WikiMechanics

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 triple point 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 symbol $T$ 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 exponential function and the constant $k_{\tau} = \sf{ 2.6 x 10 }^{\sf{56}}$ seconds. Customarily, 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.¹ A particle with a negative temperature supposedly has a longer mean-life than hydrogen. But for WikiMechanics, the only particles like this are some quarks and field quanta that are not assigned positions. All models of observed nuclear particles have a positive thermodynamic temperature. 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 the assumption of conjugate symmetry, ordinary-quarks and anti-quarks both have the same temperature. So

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

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

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