Textile fragment (detail). Chancay people, pre-Hispanic Peru. Photograph by D Dunlop.
Recall that WikiMechanics uses the reference sensation of touching ice to calibrate the measurement of temperature. So to make good measurements we are getting more precise about what we mean by 'ice'. Accordingly, here is a definition of temperature that is tied to the of water. The thermodynamic temperature $\, T \sf{(K)} \,$ is defined by

$T \sf{(K)} \ \equiv \ \mathit{T} \sf{(ºC)} + \mathrm{273.15}$

where $\, T \sf{(ºC)} \,$ is the Celsius temperature. In the following discussion, the generic symbol $T$ always refers to the thermodynamic temperature, in units called kelvins, noted by (K).

Quarks are indestructible but compound quarks may decay. Their stability is characterized by a number called the mean-life. Let particle P be described by its thermodynamic temperature $T$. Definition: The mean life of P is

$\tau \equiv k_{\tau} e^{ -T}$

where $e$ is the and the constant $k_{\tau} = \sf{ 2.6 x 10 }^{\sf{56}}$ seconds. If $\sf{P}$ is an atom of Hydrogen in its ground-state, then $T=0 \ \sf{(K)}$ and $e^{ 0} = 1$, so this constant $k_{\tau}$ is called the mean-life of Hydrogen. Particle stability is also characterized by a number called the full width which is noted by $\varGamma$ and defined as

\begin{align} \varGamma \equiv \frac{h}{2 \pi \tau} \end{align}

The total number of any specific type of quark does not vary if ordinary-quarks are swapped with anti-quarks of the same type. And with conjugate symmetry ordinary-quarks and anti-quarks both have the same temperature. So

$\tau \left( \sf{P} \right) = \tau \left( \overline{\sf{P}} \right) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sf{\text{and}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \varGamma \left( \sf{P} \right) = \varGamma \left( \overline{\sf{P}} \right)$

Particles and their associated anti-particles have the same mean-life and full-width.

 Next step: the proton.
 Summary
 Adjective Definition Thermodynamic Temperature $T \sf{(K)} \ \equiv \ \mathit{T} \sf{(ºC)} + \mathrm{273.15}$ 8-4
 Adjective Definition Mean Life $\tau \equiv k_{\tau} e^{ -T}$ 8-5
 Adjective Definition Full Width \begin{align} \varGamma \equiv \frac{h}{2 \pi \tau} \end{align} 8-6
page revision: 242, last edited: 28 Jul 2017 21:51