Soul of the World (5 page)

As a practical monument to his achievement, the Greenwich Observatory in England installed its famous time ball at the top of a tower visible to all boats in the adjacent harbour. When the ball dropped, it marked the precise hour, and maritime navigators would synchronize their ship’s clock with the Greenwich master clock. Knowing where you were depended on knowing what time it was.

M
ILLISECONDS
, N
ANOSECONDS AND
C
OASTLINES

The clock, not the steam-engine, is the key machine of the

modern industrial age.

—
Lewis Mumford

Imagine that you have been hired to measure a small nation’s coastline. It’s a big job, but you have enthusiastic assistant surveyors, an unlimited budget and a whole summer ahead of you. You begin the survey one sunny May morning at the southernmost point of the coast, right at the border. The guards on the other side wave to you, and seagulls cry as they hover on a brisk, onshore breeze. The ocean is deep blue and dotted with whitecaps. North of you is a long, white beach. You begin your work.

The beach is relatively straight and quick to measure. It turns out to be almost two miles long. You break for an early lunch. The survey crew is talkative and excited. You decide that one summer should be ample time to measure the whole shoreline.

After lunch you begin to survey the point that shelters the beach’s north end. Here you realize that you will have to simplify your measurements. Instead of measuring the gradual curve of the point, you take a series of locations around it and measure the distance between them. It’s sort of cheating, but then again, how far off the actual distance could it be? Probably not a significant amount. Measuring the point takes up the early part of the afternoon, and as you and your crew come around to the other side, you see that the shoreline extending north is nowhere near as straight as the beach you measured in the morning. It is a long series of successive points, bays and inlets, some large, some small.

The first bay is simple, though it contains a small point that, after a brief conference, you and your assistants elect not to measure. “It’s
too small,” you say. The next point has a little bay in it, perhaps only twenty feet across. If you measure the bay, it will extend the length of the shoreline by almost a hundred feet. But a decision has to be made. In the end you decide that all smaller features will be ignored. If you begin to measure every little bay and inlet, the job might take all year.

When you’ve finished for the day, you and your crew set up camp on the beach. After dinner, under the stars and around a driftwood fire, everyone talks about the day’s work. The conversation is lively and friendly at first, but then the discussion turns into an argument. One of the surveyors, a philosophy student, insists that the survey has to be done as conscientiously as possible. She didn’t like the decision to skip smaller features. “Every little bay and inlet has to be measured,” she insists. “There is an absolute length to the shoreline, and we’re being paid to measure it.”

“Hold on,” says the lead surveyor. He has a degree in mathematics and works for the department of national cartography. “Where do we stop? Let’s say we measure a small bay and it comes to forty-five feet. But what if there’s a big boulder embedded on the shore of this bay? We measure it and it adds another five feet. Do we include that?”

“Why not?” asks the philosophy student.

“Okay,” says the lead surveyor. “What if there’s an indentation in that boulder, a crack that measures a foot and a half on each side. Do we include those three feet?”

“Why not?” the philosophy student asks again.

“All right,” says the lead surveyor. “What if, in that crevice, there were a smaller crevice? Would we measure that?”

The philosophy student realizes where this is going.

“You’ve got me there,” she says. “Obviously there is no end.”

“That’s right,” says the lead surveyor. “If you measure ever smaller
features on a shoreline, going from feet to inches to hundreths of an inch, you’ll soon discover that this nation’s coastline is infinitely long!”

Our little survey crew stumbled on a fact that has a profound implication for measuring time. One of the paradoxes of Zeno’s Arrow was that it could never reach its target because the distance it had to travel could be infinitely halved. Nearly three thousand years later, in the early half of the twentieth century, a British scientist by the name of Lewis F. Richardson continued Zeno’s quest. Coastlines and borders fascinated Richardson. Visiting countries that shared a common, zigzagging border, such as Holland and Belgium or Spain and Portugal, he found that the encyclopedias in each of these countries had estimates of their common borders that varied by as much as 20 percent. The discrepancy could be blamed on bad surveying, but Richardson didn’t think so. He thought there was something more profound going on, and he was right. But it wasn’t until years later that the French mathematician and physicist Benoît Mandelbrot, the father of chaos theory, picked up on Richardson’s interest in borders and coastlines and took it to its logical conclusion. Like our imaginary surveyors, he discovered that any irregular, natural coastline is endless.

You’d think that there would be a limit to this measurement. After all, coastlines exist in the real world. They are fixed, measurable. They don’t wiggle around or fade in and out of existence. But Mandelbrot discovered otherwise. Certainly if you were measuring something like a perfect rectangle lying on the ground, there would be a final value, an ultimate, fixed distance, but he found that with an irregular, natural shoreline there was no end to the bays and peninsulas. They simply got smaller and smaller until finally you were measuring them on the
molecular and then the atomic scale. Perhaps on the atomic scale there might be an end to the measurement, a final length of the coastline. But that’s where, maddeningly, everything becomes fuzzy, because the quantum world is indeterminate.

Time, it appears, is the same. Like a shoreline, time is composed of ever smaller, divisible units of itself. A second then, at least hypothetically, ought to contain an eternity, and with the burgeoning pace of ever more accurate clocks, the second is indeed opening up into a new universe of time. After Harrison’s No. 4 Chronometer set a precedent for accuracy, it was inevitable that an even more accurate clock would be built. It happened in 1889. Siegmund Riefler of Germany constructed a clock that worked inside a partial vacuum to reduce the influence of air pressure on the moving parts. His device had an accuracy within a tenth of a second a day and could easily measure milliseconds, or thousandths of a second. It was at this point that clocks became capable of measuring actions that are beyond our ability to see…a housefly flapping its wings once every three milliseconds. But even Riefler’s preeminence was short-lived.

In the 1920s, William H. Shortt, an English railroad engineer, built the first electromechanical clock. It was based on two clocks: a “master” and a “slave.” The slave clock sent an electromagnetic impulse every thirty seconds to the pendulum master clock, which then, in turn, regulated the slave clock. This device was accurate to within one second a year, precise enough to measure microseconds, or millionths of a second. In a microsecond a sound wave will have moved only one-third of a millimetre.

Shortt’s timekeeper was usurped only eight years later, when Warren A. Marrison, an engineer at Bell Laboratories in the United States, designed the first quartz-crystal clock, using the vibrational frequency of an electrically charged quartz crystal. By the mid-1940s, quartz
clocks had achieved a degree of accuracy within one second every thirty years. The world of the very small—the crystal lattice of silicon molecules that make up quartz—had become the new pendulum.

The pace of precision timekeeping continued to accelerate. In 1948 Harold Lyons created the first atomic clock, using the natural resonant frequency of an atom. By the mid-1950s this atomic clock had evolved into the cesium-beam atomic clock, which is still in use today to broadcast Co-ordinated Universal Time and which has an accuracy of about one nanosecond a day. A nanosecond is a billionth of second, the time it takes light to travel thirty centimetres in a vacuum. Computers take between two to four nanoseconds to process a single calculation. The children’s odyssey in C. S. Lewis’s
The Lion, the Witch and the Wardrobe
, where an imagined lifetime of adventure is crammed into a couple of seconds, must have been scaled to nanoseconds, each second in that world equalling a nanosecond of ours.

This kind of accuracy has allowed scientists to measure the duration of a second, long defined (somewhat tautologically) as the “sixtieth part of the sixtieth part of the twenty-fourth part of a day.” According to the cesium-beam atomic clock, a second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom at zero degrees kelvin. It’s not an elegant definition, but it’s absolute.

Clocks have become so accurate now that a curious thing has happened: they have outstripped the master clock—the earth’s revolution—that clockmakers have always used to calibrate their most precise chronometers. With the advent of the atomic clock, the yearly slowing of the earth’s revolutions could be measured accurately—and it turned out
to be three milliseconds a year. The earth was now an unreliable timepiece. But that wasn’t all: the earth was also becoming an
irregular
timepiece. When the Boxing Day tsunami of 2004 struck, it changed the angular momentum of the planet’s spin, speeding it up like a spinning figure skater pulling her arms closer to her body. As a consequence our days are now three millionths of a second shorter. But the divorce of abstract time from earthly time is far from complete, and there is an ongoing battle between astronomers and physicists about what our atomic timepieces should be based on. Astronomers argue for “natural time,” where leap seconds are added every few years to accommodate the slowing earth, while physicists argue for “technological time,” the final separation of time from its earthly orgins. The earth might yet be relegated to chronological history.

And all the while, smaller and smaller durations of time, like the bays within bays of a shoreline, continue to be discovered. The femtosecond, one millionth of a billionth of a second, was measured soon after the nanosecond. From the perspective of the femtosecond we humans are unmoving statues that exist an eternity. There could be a whole civilization overlapped with our own for whom femtoseconds are like our seconds. The Femtonians could be living invisibly among us as if we were so many figurines. Should their science became advanced enough, a genius among them might announce that the statues are not utterly unchanging, but that they are, in fact, moving! Controversy would erupt. It would be well known that, although most of the statues’ eyes are open, some are half-closed, while a minority are completely closed. Using comparison photographs gathered from over a century, the Femtonian scientist would show how the eyelids of a particular statue with half-closed eyes have moved incrementally over the
decades. “Preposterous!” would be the response from the dissenting scientists. “How could statues move? I suppose next you’ll be telling us they’re alive?”

But the Femtonians have already been usurped by a smaller, faster civilization. Briefer even than femtoseconds are attoseconds, clocking at a staggeringly tiny portion of time: a billionth of a billionth of a second. From the perspective of an attosecond, one of our seconds lasts three million years, the same amount of time it took humans to evolve. Yet still smaller units of time are being sought after. David Blair, an Australian physicist, has built the most accurate clock yet in order to try and measure gravitational waves. Even though they knit our galaxy together, gravitational waves are ineffable, with extraordinarily weak emissions. They have never been detected. Blair hopes his new clock will be fast enough to catch them. His timepiece is not as stable as an atomic clock over long periods, but in the short term it is accurate to one part in a hundred trillion over three hundred seconds. At its heart is a sapphire crystal that is kept at –273° Celsius in a bath of liquid helium, capable of measuring a trillion-trillionth of a second.

At this scale of duration the only events that move fast enough to be measured are sub-atomic events: the lifetime of quarks and the breaking of atomic bonds. It is a jumpy, quivering world of electrons and particles. And that’s where everything converges. If our coastline surveyors insisted on measuring the entire edge of their shoreline—attending to smaller and smaller inlets and points until they were accounting for edges of pebbles, then grains of sand, then molecules and finally the edges of atoms—they would arrive at the same place, the same time frame as a cesium clock. You have to have a very fast ruler to measure subatomic shorelines; they keep changing. There comes a point, at the infinitesimal scale of things, where not only time and mass converge but also gravity and light. In that tiny, furiously
quick world, light moves like molasses and mass disappears into energy. Perhaps, as Blair hopes, the secret of gravity might be lurking there as well.

But if clocks get more accurate, particularly if they become accurate to within a millisecond in three million years, then, due to relativistic effects, simply walking around with one will slow it down measurably. Also, elevation will change the pace, since time runs slower at the surface of the planet than higher up. This effect is already measurable. Due to relativity, clocks at the top of Mount Everest run faster than those at sea level, pulling ahead by about thirty microseconds a year. Time too, when reduced to its smallest parts, becomes slippery and indeterminate. It may well be that there is a limit beyond which the smallest portions of time cannot be measured.

A
ND
Y
ET
…

“Now,” from the perspective of an attosecond, is a very fleeting thing, impossible to seize. It makes our “now” seem to stretch for an eternity, at least relatively, even if, from our perspective, the present moment is as mercurial as any small division of time. Because it is all we have, this small moment is also the most precious, an oasis in the sands of time. Yet “now” has another scale, in the opposite direction from the abyss of milliseconds and nanoseconds. There is a bigger “now.”