We were talking about experiments concerning special relativity, and I said that an atomic clock was super accurate. My son asked what exactly that meant. This question befuddled me, because I realized I couldn’t come up with a non-arbitrary way of defining a “true” second. Wikipedia informs us:
The second (symbol: s) is the base unit of time in the International System of Units (SI) and is also a unit of time in other systems of measurement (abbreviated s or sec); it is the second division of the hour by sixty, the first division by 60 being the minute. Between 1000 CE (when al-Biruni used seconds) and 1960 the second was defined as 1/86,400 of a mean solar day (that definition still applies in some astronomical and legal contexts). Between 1960 and 1967, it was defined in terms of the period of the Earth’s orbit around the Sun in 1900, but it is now defined more precisely in atomic terms. Seconds may be measured using mechanical, electric or atomic clocks.
Astronomical observations of the 19th and 20th centuries revealed that the mean solar day is slowly but measurably lengthening and the length of a tropical year is not entirely predictable either; thus the sun–earth motion is no longer considered a suitable basis for definition. With the advent of atomic clocks, it became feasible to define the second based on fundamental properties of nature. Since 1967, the second has been defined to be:
the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
In 1997, the CIPM affirmed that the preceding definition “refers to a caesium atom at rest at a temperature of 0 K.”
I encourage you to really think through the philosophical implications of the above. Obviously, humans initially adopted units of time based on convenience and the regularity of planetary events. But you can see how humans refined the very definition of units of time, over the centuries. I’m having a hard time putting into words just how mind-blowing that is. It’s not analogous, say, to refining the measurement of the charge on an electron. But it’s also not analogous to deciding that “bad” can mean “good” if used by gang members.
Something like this happens in economics and libertarian political philosophy, where the original practitioners start out with a concept, and then over time it is refined to better get at the spirit of the original concept, even though it no longer directly corresponds to the original concept. For example, how indifference curves replaced cardinal utility in the work of Pareto (if I’m remembering my Hicks correctly).