Tampan, Paminggir people. Lampung region of Sumatra, Kota Agung district, circa 1900, 38 x 37 cm. From the library of Darwin Sjamsudin, Jakarta. Photograph by D Dunlop. |

Consider a particle P that is described by $\tau$ its lifetime, its orbital period $\hat{\tau}$ and some historically ordered chain of events

$\Psi ^{\sf{P}} = \left( \sf{P}_{\it{i}} \ \ldots \ \sf{P}_{\it{f}} \right)$

If P is perfectly isolated then its initial and final events are determined by formation and decay. And with an ideal frame of reference its period does not vary. Then the elapsed time between initial and final events is P's lifetime and all these quantities are related as

$\tau = t_{\it{f}} - t_{\it{i}} \equiv \Delta t = \left( \, f-i \right) \hat{\tau}$

Let Ψ be a chain of very many events so that

$i +1 \ll f$

For this case the lifetime must be much greater than the orbital period

$\begin{align} 1 \ll \, f-i = \frac{ \tau }{\, \hat{\tau} \, } \end{align}$

and so probably P will *not* decay during any specific cycle. P is steady and consistent. One orbit will almost invariably follow another with dependable regularity. This predictability is useful for the practice of engineering, so we give the events of particles like this special names. Definition: if

$\hat{\tau} \ll \tau$

then the initial event of $\Psi$ is called a **cause** and the final event is called an **effect** of the cause. P's events are causally linked to each other. We say that P is **stable**. For example consider the proton in its ground-state. It has a period $\hat{\tau}$ of about 10^{-24} seconds, so in principle we could assign a very precise time of occurrence to events in any history of a proton. The lifetime $\tau$ is more than 10^{36} seconds so $\hat{\tau} \ll \tau$ for protons. And for electrons, the period is about 10^{-20} seconds with a lifetime of more than 10^{34} seconds. So both the proton and electron are *extremely* stable particles. This gives them starring roles in narratives connecting cause and effect.

Related WikiMechanics articles.