Internal Energy

Consider a generic particle P characterized by some repetitive chain of events noted as

 Quark Energies
 ζ z z U (MeV) 1 u u 243 2 d d 0 3 e e -32 4 g g 298 5 m m 1186 6 a a 3 7 t t 150 8 b b -85 9 s s 50 10 c c -53

$\Psi ^{\sf{P}} = \left( \sf{\Omega}_{1}, \sf{\Omega}_{2}, \sf{\Omega}_{3} \ \ldots \ \right)$

where each orbital cycle is a bundle of $N$ seeds

$\sf{\Omega} = \left\{ \sf{Z}_{1}, \sf{Z}_{2} \ \ldots \ \sf{Z}_{\it{i}} \ \ldots \ \sf{Z}_{\it{N}} \right\}$

Let each seed be described by its audibility $\varepsilon$ and its specific energy $\hat{E}$. We characterize $\sf{P}$ using a sum over all of these component seeds

\begin{align} U \equiv \sum_{i \, \sf{=1}}^{N} \varepsilon_{\it{i}} \hat{E}_{\it{i}} \end{align}

Definition: the number U is called the internal energy of P. The internal energy may be positive, negative or zero depending on a particle's composition and some choice for the calorimetric reference sensation.

To establish numerical values for the internal energy consider a down-quark defined by the pair of seeds

$\sf{d} \equiv \{ \sf{D}, \sf{O} \}$

Applying the foregoing definition of internal energy gives

$U^{\sf{d}} = \hat{E} \left( \sf{D} \right) - \hat{E} \left( \sf{O} \right)$

If a down-seed has the same specific energy as an ordinary conjugate-seed, then

$\hat{E} \left( \sf{D} \right) = \hat{E} \left( \sf{O} \right)$ and $U^{\sf{d}} =0$

Let us require experimental practice to obtain this this consistently; for example, by using the down quark as a reference particle to set the null value when measuring internal energy. Down quarks are objectified from black sensations, so this requirement could be interpreted as closing any shutters and using insulation so that a measuring instrument is completely isolated and in the dark when indicating zero. The other numbers shown in the accompanying table are obtained by juggling quark coefficients and laboratory observations1 of nuclear particles. The conventional unit used for reporting these measurements is one million electronvolts abbreviated as (MeV).

Theorem: an ordinary quark and its associated anti-quark have the same internal energy. Consider the generic quarks

$\sf{z} = \{ \sf{Z}, \sf{O} \}$ and $\bar{\sf{z}} = \{ \sf{Z}, \overline{\sf{O}} \}$

By the foregoing definition, the internal energies for these particles are given by

$U^{\sf{z}} = \hat{E} \left( \sf{Z} \right) - \hat{E} \left( \sf{O} \right)$ and $U^{ \sf{ \bar{z}}} = \hat{E} \left( \sf{Z} \right) - \hat{E} \left( \sf{\overline{O}} \right)$

But the hypothesis of conjugate symmetry asserts that

$\hat{E} \left( \sf{O} \right) = \hat{E} \left( \overline{\sf{O}} \right)$

so both quarks have the same internal energy and we can unambiguously use the quark index to refer to either one

$U^{\sf{z}} = U^{\sf{\bar{z}}} = U^{\zeta}$

 Adjective Definition Internal Energy \begin{align} U \equiv \sum_{i \, \sf{=1}}^{N} \varepsilon_{\it{i}} \hat{E}_{\it{i}} \end{align} 4-7