Let these events be historically ordered. Then and are called the initial and final events of . And if the particle is perfectly isolated then and are established by the formation and decay of P. With an inertial frame of reference, the period does not vary. Then the elapsed time between initial and final events is P’s lifetime, and all these quantities are related as
Let be a chain of very many events so that
For this case the lifetime must be much greater than the orbital period
and we say that P is stable. Then it is probable that 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, so we give the events of particles like this special names. If
then the initial event of is called the cause, and the final event is called the effect of the cause. We may say that P’s events are causally linked to each other. For example consider the proton in its ground-state. It has a period of about 10-24 seconds, so in principle we could assign a very precise time of occurrence to any events in the history of a proton. The lifetime is more than 1036 seconds, so 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.