Sunday, November 30, 2008

To Mark The Passing Of Events

Philosopher and sometime baseball player Yogi Berra is alleged to have once described time as "what keeps everything from happening all at once". As with many of his utterances, this one is as elegant a description as anything people with PhDs could come up with. The guys with PhDs would probably say that time is the passing of events, which is just another way of saying that it keeps things from happening all together.

We mark the passing of time with clocks. Clocks, of course, mark the passing of events that we know take a certain amount of time. Whether those events are the rising and setting of the Sun, the phases of the Moon, the swing of a pendulum of a particular length in Earth's gravity, or the vibration of an atom of a particular element, clocks record them and keep track of them. Through trial and error, and the gradually more sophisticated understanding of physics, our ways of measuring time have become both more accurate and more convenient.

The first events we humans almost certainly learned to record and associate with the passing of other events were the movements of the Sun and Moon. The Sun, of course, rises and sets 365 days a year. To know what a year is, though, we need to remember what a year is, which is the passing of all four seasons. Ancient people learned that the seasons were cyclical, and thus learned to mark time by their passing so that they could migrate to areas that were best for hunter-gatherers at that time of year, or plant crops once they formed agrarian societies.

For agrarian societies, these clocks often were built of stones that were placed in particular arrangements, or marked in particular places that would indicate when the Sun or Moon had reached a crucial phase. Often, these phases were solstices or equinoxes.

Image credit: Crystalinks.

This stone, the Intihuatana Stone in Machu Pichu, Peru, is an example of such a clock. It is pointed in the direction of the Sun on the winter solstice.

Interestingly, even longer events can be clocked, as the U.S. Geological Survey points out:

Image credit: U.S. Geological Survey (USGS)

In 1962, scientists of the U.S. Naval Oceanographic Office prepared a report summarizing available information on the magnetic stripes mapped for the volcanic rocks making up the ocean floor. After digesting the data in this report, along with other information, two young British geologists, Frederick Vine and Drummond Matthews, and also Lawrence Morley of the Canadian Geological Survey, suspected that the magnetic pattern was no accident. In 1963, they hypothesized that the magnetic striping was produced by repeated reversals of the Earth's magnetic field, not as earlier thought, by changes in intensity of the magnetic field or by other causes. Field reversals had already been demonstrated for magnetic rocks on the continents, and a logical next step was to see if these continental magnetic reversals might be correlated in geologic time with the oceanic magnetic striping. About the same time as these exciting discoveries were being made on the ocean floor, new techniques for determining the geologic ages of rocks ("dating") were also developing rapidly.

Magnetic stripes and isotopic clocks

Even the direction of magnetic north changes over time, sometimes dramatically. That's some comfort considering the times we're living through these days. Nothing is forever.

Another form of the passing of events is the passing of a volume of water through a standard-sized hole in a container. While modern fluid dynamics can predict how such things will work, at the time water clocks were first invented, the clocks were probably tuned using the brute force of trial and error:

Image credit: National Institute of Standards and Technology (NIST)

Water clocks were among the earliest timekeepers that didn't depend on the observation of celestial bodies. One of the oldest was found in the tomb of Amenhotep I, buried around 1500 B.C. Later named clepsydras (“water thief”) by the Greeks, who began using them about 325 B.C., these were stone vessels with sloping sides that allowed water to drip at a nearly constant rate from a small hole near the bottom. Other clepsydras were cylindrical or bowl-shaped containers designed to slowly fill with water coming in at a constant rate. Markings on the inside surfaces measured the passage of “hours” as the water level reached them. These clocks were used to determine hours at night, but may have been used in daylight as well. Another version consisted of a metal bowl with a hole in the bottom; when placed in a container of water the bowl would fill and sink in a certain time. These were still in use in North Africa this century.

Water Clocks

Some water clocks were, to say the least, a great deal more elaborate. This huge water clock was used by Chinese royalty in the 11th Century:

Image credit: National Institute of Standards and Technology (NIST)

One of the most elaborate clock towers was built by Su Sung and his associates in 1088 CE. Su Sung's mechanism incorporated a water-driven escapement invented about 725 CE. The Su Sung clock tower, over 30 feet tall, possessed a bronze power-driven armillary sphere for observations, an automatically rotating celestial globe, and five front panels with doors that permitted the viewing of changing manikins which rang bells or gongs, and held tablets indicating the hour or other special times of the day.

NIST: Early Clocks

And I thought GPS was complicated...

Of course, water clocks do have their drawbacks. One obvious one is that they require lots of maintenance. When you're a despot, this isn't much of a problem. Heads could quite literally roll if things aren't up to snuff. For ordinary citizens, labor relations were more complicated, even in the good old days of slavery. In addition, water has an effect on its container. Over time, it can wear holes, soften or corrode containers, evaporate, and spill. This latter property made them particularly difficult to use on ships. For these and other reasons, pendulum clocks became much more popular:

The pendulum clock was invented and patented by Dutch scientist Christiaan Huygens in 1657, inspired by investigations of pendulums by Galileo Galilei beginning around 1602. Galileo discovered the key property that makes pendulums useful timekeepers: isochronism, which means that the period of swing of a pendulum is approximately the same for different sized swings. Galileo had the idea for a pendulum clock in 1637, partly constructed by his son in 1649, but neither lived to finish it. The introduction of the pendulum, the first harmonic oscillator used in timekeeping, increased the accuracy of clocks enormously, from about 15 minutes per day to 15 seconds per day leading to their rapid spread as existing clocks were retrofitted with pendulums.

Wikipedia: Pendulum Clock

With care, these clocks could be used on board ships, where they were used to determine the longitude of the ship's location. In the 18th Century, the British empire announced a reward for a clock design that could be carried on board their ships. This is the inspiration for the movie Longitude.

This is an illustration of Huygen's second design:

Image credit: Wikimedia Commons.

The second pendulum clock built by Christiaan Huygens, inventor of the pendulum clock, around 1658. Drawing is from his treatise Horologium Oscillatorium, published 1673, Paris, and it records improvements to the mechanism that Huygens had illustrated in the 1658 publication of his invention, titled Horologium. It is a weight driven clock (the weight chain is removed) with a verge escapement (K,L), with the 1 second pendulum (X) suspended on a cord (V). The large metal plate (T) in front of the pendulum cord is the first illustration of Huygens' 'cycloidal cheeks', an attempt to improve accuracy by forcing the pendulum to follow a cycloidal path, making its swing isochronous. Huygens claimed it achieved an accuracy of 10 seconds per day. Each gear is labeled with the number of teeth it has. Alterations to image: Cropped out figure number, converted to 32 color PNG.

Labeled parts: (A) front plate, (B) back plate, (C) minute wheel, (D) weight chain pulley, (E) third wheel pinion, (F) third wheel, (G) third (seconds) wheel, (H) contrate wheel, (I) crown wheel pinion, (K) crown wheel, (L) pallets, (M) verge, (N,P) verge supports, (Q,R) crown wheel shaft supports, (S) crutch, (T) cycloidal cheeks, (V) pendulum rod, suspended from two cords hidden behind cycloidal cheeks, (X) pendulum bob, (Y) hour hand, (Z,λ) second hand (ζ) hour wheel (Δ) rate adjustment weight.

Wikipedia: Huygens Clock

What makes pendulum clocks so handy is that the period of a clock swing depends only on its length. This makes the timing extremely predictable. Here, courtesy of Wikipedia, is the equation that predicts that period (T0):

The 'l' in that equation stands for the length of the pendulum, and 'g' is the force of gravity. The bit on the right means that we're assuming that the arc the pendulum travels is considerably less than a full circle. Pretty simple, isn't it? Of course, nearly all materials that a pendulum could be made out of stretch or deform in some way under stress, and gravity isn't the same everywhere, even on Earth. So pendulums can only be so accurate.

For real accuracy, you need an atomic clock.

One important aspect of the Global Positioning System's operation is knowing exactly what the time is, down to the nanosecond. Thanks to atomic clocks, the GPS satellites know where they are, much as the mariners of the 18th Century.

image credit: U.S. Naval Observatory

This is one such atomic clock. The U.S. Naval Observatory describes it thus:

USNO Cesium Clocks

Most of the Observatory's cesium clocks are model HP5071A, made by Agilent Technologies, Inc. of Santa Clara, California. With an improved cesium tube and new microprocessor- controlled servo loops, the 5071A vastly outperforms the earlier 5061 cesium frequency standards. The Naval Observatory 5071A's feature HP's optional high-performance cesium beam tube, with accuracy 1 part in 10E12, frequency stability 8 parts in 10 to the 14th, and a time domain stability of < 2 parts in 10 to the 14th with an averaging time of 5 days. Other companies that produce cesium clocks include Datum, Inc. of Beverly, MA and Frequency Electronics, Inc. of Uniondale, NY.

Cesium Atoms at Work

It's your tax dollars at work, and working pretty well, I might add.

Your tax dollars have also been at work developing this, courtesy of the NIST:

Image credit: NIST

This is a "chip scale" atomic clock introduced by the NIST back in 2004. "Chip scale" means it's about the size of a typical integrated circuit. Someday, you may have one in your house and you'll never have to set the thing again (as long as you remember to change the batteries, of course):

The heart of a minuscule atomic clock—believed to be 100 times smaller than any other atomic clock—has been demonstrated by scientists at the Commerce Department’s National Institute of Standards and Technology (NIST), opening the door to atomically precise timekeeping in portable, battery-powered devices for secure wireless communications, more precise navigation and other applications.

Described in the Aug. 30, 2004, issue of Applied Physics Letters, the clock’s inner workings are about the size of a grain of rice (1.5 millimeters on a side and 4 millimeters high), consume less than 75 thousandths of a watt (enabling the clock to be operated on batteries) and are stable to one part in 10 billion, equivalent to gaining or losing just one second every 300 years.

In addition, this “physics package” could be fabricated and assembled on semiconductor wafers using existing techniques for making micro-electro-mechanical systems (MEMS), offering the potential for low-cost mass production of an atomic clock about the size of a computer chip and permitting easy integration with other electronics. Eventually, the physics package will be integrated with an external oscillator and control circuitry into a finished clock about 1 cubic centimeter in size.

NIST Unveils Chip-Scale Atomic Clock

Some of your tax dollars really are spent well. How does it work? Well, like this:

The new clock is based on the same general idea as other atomic clocks such as the NIST-F1 fountain clock—measuring time by the natural vibrations of cesium atoms, at 9.2 billion “ticks” per second—but uses a different design. In the chip-scale clock, cesium vapor is confined in a sealed cell and probed with light from an equally small infrared laser, which generates two electromagnetic fields. The difference in frequency of these two fields is tuned until it equals the difference between two energy levels of the atoms. The atoms then enter a “dark state” in which they stop absorbing and emitting light; this point defines the natural resonance frequency of cesium. An external oscillator, such as quartz crystal like those found in wristwatches, then can be stabilized against this standard.

The important point is that the resonant frequency is a well-known physical constant, and once it's reached that frequency, it will tend to stay there.

The NIST Small Clock program is continuing to refine this design, and maybe we'll start seeing products based on this technology in a few years.

We've come a long way in the last few thousand years when it comes to measuring time. Maybe some day our descendants will be as amazed that we tried to mark the passing of events with atomic clocks as we are that our ancestors once tried to keep rocks pointed in the right direction. The only thing we can be assured of is that they will be able to do it better than we.

NOTE: Those of you who think you recognize some parts of this article may be right. Some of the text of this article is taken from a series of articles on the Scooter Libby trial that I wrote in 2007.


Dana Hunter said...

This is outstanding! Love it, and thank you very much for allowing me to filch.

I owe my NaNo success to you, because if I'd had to break off for Sunday Sensational, I would've been deep in the brown and sticky.

Muchos gracias, mi amigo!

Cujo359 said...

I think your success is largely due to your having written a lot of words on a particular subject, but you're welcome.