Time measurement: general concepts
Accuracy in specifying time is needed for civil, industrial, and scientific purposes. Although defining time presents difficulties, measuring it does not; it is the most accurately measured physical quantity. A time measurement assigns a unique number to either an epoch, which specifies the moment when an instantaneous event occurs, in the sense of time of day, or a time interval, which is the duration of a continued event. The progress of any phenomenon that undergoes regular changes may be used to measure time. Such phenomena make up much of the subject matter of astronomy, physics, chemistry, geology, and biology. The following sections of this article treat time measurements based on manifestations of gravitation, electromagnetism, rotational inertia, and radioactivity.
Series of events can be referred to a time scale, which is an ordered set of times derived from observations of some phenomenon. Two independent, fundamental time scales are those called dynamical--based on the regularity of the motions of celestial bodies fixed in their orbits by gravitation--and atomic--based on the characteristic frequency of electromagnetic radiation emitted or absorbed in quantum transitions between internal energy states of atoms or molecules.
Two time scales that have no relative secular acceleration are called equivalent. That is, a clock displaying the time according to one of these scales would not--over an extended interval--show a change in its rate relative to that of a clock displaying time according to the other scale. It is not certain whether the dynamical and atomic scales are equivalent, but present definitions treat them as being so.
The Earth's daily rotation about its own axis provides a time scale, but one that is not equivalent to the fundamental scales because tidal friction inexorably decreases the Earth's rotational speed (symbolized by the Greek letter omega,). There are also other sources of variation. Rotational time is needed for civil purposes, celestial navigation, and tracking of space vehicles.
The decay of radioactive elements is a random, rather than a repetitive, process, but the statistical reliability of the time required for the disappearance of any given fraction of a particular element can be used for measuring long time intervals.