Lifetime
//Textile fragment// (detail). Chancay people, pre-Hispanic Peru. Photograph by D Dunlop.
Textile fragment (detail). Chancay people, pre-Hispanic Peru. Photograph by D Dunlop.
knut.jpeg
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 pointXlink.png 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 exponential functionXlink.png 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.

Right.png 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
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License