I was supposed to give a talk on timekeeping this past weekend, but it got shot down (Mendozaaaa! Congress!), and I also see that Chad has posted slides on a talk he recently gave on the topic, entitled A Brief History of Timekeeping. That gives me a nudge to try and finish my series.

Posting slides is great, but that tells you little about the actual talk — the slides for good talks are an outline, and diagrams/pictures that save you the thousands words of description; when the speaker just reads the slides it’s generally not a particularly good talk. (I’ve never attended a talk by Chad, but given his track record with his blog, I imagine they are good.) I’ll start this with a comment, and I don’t know what the narrative was for those slides — so Chad might have mentioned this, but perhaps not.

A clock is something that ticks. This is true, but it doesn’t tell the whole story; a clock is something more than that. You need a recording device, too. Time is the phase of an oscillation, and as that phase accumulates you need to keep track of it, which is why we have displays that get updated with each “tick,” or something equivalent to that. If you lose the phase information, or never had it, you don’t know what time it is. A pendulum clock without the hands, gearing, etc. is just a pendulum. Think of it this way: a clock that is powered up (new, or after an interruption) isn’t a particularly useful device. What’s the first thing you do at that point? You check a working device, because you want to synchronize your clock, i.e. you want to transfer the phase information, and set the phase of your device. And that’s an important distinction, because most devices that are called “clocks” are really frequency standards. They get turned on an off regularly, running only part of the time; the phase information is recorded by other devices that stay on continuously, as a sort of flywheel. The overall performance is going to depend on how often your frequency standard runs, and how good your flywheel is.

We’ve used numerous devices to build clocks over the course of history, including the earth’s rotation and orbit. The earth is not really a great clock, because the orbit is elliptical and the axis is inclined, which leads to variation in the length of the day and having the sun not be overhead (or on the line going overhead) at noon. But you can correct for these effects, and that’s an important point — a bad clock that is predictably bad is actually a better clock, because you can make the corrections to figure out what time it is. Some of us have experience with this — the people that set their clocks ahead to try and trick themselves into not being late. The problem is that they know that their clock is 10 minutes fast, and they do the math to figure out what time it really is. (This is similar conceptually to a paper clock, where you have a calculated time, but not an actual device displaying it.) NYC does this in reverse (as it were) with trains; they set the departure time a minute late. How will it work now that the cat is out of the bag?

When the earth was the “master clock,” the other devices (pendulum clocks, water clocks, candles, hourglasses, etc.) were the flywheels to carry us through to the next day (or next sunny day), at which time you could recalibrate your flywheel device. Eventually these other devices got better, and we realized that the earth had limitations, and with the maturation of atomic clocks, we made a transition from having the earth (a single artifact) represent the “truth” of time, to having a recipe for building a standard, based on Cs-133’s ground-state hyperfine transition at 9192631770 Hz. This is the way it has proceeded for other standards as well — once experimental realizations are better than a physical artifact, we’ve abandoned the artifact for a recipe on how anyone can realize the standard. We’ve gotten rid of the meter, which used to be a metal bar, and once the technology improves enough, we will abandon the physical kilogram.

What we gain in this is better precision and accuracy, but what we lose is that there is no “truth” anymore. To answer that old question asked by Chicago, nobody really knows what time it is (though lots of people do, in fact, care). We have these devices, which we use to measure time as precisely as possible, but none of them is “right.” We arrive at a solution for time by intelligently measuring and averaging clock signals, but it’s now a “voted” quantity, rather than there being a defined truth. However — and this goes for all science — the important thing is that “not knowing exactly” is not the same as “have no idea whatsoever.” Time (or a time interval) is perhaps the most precisely measured phenomenon, with fractional frequency stabilities for the latest frequency standards measured at parts in 10^18.

Another nit I had with Chad’s slides is that he didn’t show enough variety in his fountain clocks. Some images are hard to find, but not impossible (though the resolution isn’t great). Here’s one of the USNO Rubidium Fountain clocks (actual clock, not frequency standard)