Cause and Effect
//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.
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 a rigid 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. More vaguely, we say that P is stable. P's events are causally linked to each other. 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 1036 seconds so $\hat{\tau} \ll \tau$ for protons. And for electrons, the period is about 10-20 seconds with a lifetime of more than 1034 seconds. So both the proton and electron are extremely stable particles. This gives them starring roles in narratives connecting cause and effect.

Right.png Next step: decay.
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