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Frequency metrology outperforms any other branch of metrology in accuracy (parts in $10^{-16}$) and small fluctuations ($<10^{-17}$). In turn, among celestial bodies, the rotation speed of millisecond pulsars (MSP) is by far the most stable…

Terrestrial timescales show instabilities due to the physical limitations of the atomic clocks. Stricter environmental isolation and increased numbers of improved cesium clocks and cavity-tuned hydrogen masers have resulted in time scales…

Millisecond and binary pulsars are the most stable astronomical standards of frequency. They can be applied to solving a number of problems in astronomy and time-keeping metrology including the search for a stochastic gravitational wave…

Millisecond and binary pulsars are the most stable natural frequency standards which admits to introduce modified versions of universal and ephemeris time scales based correspondingly on the intrinsic rotation of pulsar and on its orbital…

Pulsars are the most stable macroscopic clocks found in nature. Spinning with periods as short as a few milliseconds, their stability can supersede that of the best atomic clocks on Earth over timescales of a few years. Stable clocks are…

Pulsars are natural cosmic clocks. On long timescales they rival the precision of terrestrial atomic clocks. Using a technique called pulsar timing, the exact measurement of pulse arrival times allows a number of applications, ranging from…

The phenomenal rotational stability of millisecond pulsars allows them to be used as precise celestial clocks. An array of these pulsars can be exploited to search for correlated perturbations in their pulse times of arrival due to…

We show how pulsar observations may be used to construct a time standard that is independent of terrestrial time standards. The pulsar time scale provides a method to determine the stability of terrestrial time standards over years to…

Pulsars are amongst the most stable rotators known in the Universe. Over many years some millisecond pulsars rival the stability of atomic clocks. Comparing observations of many such stable pulsars may allow the first direct detection of…

Radio pulsars are often used as clocks in a wide variety of experiments. Imperfections in the clock, known as timing noise, have the potential to reduce the significance of, or even thwart e.g. the attempt to find a stochastic gravitational…

Circadian clocks are the central timekeepers of life, allowing cells to anticipate changes between day and night. Experiments in recent years have revealed that circadian clocks can be highly stable, raising the question how reliably they…

Pulsars are remarkably precise "celestial clocks" that can be used to explore many different aspects of physics and astrophysics. In this article I give a brief summary of pulsar properties and describe some of the applications of pulsar…

Statistical estimation theory determines the optimal way of estimating parameters of a fluctuating noisy signal. However, if the estimation is performed on unreliable hardware, a sub-optimal estimation procedure can outperform the…

The radio millisecond pulsar J1713+0747 is regarded as one of the highest-precision clocks in the sky, and is regularly timed for the purpose of detecting gravitational waves. The International Pulsar Timing Array collaboration undertook a…

Optical clocks have improved their frequency stability and estimated accuracy by more than two orders of magnitude over the best caesium microwave clocks that realise the SI second. Accordingly, an optical redefinition of the second has…

We develop an abstract model of atomic clocks that fully describes the dynamics of repeated synchronization between a classical oscillator and a quantum reference. We prove existence of a stationary state of the model and study its…

Pulsar timing, i.e. the analysis of the arrival times of pulses from a pulsar, is a powerful tool in modern astrophysics. It allows us to measure the time delays of an electromagnetic signal caused by a number of physical processes as the…

Precision pulsar timing requires optimization against measurement errors and astrophysical variance from the neutron stars themselves and the interstellar medium. We investigate optimization of arrival time precision as a function of radio…

Pulsars are the most stable natural frequency standards. They can be applied to a number of principal problems of modern astronomy and time-keeping metrology. The full exploration of pulsar properties requires obtaining unbiased estimates…

Analysis of high-precision timing observations of an array of approx. 20 millisecond pulsars (a so-called "timing array") may ultimately result in the detection of a stochastic gravitational-wave background. The feasibility of such a…