Measuring time

• SUMMARY: A variety of mathematical calculations are used to define, measure, and apply measurements of time.

Time measurement (chronometry) serves two tasks: (1) indication of temporal instants, which are events occurring in time, and (2) determination of temporal extensions (durations), which are amounts of time between events. Both types of tasks are essential for practical purposes, such as the organization of life in civilized societies or intersubjective synchronization of various activities, as well as for the scientific study of nature and society. Time measurement relies upon the arithmetic model of time: events are mapped onto a numerical continuum so that if event A precedes event B, the relation tA < tB holds between their time indices; such a mapping is called a “timescale.” Given a timescale t, durations can be calculated as differences between time indices, and conversely, time indices can be defined by durations elapsed from a certain reference event (epoch).

Clocks and Timescales

Theoretical chronometry studies the mathematical properties of timescales, while practical chronometry (called “horology”) is concerned with devices realizing timescales, such as clocks. Any physical system, natural or artificial, producing a series of distinct and observable—thus countable—events can serve as a clock. Periodic processes in our lifeworlds, such as the day/night cycle, the lunar cycle, or seasonal changes, provide natural bases for timekeeping and measurement. Counting recurrent observable events yields a measure of durations longer than the clock’s basic period; measurement of shorter times than the clock’s base period enforces a subdivision of the period into equal sub-units—a refinement of the timescale. Therefore, time measurement spanning several orders of magnitude requires the alignment of timescales defined by different physical processes, periods of which are in constant arithmetic relations and, thus, together, define a common timescale. For this purpose, timescales generated by artificial clocks are used.

Predecessors of clocks were devices used to indicate one standard time period, for example, outflow water clocks (clepsydrae), sand glasses, or burning candles. A clock, in the proper sense of the word, generates a series of events at equal periods between them. In history, different physical principles have been used to ascertain isoperiodic clock action, including mechanical oscillations of a pendulum or a balance wheel, vibrations of quartz crystals or molecules in electromagnetic fields, and electromagnetic radiation emitted/absorbed by atoms, providing high-precision frequency standards. Base periods of clocks vary from a few seconds to fractions of a second in mechanical clocks, down to an accuracy of 10-10 seconds per day for atomic clocks, as established by national standards agencies.

The Second

The second (s) is the fundamental unit of temporal duration. Originally, the second was defined as a constant fraction (1/86,400) of the solar day. Hence its name: 1 day is 24 hours, 1 hour is 60 minutes (pars minuta prima, which means “first minor part”), 1 minute is 60 seconds (pars minuta secunda, which means “secondary minor part”). With increasing precision of time measurement, fluctuations of the Earth’s rotation period had become evident; thus, the second was redefined in the 1950s as a constant fraction (1/31,556,926) of the period of the Earth’s orbital motion around the sun (ephemeris time). In 1967, a new definition of the second was adopted; one second is defined as a constant multiple (9,192,631,770) of the period of electromagnetic radiation emitted by cesium atoms in transition between two defined energetic states under precisely specified conditions. Thereby, astronomic definitions were abandoned in favor of standards derived from the inner structure of matter, which is considered constant throughout the Universe.

Time Measurement Technologies

Advanced time measurement and synchronization technologies allow people to define a unique time scale to be used worldwide. Historically, the first universal timescale was Greenwich Mean Time (GMT), based on telescopic observations at the Royal Observatory in Greenwich, England, which was later replaced by the international Universal Time (UT). One of the most precise basis for timekeeping is International Atomic Time (TAI), based on a worldwide network of atomic clocks. Coordinated Universal Time (UTC) is the basis for international timekeeping. UTC differs from TAI by an integer number of seconds to approximate UT. Irregularities in Earth’s rotation are compensated by adding or subtracting a leap second to/from the UT-TAI offset, if necessary; the corrections take place on June 30 or December 31. In this way, uniformity of UTC with respect to the atomic time unit definition is maintained, and continuity with the astronomical timescale is preserved. One of the most accurate types of clocks is the cesium clock, which uses the resonant frequency of the cesium nucleus to establish a time standard. However, in mid-2024, researchers achieved a breakthrough in nuclear timekeeping that they hoped would lead to the development of the first ultra-precise nuclear clock.

Time Calculations

Irreversible natural processes, laws of which are well known, can be used to calculate time extensions, particularly those escaping direct observation and measurement. Of special importance are estimations of geological or archaeological age based on radioactive decay of certain elements or particular isotopes of otherwise stable elements. Estimates of time extensions in astrophysics are largely theory-based (for example, dependent on stars’ evolution models). This dependency applies a fortiori to time magnitudes discussed in cosmology. Any time measurement implies observational (or at least conceptual) separation between the measured process and the reference process, defining the timescale. If the universe as a whole is considered, such separation is no more possible, so that the notion of the universal “cosmic” time meets logical difficulties.

Finally, there is no direct evidence that timescales defined by different classes of physical processes (inertial motions, light radiation, or radioactive decay) are really equivalent: the “unity of time” in physics is a convenient hypothesis, not an empirically secured fact. Since precise time measurements are available only for a short historical period—negligibly short relative to cosmological orders of magnitude—the alignment of radiation-based and motion-based timescales is merely temporally “local.” Some cosmologists suggested that different classes of physical phenomena may define different timescales between which a nonlinear relation may hold. Consequently, two or more different time measures might be needed to adequately describe cosmic processes on a large scale. However, research concerning the measurement of time and its accuracy continues to evolve. In 2022, researchers from Sweden's Uppsala University discovered a revolutionary way of measuring time that does not require a starting point using the Rydberg state of atoms.

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