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...)

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Quartz watches can be good to a few seconds a month, good quartz clocks are good to a few seconds per year.

Why the difference?

(And now that a new version of MT is out, are the web developers going to upgrade and bring back the identity cookies?)

Why the difference [between watches and clocks]?

The oscillation frequencies of quartz crystals are very slightly temperature dependent, and that's easier to control in a stationary clock than a mobile wristwatch. The best quartz clocks also use radio signals from atomic clocks to make small corrections to the timing, which is harder to incorporate into a watch.

Because I have never understood laser physics, it has always puzzled me that once you make a laser that outputs at the desired frequecy, why bother with the Cesium atoms?

Because I have never understood laser physics, it has always puzzled me that once you make a laser that outputs at the desired frequecy, why bother with the Cesium atoms?

The atoms are what you use to verify that you're at the desired frequency. I'll talk about this more tomorrow, or whenever I get to the next installment.

"ticking" just refers to some regular, repetitive behavior that takes place in a periodic fashion

Is there anything more random than radioactive decay? Radioactive isotope dating by decay product accumulation, activity decline, or remaining undecayed isotope (e.g., accelerator mass spec and C-14).

The atoms are what you use to verify that you're at the desired frequency. I'll talk about this more tomorrow, or whenever I get to the next installment.

Ah, so you tune your laser based on your oscillator? This is one of the couple oscillator problems I should have paid attention to in Mechanics, isn't it?

"Is there anything more random than radioactive decay? Radioactive isotope dating by decay product accumulation, activity decline, or remaining undecayed isotope (e.g., accelerator mass spec and C-14)."

Yes, radioactive decay events are random. Which is why nobody tries to date an artifact based on the decay of a single carbon atom.

the modern state of the art is good to about a part in 10^15, or something like one nanosecond in twenty million years.

I think you mean one second in twenty million years?

Uncle Al,

The fact that radioactive decay consist of random events of known probability is why it can be used to date things. For example, if someone flipped a coin an unknown number of times and the total number of times it came up heads was 5000, then the coin was probably flipped around 10000 times - the same priniciple can be applied with half-lifes.

If Cesium clocks are the operational clocks onboard GPS satellites, why are Rubidium clocks used for the Cesium backups?

How many ticks of the Rubidium crystal = 1 second?

Since there are Ce and Rb clocks onboard GPS satellites, how do the GPS satellites average out time from the mix of Ce and Rb clocks?

I don't think anyone will ever have a true grasp of time as it is different throughout the entire universe. Only when you can escape gravity completely (impossible of course), would you get a true reading of unbiased time.