Conservation of Momentum

Consider some particle P that is characterized by its momentum p which has been defined using the total number of quarks $N$ and their wavevectors $\overline{\kappa}$ as

//Bead Panel// from a baby carrier, Basap people, Borneo 19th century, 39 x 20 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop.
Bead Panel from a baby carrier, Basap people, Borneo 19th century, 39 x 20 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop.

$\begin{align} \overline{p} \equiv \frac{ h }{ 2 \pi } \left( \overline{ \kappa }^{ \sf{P}} \! - N^{ \sf{P}} \, \widetilde{ \kappa }^{ \sf{F}} \right) \end{align}$

Recall that quarks are indestructible so if some compound quarks $\mathbb{X}$, $\mathbb{Y}$ and $\mathbb{Z}$ interact like

$\mathbb{X} + \mathbb{Y} \leftrightarrow \mathbb{Z}$

and if these particles are otherwise isolated then

$N ^{ \mathbb{X} } + N ^{ \mathbb{Y} } = N ^{ \mathbb{Z} }$

Also, as shown earlier, wavevectors are combined as

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

so that overall

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

We say that momentum is conserved when compound quarks are formed or decomposed. Newtonian mechanics is founded on this relationship, it is important but not unique. Recall that we also have conservation rules for seeds, quarks, charge, lepton number, baryon number, internal energy and enthalpy. All of these conservation rules follow from the logical requirements of our descriptive method. WikiMechanics depends on mathematics. Therefore we are constrained by the law of noncontradictionXlink.png and the associative propertiesXlink.png of addition and subtraction. So any characteristic defined by sums or differences of quark coefficients will be conserved.
Right.png Next step: what Louis de Broglie thinks about momentum.
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