Temperature

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

Quark Temperatures
ΞΆ z z T (C)
1 u u 96
2 d d 1,906
3 e e -57
4 g g 1,398
5 m m 11
6 a a -122
7 t t 91
8 b b 0
9 s s 33
10 c c 100

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

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

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

and each seed is known by its audibility $\varepsilon$ and its vis viva $\hat{K}$. The particle is characterized by a sum over these component seeds

$\begin{align} T \equiv \frac{2}{Nk_{B}} \sum_{i\sf{=1}}^{N} \varepsilon ^{\it{i}} \it{\hat{K}}^{\it{i}} \end{align}$

where $k_{B}$ is Boltzmann's constant. Definition: the number $T$ is called the temperature of P. The temperature may be positive, negative or zero depending on the particle's composition and the choice of a thermometric reference sensation. To establish numerical values start with the bottom-quark

$\sf{b} \equiv \{ \sf{B}, \sf{O} \}$

for which

$T^{ \sf{b}} \, k_{B} = \it{\hat{K}} \left( \sf{B} \right) - \it{\hat{K}} \left( \sf{O} \right)$

If a bottom-seed has the same vis viva as a conjugate-seed

$\it{\hat{K}} \left( \sf{B} \right) = \it{\hat{K}} \left( \sf{O} \right)$ and $T^{\sf{b}} =0$

knut.jpeg
Consider experimental practice to obtain this consistently; for example, by using bottom quarks as a reference to calibrate the measurement of temperature. This would depend on what we mean by touching ice because this feeling was used to define cold reference sensations and objectified to define bottom seeds. But there are many different kinds of ice and to make reliable measurements we therefore need to specify the reference sensation more precisely. So, by "touching ice" we mean; touching a slushy mix of frozen solid water and clean pure liquid water in an open container near sea level on Earth. This is a utterly conventional way of defining zero on the Celsius temperature scale. So we note such a convention by calling T the Celsius temperature and using the CelsiusXlink.png degree (C) for a temperature unit.
steam.jpg
We have also defined the charmed quarks using the reference sensation of touching steam. And since there are different kinds of steam we also need to specify this sensation more carefully. So, by "touching steam" we mean; touching the vapors rising from an open container of pure boiling water near sea level on Earth. This is a very traditional way of defining 100 (C). Charmed quarks are objectified from this sensation, so we require that their temperature is 100 (C). The other temperatures listed in the accompanying table are obtained by juggling quark coefficients and laboratory observations1 of nuclear particles.

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

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

By the foregoing definition, the temperature of these particles is given by

$T^{\sf{z}} \it{k_{B}} = \hat{K} \left( \sf{Z} \right) - \hat{K} \left( \sf{O} \right)$ and $T^{ \sf{\bar{z}}} \it{k_{B}} = \hat{K}\left( \sf{Z} \right) - \hat{K} \sf{(} \sf{\overline{O}} \sf{)}$

But the hypothesis of conjugate symmetry presumes that

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

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

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

Click here for more about the temperature of compound quarks.

Summary
Adjective Definition
Temperature $\begin{align} T \equiv \frac{2}{Nk_{B}} \sum_{i\sf{=1}}^{N} \varepsilon ^{\it{i}} \it{\hat{K}}^{\it{i}} \end{align}$ 4-8
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