Caesium Seconds

The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical frequency ΔνCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s⁻¹

NIST F2 and friends

Imagine a single caesium atom (or "cesium" atom if you stick to the American English spelling). Imagine this atom alone, at rest, undisturbed, at a temperature of absolute zero. Counterfactually, suppose that the unpaired electron of this atom in its ground state were to be irradiated with the precise frequency of light to bump the electron from its lowest energy state into the next lowest energy state, and then that the resulting radiation released as the electron returned to its lowest energy state is recorded. Call the frequency of the resulting radiation ΔνCs. By fiat, set ΔνCs = 9,192,631,770 Hz. Since the unit Hz expresses cycles per second, this means that, by definition, the duration of a second is precisely 9,192,631,770 cycles of the radiation resulting from this particular energy transition in the ceasium atom. 

Why choose the caesium standard? One reason is that this definition allows of high precision. Another, is that the second thereby defined is very close to the historical definition of the second, which referenced astronomical phenomena.

But as is immediately obvious, there isn't any actual, physical clock that perfectly instantiates the idealized system described in the definition of the second. Real clocks cannot be cooled to absolute zero. They can be cooled to close to absolute zero, but not exactly zero. Even if they could, one couldn't make measurements of such a system without disrupting this pristine state. 

Does this mean that no actual clock really measures time? It turns out that this is a difficult question to answer! 

Actual "standard" clocks, like the NIST F2 caesium fountain clock depicted above involve bunches of caesium atoms that are cooled and temporarily held in place by lasers, guided through a cavity in which they absorb some microwave radiation (the frequency of which can be adjusted), and then are allowed to fall back into a position where the radiation that the atoms emit can be detected. The microwave frequency in the cavity is adjusted via a feedback loop to maximize the peak of the the radiation emitted by the caesium atoms. If the radiation in the cavity is not quite "in tune" with the energy that the caesium atoms needs to absorb to bump their electrons up to the next energy level, then the signal from the bunch of caesium atoms won't be very strong. But when the frequency is tuned just right, many atoms in the bunch will be able to absorb the radiation and then re-emit radiation at that "just right" frequency. Whatever the frequency of radiation is that gets the maximum signal is defined to be 9,192,631,770 Hz. 

One way of thinking about what is going on here is that the duration measured by an actual, physical caesium fountain clock approximates the true duration of a terrestrial second, which is not actually measurable in practice due to the idealized nature of the definition of the second. (I say "terrestrial" second, because on account of relativistic time effects, we also have to suppose that the ideal caesium clock is positioned on a "geoid" at sea level and read by a distant observer, see Tal 2016, 302). Actually, the story of the measurement of time is even more complicated, because the standard second that people actually use does not derive from even a single caesium fountain clock, but rather from a significantly more complicated procedures involving several such "primary" clocks that are used to periodically calibrate hundreds of "secondary" clocks all over the world, whose results are then combined into a weighted average, to which further "steering" corrections are then made. This calculated time is called international atomic time (TAI). To get coordinated universal time (UTC), "leap seconds" are occasionally added to TAI in order to keep our time standard in step with astronomical/geological phenomena (see this fun article from Slate to learn about why we need leap seconds--hint: it has to do with the Moon). So one could think about the the calculated UTC as approximating real terrestrial time.

However, in his 2016 article "Making Time: An Study in the Epistemology of Measurement", Eran Tal cautions against this sort of interpretation: 

UTC is not an estimator of a mind-independent parameter whose value metrologists are trying to approximate, but an abstract artefact in its own right that metrologists attempt to stabilize (much like their attempts to stabilize material artefacts) (fn 21)

 In other words, there is a sense in which UTC is not an estimation or approximation of time, but rather time as constructed by metrologists! Tal is willing to say that metrologists still "measure time" but what this means is a bit subtle. For Tal, metrologists successfully stabilize measurement standards (like UTC) via "interlocking steps of legislation and empirical discovery, both of which are mediated by models" (2016, 328). In particular, metrologists "legislate" in the sense that they made decisions about which measuring systems to use and how to model them. But metrologists also pay attention to "gaps" that arise in concrete applications--discrepancies in the applications of the same time concept in different instruments and circumstances (Tal 2016, 327). Metrologists inform their legislative decisions in part based on what they learn from the presence or absence of such discrepancies. So, on Tal's view (the "model-based account") standard clocks do not measure terrestrial time, rather the measurement outcomes of such clocks are standardized through an iterative process involving choices made by human beings and information gleaned from the operation of physical instruments in order to "co-constitute" standard time (2016, 328-329). Noting that pragmatic, social, economical, and political considerations enter into the choices that metrologists make in calculating UTC (see p. 305) helps to clarify the senses in which UTC differs from time in theoretical physics.