A couple fun facts about time

I recently finished Time: From Earth Rotation to Atomic Physics (Internet Archive), an exceptionally nerdy book. There’s a lot (probably most of it) I didn’t understand (turns out Earth’s rotation and other motion is hella complicated!), but it’s satisfying just to know that there’s so much knowledge out there.

Since today is change-the-clocks day here in the US, I wanted to share a couple fun facts that stood out to me.

Sometimes, assumptions need checking

In 1695, Edmund Halley (of comet fame) noticed that the Moon’s motion was speeding up. For the next one-and-a-half centuries, astronomers tried to find a physical explanation for this acceleration. Finally, in 1846, Charles-Eugène Delaunay concluded that it wasn’t the Moon that was speeding up, but that Earth’s rotation was gradually slowing down.

See, without mechanical clocks, the rotation of the Earth was assumed to be constant so was used to define the length of a day. Speed, however, is measured as distance (in this case angular distance) over time. Observers without accurate mechanical clocks assumed the numerator was getting larger (more distance traversed per constant unit time) when in fact the denominator — the unit of time — was getting longer so more distance was traversed.

It took until the advent of sufficiently accurate methods of measuring constant time to understand that the Earth was slowing down, not that the Moon was speeding up. (That said, the dynamics of the Earth–Moon system are extremely complicated, and there’s still a lot about the motion of both bodies that has to be determined empirically rather than fully from models.)

Atomic clocks aren’t what you think they are

As I read the chapter on atomic clocks I realized I completely misunderstood what an atomic clock is. I’d always heard that a second was defined as 9,192,631,770 oscillations of something or other with a cesium atom. Without thinking about it, my stupid brain naively assumed that an atomic clock involves counting vibrations or oscillations or whatever, ticking off a second each time ~9.2e9 go by.

But of course that’s not what happens at all. You can’t even observe a single atom do something like that because of the Heisenberg uncertainty principle. I should have realized it, but I guess I never gave it enough thought.

The quantum-mechanical process in question is a resonance that occurs at a particular frequency. So what happens is that an atomic clock uses an oscillator of some kind (sometimes even a plain old quartz crystal!) to drive a resonator at (approximately) the right frequency, 9.2GHz. As I understand it, since the oscillator is only so accurate, you then tune around (using a fancy control system, no doubt) to see whether you get more response when slightly “detuned”. You find the maximum resonance, then redefine that new frequency as exactly 9,192,631,770Hz.

You can change the numerical value of a frequency by changing the number of oscillations per unit time, which is how we normally do it, but you can also change the denominator, the unit of time! By observing a phenomenon with a defined frequency, you can then define a second.

We like think of time as constant, but these facts are a fun reminder that sometimes that constant denominator, the base of so much in our lives, isn’t quite as constant as we like to think. And we haven’t even talked about Relativity!