Time, Operational Definition of

All the quantities physicists call “observables” are operationally defined; that is, they are specified in terms of measurements performed [Page 1294]by well-prescribed measuring procedures. Temperature is what we measure with a thermometer. Voltage is what we measure with a voltmeter. Following Einstein, time is operationally defined by what is measured on a clock. Whatever its construction, a clock will provide a series of ticks and a counter of those ticks.

Almost any series of repetitive events, such as your own heartbeats, can be used as a clock. However, defining time by your heartbeats would result in physics equations that would have to be written in such a way as to take into account your daily activity. The time it takes an object to fall from a given height would be less on a day that you sat around at the computer than on a day when you ran a marathon. Obviously, for the sake of simplicity and the desire to describe reality in an objective way, we should use some more universal measure of time.

Throughout history, time has been measured by highly repeatable, nonsubjective events such as day and night, the phases of the moon, and other observations in the heavens. While astronomical calendars, divided into days and hours, suffice for the timing of familiar events, science has required a finer scale that does not have to be constantly recalibrated because of the irregularity of earth's movements. Galileo introduced the pendulum as a timing device for experiments, and even today mechanical clocks and watches rely on the pendulum to provide uniformity and accuracy. However, science has greatly improved the methods for standardizing time, and the mechanical clock has become obsolete except as an attractive piece of antique jewelry or furniture.

Today the standard of time is set by atomic clocks. The second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine energy levels of the ground state of the cesium-133 atom at rest at absolute zero. Since observing such an atom is impossible, this requires a theoretical extrapolation to get the above value. The National Institute of Standards and Technology (NIST) and the United States Naval Observatory now provide a time source stable to 100 picoseconds (10∼10 second) per day as a satellite signal. However, the primary time and frequency standard is now provided by averaging a set of Cesium Fountain atomic clocks at the NIST laboratory in Boulder, Colorado, which at this writing will not gain or lose a second in more than 60 million years.

All of the observables in physics are now calibrated against the time measured on the standard clock. In particular, the distance between two points in space was defined by international agreement in 1983 to be proportional to the time measured on a standard clock for light to travel between the two points in a vacuum. Specifically, the international standard unit of length, the meter, is the distance traveled by light in 1/299,792,458 of a second in a vacuum.

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