Conservation of Quantum Numbers
 Bead Panel from a baby carrier, Basap people, Borneo 19th century, 30 x 21 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop.

Quarks are indestructible so the overall quantity of each quark type in any given description may not change. Whenever some generic compound quarks $\mathbb{X}$, $\mathbb{Y}$ and $\mathbb{Z}$ interact, if

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

then the quark coefficients $n$ of any sort of quark q are related as

$n^{\sf{q}} \left( \mathbb{X} \right) + n^{\sf{q}} \left( \mathbb{Y} \right) = n^{\sf{q}} \left( \mathbb{Z} \right)$

But the lepton number for example, is defined from sums and differences of quark coefficients. So by the of addition and subtraction

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

and we say that the lepton number is conserved. By the same reasoning the baryon number and charge are conserved too so that

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

and

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

Overall, baryon-number, lepton-number and charge are quantized and conserved because quarks are quantized and conserved. But the strangeness and angular momentum quantum numbers are defined using absolute-value functions which are not generally associative. So $𝘑$ and $S$ are not always conserved when compound quarks are formed or decomposed.

 Next step: enthalpy.

Related WikiMechanics articles.

page revision: 137, last edited: 04 Feb 2019 18:36