Counting quarks is way to scientifically describe sensation. More exactly, we start by counting seeds. Let P be a generic particle composed of some aggregation of seeds. A simple way to make a mathematical description of P is just to sort-out the number of different types of seeds in P. To satisfy Anaxagorean narrative conventions, Cantor’s definition of a set, and Pauli’s exclusion principle, we require that seeds are perfectly distinct. Therefore seed counts always report a positive integer or zero, never fractions or negative numbers.
If all seeds are paired in quarks, then P can also be represented as a set of quarks and mathematically described by counting quarks. We note the results of such an inventory using the letter . These numbers are called quark coefficients because they can be interpreted as factors in a nuclear reaction that yields P. For example if then the quark coefficients of P are and . Quark coefficients are always integers because quarks are defined by pairs of perfectly distinct seeds.
|the total number of Z-type quarks|
|the net number of Z-type quarks|
|the total number of all types of quarks|
Recall that the Roman letter Z, or the Greek letter are used to indicate quark-type. In general, we use the symbols or to note the coefficients of ordinary quarks. Coefficients of anti-quarks are written with an overline as or A few other numbers used for describing particles are defined in the accompanying table. The letter indicates the use of summation notation.
Note that if Z represents a thermodynamic or chemical quark, then also gives the number of these sorts of seeds in P. This is because there is just one Z-type seed for each quark, and all quarks are named after their non-conjugate seed. So we often call a seed coefficient when discussing thermodynamic seeds.
Counting Quarks and Anti-Quarks
By the foregoing definitions, the net number of quarks in particle P and its anti-particle are related as
This is just an arithmetic fact, little more than a tautology. It follows directly from the anti-commutative properties of subtraction. However, when we apply it to counting quarks it expresses a fundamental physical symmetry between matter and anti-matter. So we will come back to it later. But next we look at some measurable particle properties like energy, temperature, and other quark traits.