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Quarks are Conserved

Quarks are conserved because physics depends on mathematics. Recall that a logical style of description employing mathematics requires that seeds are conserved. For the same reason, when we shift the description to counting quarks, then quarks must be conserved too. The overall quantity and quality of the quarks in a description cannot change. As a narrative convention, we say that quarks are indestructible. Whenever some compound quarks \mathbb{X}, \mathbb{Y} and \mathbb{Z} are combined or decomposed, if

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

then the coefficients of any specific type of quark  n^{\mathsf{q}} are related as

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

And a sum over all types of quarks N_{\mathsf{q}} is constrained as

N_{\mathsf{q}} ^{\mathbb{X} } + N_{\mathsf{q}}^{ \mathbb{Y} } = N_{\mathsf{q}} ^{ \mathbb{Z} }

Quark Coefficients are Integers

To satisfy Anaxagorean narrative conventions, Cantor’s definition of a set, and Pauli’s exclusion principle, we require that every seed Z is perfectly distinct. Therefore seed counts always report a positive integer or zero, not fractions or negative numbers

N^{\mathsf{Z}}  = 0, \,  1, \,  2, \, 3 \  \ldots           \  \  \forall  \, \mathsf{Z}

For the same reason, when we define quarks from seeds, and shift the description to counting quarks, then the coefficient of any quark  n^{\mathsf{q}} must always be a non-negative integer as well

n^{\mathsf{q}}  = 0, \,  1, \,  2, \, 3 \  \ldots           \  \  \forall  \, \mathsf{q}

The relationships on this page are the logical basis for a variety of conservation laws that are found throughout physics. We often refer back to them. But next we look at how these quark-coefficients are related to quantum numbers.

Quarks are conserved and so are the beads shown in this 19th century weaving from Borneo.
Baby Carrier Panel, Basap people. Borneo 19th century, 27 x 19 cm. Photograph by D Dunlop.