A clock is an instrument for the measurement of time (e.g. in seconds). It supplies a numerical comparison between the durations of different time intervals. For example, a clock will provide the ratio of the duration of one day to the duration of a different day (e.g. the earth could be spinning slower today than it did a billion years ago. If the earth's spin is used as a clock its spin will be exactly constant by definition.)
The notion of an ideal clock
An ideal clock appropriately measures the ratio of the duration of natural processes, and thus will give the appropriate time measure for use in physical theories. Therefore, to define an ideal clock in terms of any physical theory would be circular. An ideal clock is more appropriately defined in relationship to the set of all physical processes. This leads to the following definition: An ideal clock is a recurrent process which makes the most other recurrent processes periodic..
This definition can be further improved by the consideration of successive levels of smaller and smaller error tolerances.
While not all physical processes can be surveyed, the definition should be based on the set of physical processes which includes all individual physical processes which are proposed for consideration. Since atoms are so numerous and since, within current measurement tolerances, they all beat in a manner that if one is chosen as periodic then the others are all deemed to be periodic also, it follows that atomic clocks presently represent ideal clocks to within present measurement tolerances and in relation to all presently known physical processes. However, they are not so designated by fiat. Rather they are designated as the current ideal clock because they are currently the best instantiation of the definition.