In theoretical physics, the word “oscillator” refers to a physical object or quantity oscillating sinusoidally – or at least periodically – for a long time, ideally forever, without losing its initial energy. An example of an oscillator is the classical atom, where the electrons rotate steadily around the nucleus. Conversely, in experimental science the word “oscillator” stands for an artifact that delivers a periodic signal, powered by a suitable source of energy. In this book we will always be referring to the artifact. Examples are the hydrogen maser, the magnetron of a microwave oven, and the swing wheel of a luxury wrist watch. Strictly, a “clock” consists of an oscillator followed by a gearbox that counts the number of cycles and the fraction thereof. In digital electronics, the oscillator that sets the timing of a system is also referred to as the clock. Sometimes the term “atomic clock” is improperly used to mean an oscillator stabilized to an atomic transition, because this type of oscillator is most often used for timekeeping.

A large part of this book is about the “precision” of the oscillator frequency and about the mechanisms of frequency and phase fluctuations. Before tackling the main subject, we have to go through the technical language behind the word “precision,” and present some elementary mathematical tools used to describe the frequency and phase fluctuations.