WikiMechanics

Horlogerie, Plate 1. Encyclopédie, ou Dictionnaire Raisonné des Sciences, des Arts et des Métiers. Edited by Denis Diderot and Jean le Rond d'Alembert, Paris 1768. Photograph by D Dunlop.

Let particle P be described by a chronologically ordered chain of events

and let this history of P be a repetitive sequence of sensations so that Ψ can also be written as

where each cycle is given by

Definition: particles like P are called clocks because chronological order implies that

where ϵ is the phase. So clocks juxtapose a regular variation in phase with a repetition of the sensations associated with P. The bundle of sensations Ω is called a clock cycle. Any set of sensations with this sort of lockstep relationship with the phase can be objectified as a clock. Historical examples include hearing a bell ring, or seeing a shadow move. Communally, some clocks are prefered for being exceptionally stable, cheap or accessible. We note these special clocks using the symbol Ω*. Traditionally, the daily variation in terrestrial events met this function. Now the standard is provided by microwaves emanating from vibrating caesium atoms.

Sensory interpretation: if the Earth is used as a frame of reference, then changes of phase are associated with the variation between day and night. Then the clock cycle Ω is a composition of one diurnal and one nocturnal event; a circadian cycle or nychthemeron. For this case, the index j is just a count of passing days.