Pressure
//Leptomedusae,// Ernst Haeckel, Kunstformen der Natur. Chromolithograph 32 x 40 cm, Verlag des Bibliographischen Instituts, Leipzig 1899-1904. Photograph by D Dunlop.
Leptomedusae, Ernst Haeckel, Kunstformen der Natur. Chromolithograph 32 x 40 cm, Verlag des Bibliographischen Instituts, Leipzig 1899-1904. Photograph by D Dunlop.

Let some particle P be represented by a chain of repetitive events

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

which are described by the total number of ordinary-quarks $N_{\sf{o}}$ that they contain, and $\tilde{ U } _{\! \sf{o}}$ the average internal energy of these ordinary-quarks. Moreover, let P be made of atoms so that it can be modeled as a cylinder of volume $V$ in a Euclidean space. Definition: the pressure inside P is the number

$\begin{align} P \equiv \frac{ -2 \, N_{\sf{o}} \tilde{ U} _{\! \sf{o}} }{V} \end{align}$

This expression describes ordinary quarks only, no anti-quarks included. But for particles with a lot of phase anti-symmetry like photons, quarks and anti-quarks are almost evenly matched. Then the total number of ordinary-quarks is close to half the number of all quarks $N_{\sf{o}} \simeq N /2$. Also, on average both sets of quarks will have the same internal energy $\tilde{U}_{\! \sf{o}} \simeq \tilde{U} \equiv U / N$. Then overall

$\begin{align} P \simeq \left( \frac{-2}{V} \right) \left( \frac{N}{2} \right) \left( \frac{U}{N} \right) = - \frac{U}{V} \end{align}$

and the pressure approximates an energy density due to all the quarks in P, not just the ordinary quarks.

$H-U = P V$

Right.png Next step: length.

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