It's About Time, Part III

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)


Is Gravity Ruining Time?

I’ve mentioned I’m at a conference — it’s the 7th Symposium of Frequency Standards and Metrology being held near Monterey. It’s a bunch of scientists getting together every ~7 years to discuss the state-of-the art in frequency standards, clocks, and precision measurements, and float ideas for future experiments. The last one was in St. Andrews, Scotland in 2001 (unfortunately it spanned 9/11/2001, which was a bit of a distraction, to say the least.)

There have been a lot of talks that I couldn’t possibly distill into coherent summaries, but I’ll try to do one or two when I get the chance. I’ve got one for now, though, that doesn’t require as much heavy lifting.

Dan Kleppner gave the first talk (Is Gravity Ruining Time?) as a sort of introduction, and gave some perspective on timekeeping, since he has been doing physics from before the development of the hydrogen maser (making him, as he put it, prehistoric). Two main things came out of this talk: an appreciation of a limitation on how we define the second, and a story about I.I. Rabi.

The second is defined as 9,192,631,770 oscillations between the hyperfine states of an unperturbed cesium-133 atom, but this definition does not explicitly mention anything about relativity, of which gravity is a part. It’s basically taken by convention that we use devices at rest on the geoid (an idealized surface of the earth, basically what it would look like without tides) but devices have reached the point where this may not be good enough. The gravitational redshift is given by gh/c^2 near the earth, and this is about a part in 1016 per meter change in height. Clocks need to be adjusted for their altitude/elevation, and this has been necessary for some time; the effect has been measured in the Pound-Rebka experiment and in the rocket launch of a hydrogen maser by Robert Vessot, and is accounted for in GPS and every other satellite carrying a clock. But ground-based clocks are now getting to be good enough to where sub-meter changes in height will need to be taken into account. And since the geoid can only be determined to several cm and it changes with time (and clocks move with respect to the geoid via earth tides of about 30 cm), this will soon become a significant term in the error budgets of frequency standards. So the point of the talk was that gravity is going to take a more prominent role in frequency and time measurements, and may in fact require a redefinition of the second, though it would not impact “everyday” time.

The story he told about Rabi went something like this: Rabi didn’t like writing articles, so there is no formal writeup of his proposal to use an oscillator tuned to a hydrogen transition as a time measurement device — the idea that would eventually become the hydrogen maser and used in other atomic clocks. But in 1945, after he had the Nobel prize, he gave the Richtmyer lecture to the American Association of Physics Teachers on the topic of using a hydrogen magnetic resonance measurement as a potential timekeeping device, and it was written up by the New York Times science correspondent, William Laurence, in an article called ‘Cosmic Pendulum’ For Clock Planned, in which he gives a very basic summary of the principles Rabi had explained. So the cutting-edge science was “formally” proposed in the Times rather than a science journal. In the AAPT’s list of Richtmyer lectures, Rabi’s is one of the few from that era that were not written up and presented in the American Journal of Physics.

(The Times article is here but the archive is paywalled)

Dropping the Minus Sign

Or, in this case, the “not”

Why aluminum should replace cesium as the standard of time

The technique involved is neat: for some atoms you can find wavelengths where the AC Stark shift is the same for the two levels in the clock transition, so the atom is unperturbed by the presence of the trapping light. So you trap them in an optical lattice, with confinement like a far off-resonance dipole force trap (FORT). This means you can continue to confine the atoms while it is in the superposition where it is oscillating between the two clock states.

The big advantage of this method is that you can trap millions of atoms easily in an optical lattice and that should make such a clock much more robust than a fountain, while achieving at least the same kind of accuracy.

Actually, that’s not the big advantage. Fountains trap millions of atoms (even billions, depending on your collection technique). The advantages are that you’d keep that many atoms (fountains lose signal from the original collection because the cloud spreads out, so the number you toss is an order of magnitude bigger than the number that return), you can interrogate the atoms for a longer period of time (an advantage shared by ion trap clocks/frequency standards) and avoiding cold-collision frequency shifts (atoms in close proximity tend to interact strongly, as they can interact for a relatively long time, and this changes the state of the atom, introducing an error in the signal)

However, “at least the same kind of accuracy” isn’t enough. I’ve noted before that international standards are a political issue. Cesium beam standards are commercially available. Furthermore, dozens of labs have or are building fountains, at some investment of time and money to gain the expertise in doing so (because atomic fountains are not, nor are they likely to become, a commercially available item). The countries doing this will likely be reluctant to switch to a standard that requires even more money and acquired expertise in a new technique for marginal gain in accuracy and precision. Especially in light of how many new options for secondary standards have emerged in just the last decade — an even better candidate may emerge as technology advances.