Forty feet underground, secured in a temperature- and humidity-controlled vault here, lies Kilogram No. 20.

It’s an espresso-shot-sized, platinum-iridium cylinder that is the perfect embodiment of the kilogram -- almost perfect.

In the more than a century since No. 20 and dozens of other exact copies were crafted in France to serve as the world’s standards of the kilogram, their masses have been mysteriously drifting apart.

The difference is on average about 50 micrograms -- about the weight of a grain of fine salt. But the ramifications have rippled through the world of precision physics, which uses the kilogram as the basis for a host of standard measures, including force of gravity, the ampere and Planck’s constant -- the omnipresent figure of quantum mechanics.


In essence, no one really knows today what a kilogram is.

“How do I trust what I have?” asked Zeina Jabbour, the physicist at the National Institute of Standards and Technology, or NIST, in charge of maintaining No. 20, the official U.S. kilogram.

The kilogram crisis has kicked off an international race to redefine the measure. Instead of using an object, scientists are searching for some property of nature or scientific constant, such as the vibrations of a cesium atom now used to define a second.

The kilogram is the last of seven base units in the International System of Units that is still based on a physical object, a remnant of the era before relativity and quantum mechanics transformed our understanding of the universe.


“The real problem is, people in other areas of science don’t want to measure, say, fundamental constants with respect to this artifact made in the 19th century,” said Richard Davis, head of the mass section at the International Bureau of Weights and Measures in France.

Besides, Jabbour added: “You could drop it.”

In fact, at least six copies of the kilogram have been lost or damaged over the years from war, clumsiness or other reasons.

Two ideas have emerged as the leading contenders to redefine the kilogram. One involves counting the trillion trillion atoms in the most perfect silicon sphere ever made. The other attempts to measure the electrical current necessary to balance a one kilogram weight against Earth’s gravity.


Serious complications ensnare both approaches.

“We’re running into the wall of measurement,” said Richard Steiner, the physicist heading NIST’s effort to define a new kilogram.

In the 18th century, hundreds of thousands of different weights and measures were in use around the world. The French alone employed about 250,000 different units of measure.

The Enlightenment and the French Revolution spurred the idea of standardization, said Ken Alder, a historian at Northwestern University in Evanston, Ill. People could only be free if they could calculate for themselves the weight and cost of things they bought, philosophers reasoned.


The French government created the kilogram in 1795, defining it as the mass of a liter of distilled water at the temperature of melting ice. A century later, the Treaty of the Meter established the kilogram as an international standard.

The foundation of the standard was a cylindrical ingot of 90% platinum and 10% iridium created in 1878 that became known as Le Grand K, or more officially the International Prototype. Forty copies were made and distributed a decade later to governments around the world. Another 50 were made later.

These 90 copies serve as national standards, used to calibrate working weights in science and industry.

About every 50 years, the national prototypes are returned to the headquarters of the International Bureau of Weights and Measures in Sevres, France, to be compared with the International Prototype. During the first major comparison about 1950, scientists noticed discrepancies between the average masses of Le Grand K and its copies. They were concerned but could not discern a trend.


Science was already grappling with inconsistencies in other units and was trying to replace the pieces of metal and other artifacts that delineated the old world. The meter, for example, was changed in 1960 from two scratches on a platinum-iridium bar to a certain number of wavelengths of light emitted from a particular kind of krypton. In 1983, it was changed again to the distance traveled by light in a specific fraction of a second.

At the last major kilogram comparison done in and around 1990, some copies had gained as much as 132 micrograms. A few had lost up to 665 micrograms. The United States’ No. 20 was 18 micrograms heavier.

There was no way to tell which was changing: Le Grand K, its copies or both.

Perhaps the platinum in the cylinders was sopping up mercury from the atmosphere. Maybe dissolved gas was escaping from the cylinders. One idea was that cleaning the cylinders with distilled water and ether had altered their weights.


“Nobody has a really good idea why,” said Davis of the International Bureau of Weights and Measures. “It’s all speculation.”

Just outside a sealed chamber situated on a lonely corner of the NIST grounds, Steiner laid his wallet and wristwatch on a wooden desk. The magnetic field in the room was strong enough to erase the magnetic strips on his credit cards and stop the gears in his watch.

The elfish 53-year-old physicist with graying light brown hair pulled aside the heavy door and stepped into the warm glow of the room, sheathed in shiny copper plates to shield out radio and radar waves. Wires threaded across the walls.

At the heart of the chamber hummed Steiner’s hulking machinery he hopes will lead to the next kilogram -- a two-story device with a pair of superconducting magnets the size of fire hydrants.


Steiner came to NIST here in Gaithersburg 23 years ago, a freshly minted physics PhD from the nearby University of Virginia. He signed on to the kilogram project about 14 years ago.

The NIST device is known as a watt balance, but Steiner affectionately calls it “my UFO.”

The idea is to standardize the kilogram relative to a constant in quantum mechanics known as Planck’s constant. If scientists know the current, the strength of the magnetic field and Planck’s constant, they can accurately determine the mass of an object.

The problem with Steiner’s watt balance is that it can be finicky. Distant earthquakes, motors from nearby office buildings and tides have shaken up the measurements, he said. There are about 20 potential sources of error, including the buoyancy of air, electrical current leaks and the changes in local gravity.


Peter Becker, a physicist at Germany’s National Metrology Institute, thinks he has a simpler solution: Count atoms. The idea is to define the kilogram as the number of atoms of a specific element.

Becker’s hopes ride on two silvery croquet-ball-sized spheres of the purest silicon that cost $3.2 million to make. They are the roundest objects ever made -- within 30 nanometers of perfection, about the width of a few atoms, he said.

Becker, a trim, jolly 63-year-old man with a graying mustache, has been working on X-ray optics since the 1970s. In the mid-1990s, when the drift in the kilogram copies’ masses started to cause concern, Becker and his collaborators realized their work could be used to help solve the problem.

It’s impossible to count atoms individually, but Becker’s group, known as the International Avogadro Project, used X-rays to determine the spacing of atoms in an object. Once that was known, and the volume of an object determined using precise laser measurements, they could derive the number of atoms -- about 20 trillion trillion for a kilogram of silicon.


Such calculations, however, require a material with a very regular spacing pattern. The group settled on silicon because its atoms are laid out in a nearly perfect cubic lattice.

The group initially used natural silicon and manufactured about 20 spheres for their measurements in their last 14 years of collaboration. They calculated a fairly accurate value, but it was still off, largely because natural silicon contains a variety of isotopes with different lattice spacing.

The scientists realized they needed a purer material, preferably a crystal composed entirely of one kind of silicon.

Russia’s Nuclear Ministry and Institute for Ultrapure Materials produced a large silicon crystal, and the Institute of Crystal Growth in Germany repeatedly melted the material to remove contaminants, resulting in 99.99% pure silicon-28, the most common isotope. The spheres were ground using progressively smaller grains of aluminum oxide at the Australian Center for Precision Optics.


“If you look at the experiment, it looks very easy,” said Becker, who just picked up the new spheres this month. “The devil is in the details.”

After decades of work, both efforts have so far produced stunningly precise measurements -- but still too inconsistently to prove the accuracy of their methods.

Steiner’s latest calculation of uncertainty is less than the 50-microgram average difference between the kilogram copies and Le Grand K. But a few months ago, a British team used a watt balance of its own design to generate a value that was significantly different. Neither lab can explain the gap.

The disagreement has given Becker’s atom-counting effort some hope.


He said his group should be able to make a better calculation next year using the new spheres. “Our goal is to reduce [the uncertainty] by a factor of 10 or better,” Becker said. “We are convinced we can reach it.”

The watt balance approach, however, has an advantage in that it doesn’t require each country to manufacture its own ultra-pure silicon spheres.

And so the quest continues.

Steiner said that even after 14 years, it is still difficult to explain why he feels so strongly about his work. “Basically, I can never really justify [to my friends and relatives] that they’re going to be able to buy some new thing based on what I work on,” he said.


Even if he succeeds, he knows it’s only a matter of time before scientists demand something even more precise. Just last month, NIST announced the development of two new atomic clocks that surpassed the accuracy of the current ones, which lose one second over about 80 million years.

The new clocks lose less than a second over 1 billion years.

“You’ll never get perfect,” Steiner said. “There’s always a whole lot more digits out there.”

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jia-rui.chong@latimes.com