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 271
2 d d 0
3 e e -0.1
4 g g 0.07
5 m m 0.03
6 a a 0.02
7 t t 149
8 b b -85
9 s s 50
10 c c -53

\mbox{\fontsize{14}{18}\selectfont $ \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

\mbox{\fontsize{14}{18}\selectfont $ \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 and its specific energy Ê. We characterize P using a sum over all of these component seeds

\mbox{\fontsize{14}{18}\selectfont $ \it{U} \equiv \sum_{i\sf{=1}}^{N} \sf{\grave{\varepsilon}}^{\it{i}} \it{\hat{E}}^{\it{i}} $}

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.

achromatic.jpg
To establish numerical values for the internal energy, consider a down-quark d for which

\mbox{\fontsize{14}{18}\selectfont $ U^{\,\sf{d}} = \hat{E}^{\sf{D}} - \hat{E}^{\sf{O}} $}

If the calorimetric reference sensation is chosen so that a down-seed has the same specific energy as an ordinary conjugate-seed, then

\mbox{\fontsize{14}{18}\selectfont $ \hat{E}^{\sf{D}} = \hat{E}^{\sf{O}} \ \ \ \ \ \ \ \text{\large{\sf{and}}} \ \ \ \ \ \ \ U^{\,\sf{d}} =0 }$}

Let us do this consistently so that the down-quark serves as a reference particle for setting the energy null value. The other numbers shown in the accompanying table can be obtained from laboratory observations of nuclear particles. The conventional unit used for reporting these measurements is one million electron-volts abbreviated as (MeV).

Theorem: an ordinary quark and its associated anti-quark have the same internal energy. To see this, consider the generic quarks

\mbox{\fontsize{14}{18}\selectfont $ \sf{z} = \left\{ \sf{Z}, \sf{O} \right\} \ \ \ \ \text{\large{\sf{and}}} \ \ \ \ \overline{\sf{z}} = \left\{ \sf{Z}, \overline{\sf{O}} \right\} $}

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

\mbox{\fontsize{14}{18}\selectfont $ U^{\,\sf{z}} = \hat{E}^{\sf{Z}} - \hat{E}^{\sf{O}} \ \ \ \ \ \ \ \text{\large{\sf{and}}} \ \ \ \ \ \ \ U^{\,\sf{\overline{z}}} = \hat{E}^{\sf{Z}} - \hat{E}^{\sf{\overline{O}} }$}

But the hypothesis of conjugate symmetry asserts that

\mbox{\fontsize{14}{18}\selectfont $ \hat{E}^{\sf{O}}} = \hat{E}^{\sf{\overline{O}}}} $}

so both quarks have the same internal energy

\mbox{\fontsize{14}{18}\selectfont $ U^{\,\sf{z}} = U^{\,\sf{\overline{z}}} = U^{\,\zeta} $}

and we can unambiguously use the quark index to refer to either one.

Right.png
Next step: temperature.
page_revision: 776, last_edited: 1283445858|%e %b %Y, %H:%M %Z (%O ago)
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