Ask Ethan #30: Long-term timekeeping

In this week’s Ask Ethan, we take on perhaps the longest question of them all, and look at how to keep time for arbitrarily long times.

It’s a good post as usual, though there are a few things Ethan glosses over, which is where I step in.

[millisecond pulsars] are also the most accurate clocks we’ve ever discovered. They are so regular that we could watch one, look away for a year, and know — when we look back — whether ten billion pulses have gone by… or whether it’s ten billion-and-one. In fact, we can get down to around microsecond accuracy to their timing over periods of many decades, meaning we can get timing accuracy to around one part in 10^15!

This is bettered only by the most advanced atomic clocks on Earth

In terms of fractional stability that’s true (and I think he means precision rather than accuracy here), but Tom- man-made atomic clocks reach this stability in a matter of hours or days, not years. It’s only by having these good clocks that we can measure how well the pulsars are doing.

I have a recollection of a discussion about timing with pulsars from years ago (this isn’t a new idea). Pulsars don’t actually have an inherently stable frequency — they are slowing down, just like other macroscopic spinning objects, so the timing will show a drift. But pulsars do this at a very predictable rate, so you can characterize them and account for the drift. Some pulsars haven’t “settled in” and can undergo a star quake, which changes their rotation abruptly, but I think the ones under discussion are past that age.

From his followup post

Atomic clocks require a lot of power to continuously stimulate atomic transitions, and a lot of cryogenic fuel to keep the atoms at ultra-low temperatures. Not such a big deal when you’re talking about doing this in a continuously powered laboratory on Earth, but that’s a lot of resources to devote to keeping a simple clock running. The mechanism I gave in the original article — counting atoms or looking at a pulsar — has the advantage that all you have to do is look once at the beginning and once at the end, and requires no devoted power in the intermediate time.

The cryogenics part is a common misconception, since the best clocks are cold-atom clocks. So the assumption is understandable, but these clocks are all offshoots of laser cooling and trapping. Some crystal oscillators in frequency standards are cryogenic, but not in any continuously-runnung clock. That’s a logistical nightmare.

I think our clocks are not getting quite as much respect as they deserve — the pulsars have to be characterized to be useful, and no two pulsars are going to have the same frequency. You could, in principle make a stable reference from measuring several of them, but to actually tell time you have to tie it back to a standard, which means a man-made device.

The second part, about radioactive decays, stresses the longevity of the clock but ignores the precision of the measurement. Unless you have a huge chunk of the material and can determine the number of atoms precisely, your counting statistics will limit the precision of your measurement.

The upshot of all this is that timing is a little more subtle than having something that will tick for a long time. Accuracy, precision and durability aren’t interchangeable attributes. There are often tradeoffs between each of them, so it depends on which is more important.