning 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 Aristotle refers¹ to the primordial atomic mass as πανσπερμία or a seed-aggregate. So to make a seed-aggregate model for the proton we express $\sf{\Omega}$ as a bundle of seeds

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

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

+ →

+ → + →

Then a proton is represented by a bundle of twelve quarks. And here is an iconic image of a proton.

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

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.

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, they are distinguished by the spin of the reference frame as noted by ${\sf{F}}_{\LARGE{\circ}}$ or ${\sf{F}}_{\LARGE{\bullet}}$. 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

$\sf{\Omega} \left( \sf{p^{+}} \right) \equiv \left\{ \; \left\{ \left\{ \sf{d}, \sf{b} \right\}, \left\{ \sf{d}, \bar{\sf{t}} \right\}, \, \sf{b}, \, \bar{\sf{t}}, \, {\sf{F}}_{\LARGE{\circ}} \vphantom{X^{X^2}} \right\}, \; \left\{ \left\{ \sf{d}, \sf{b} \right\}, \left\{ \sf{d}, \bar{\sf{t}} \right\}, \, \sf{b}, \, \bar{\sf{t}}, \, {\sf{F}}_{\LARGE{\bullet}} \vphantom{X^{X^2}} \right\} \vphantom{X^{X^{X^{X^{X}}}}} \; \right\}$

To illustrate this model, we show quarks with a background that is dark or bright depending on their phase. Then movies can be made that use shadows, horizons and background brightness to suggest a quark's relationship with the frame-of-reference.

The 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 background radiation. It is often said this background radiation is 'cosmic', and to assert that it comes from a 'big-bang'. But perhaps just seeing protons, bare naked in their ground-states, could offer another pathway for interpretation. 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, almost indestructible. This gives it a starring role in narratives connecting cause and effect.