Real Clock Tutorial: History

Over at A Blog Around the Clock, Bora put up a sixteen part series of posts talking about clocks. Unfortunately, he was talking about biological clocks, which are a specific and sort of messy application, from the standpoint of physics.

I talk a bit about clocks for our first-year seminar class, as a part of my two-week module on laser cooling (laser-cooled atomic clocks being one of the major applications). Like most of the other good bits of that module, this is shamelessly stolen from talks I’ve heard Bill Phillips give, but it works pretty well.

In order to really discuss the physics of timekeeping, you need to strip the idea of a clock down to the absolute bare essentials. At its core, a clock really has only one defining characteristic: A clock is a thing that ticks.

OK, I’m using a fairly broad definition of “tick,” here, but if you’ll grant that leeway, “ticking” is the essential property of clocks. In this context, “ticking” just refers to some regular, repetitive behavior that takes place in a periodic fashion. The periodic behavior could be a swinging pendulum, or a vibrating quartz crystal, or a kid counting “One mississippi, two mississippi…” before rushing the quarterback in a backyard football game. If you’ve got some system that performs a regular action over and over again, you can use it to keep time.

The earliest example of “tick” is astronomical– the motion of the Sun and Moon and other planets. It’s so obvious that it seems sort of stupid to even mention it, but you can keep time just by watching the apparent motion of the Sun. It happens more or less the same way on successive days, and you can use that motion for a coarse sort of timekeeping. If you want to get a little more refined, you can track the motion of the Sun over a period of years, and make corrections for the changing length of a day, and so on.

This still doesn’t get you very fine resolution, and isn’t a great deal of help on a cloudy day, so people started to develop new sorts of clocks. The earliest type of constructed clock is basically a container with a hole in it. You fill the container with something– sand or water are the traditional media– and let it run out through the hole. When it’s empty, you fill it back up, and start again. Assuming it takes about the same amount of time to empty out each time, you can use this as a timekeeping device, and get better time resolution.

Of course, water clocks and hour glasses have their own issues, repeatability being high on the list. If you make the container a little bigger or a little smaller, or change the size of the hole, or change the medium you fill it with, you get different durations. You also need to remember to re-start them on a regular basis.

The next big advance in clock-making is the pendulum clock. The key realization is that a mass swung at the end of a string will, to a very good approximation, oscillate back and forth in a regular fashion with the period of the motion (time required to complete a swing) depending only on the length of the string. A particularly nice feature about this is that the period does not depend on the mass, or the amplitude of the swing. As long as the length is right, nothing else matters.

You can use this pendulum motion to make a really good clock. The best pendulum clocks were really remarkably good, losing only a fraction of a second a day. This was pretty much the state of the art into the Twentieth Century.

Modern clocks and watches keep time with a different sort of “tick,” based on the vibrations of a quartz crystal. When a voltage is applied to a crystal in the right way, it sets up a vibration that can be used to keep time. This frequency varies somewhat from one crystal to the next, but for a given crystal, it’s very stable. Quartz watches can be good to a few seconds a month, good quartz clocks are good to a few seconds per year.

The development of quantum mechanics provided a way to realize an even better clock, using the light emitted and absorbed by atoms. Quantum mechanics tells us that atoms have discrete energy states, and move between those states by absorbing or emitting light. The frequency of the light absorbed or emitted by an atom is determined by the energy difference between states, and that difference is fixed by the laws of physics. The energy difference between the hyperfine levels of the ground state of a cesium atom is the same for all cesium atoms, and is the same here on Earth as it is in a distant galaxy.

So, the radiation emitted and absorbed by cesium atoms can be considered as close to a perfect clock as we’re ever going to get. You just prepare a source of radiation at exactly the right frequency, and then count oscillations to keep track of the time. Of course, realizing this experimentally is a little tricky, but the best clocks do an amazingly good job– the modern state of the art is good to about a part in 10¹⁵, or something like one nanosecond in twenty million years.

“How do they do that?” you ask. I’ll explain that in another post…

(Fun clock facts are available from NIST’s Time site, if you’re interested in that sort of thing…)