In an underground vault beneath a hill overlooking Paris, behind a steel door whose lock requires three keys—only two of which are in France—and protected by three glass covers, lives the kilogram. Not a kilogram but The kilogram. For the past 125 years, this sleek cylinder of platinum-iridium has defined mass for the world.

The vault is buried under the Bureau International des Poids et Mesures (BIPM), a whitewashed stately home a discreet distance from Paris, with extensive gardens for physicists to roam in and views across a grand meander of the Seine. The BIPM exists to control, define and distribute the Standard International (SI) units by which science—and indeed non-science—makes its measurements: the second, the metre, the mole, the candela, the ampere, the kelvin and the kilogram. You might call it the spiritual centre of the metric system—if the rational world of revolutionary France’s metrification programme allowed room for anything as irrational as the spiritual.

Whatever the intentions of the scientists and philosophers who sought to order our planet’s measure­ments—doing away with the bushels of corn that varied from village to village and the king’s feet that varied from king to king—something unexpected is happening to one of our vital units. There is strong evidence that the BIPM’s kilogram, the one mass in the world that cannot be allowed to vary, is varying.

Philosophically speaking, such a statement is nonsense: it is impossible for the kilogram to be anything other than a kilogram. As Dr Richard Davis, who has worked in the laboratory’s mass department for much of his career, puts it, “Technically, if you cut it in half, it would still be a kilo.” In those circumstances everything else in the world would instantly weigh twice as much—at least when measured in kilograms.

No one is cutting the kilogram in half. Only a handful of people have been allowed to see it, and fewer still to touch it. Even so, as experimental methods get more precise, and physicists work at ever smaller scales, the vanishingly slight variations in the kilogram have become increasingly inconvenient.

At a meeting in Versailles in November, scientists will discuss whether the technology now exists to switch to a mass standard that cannot ever change. Is it time to redefine the kilogram?

The kilogram as we know it was created at the first General Conference on Weights and Measures, held in France in 1889 and attended by 20 of the world’s more science-minded nations. As the Enlightenment progressed, spreading knowledge and developing the modern empirical methods, it became clear that, for science to work, its practitioners had to agree on units. If an experiment in Rio de Janeiro used a gram of catalyst heated to 75 degrees, someone repeating that experiment in Tokyo needed to know that a gram and a degree meant the same on both sides of the Pacific.

Following almost a century of discussion, the conference defined the key units of measurement, and the kilogram was forged and incarcerated. In the years since 1889, around 100 daughter kilograms have been made, some in platinum-iridium, others in stainless steel. Most have been distributed around the world to provide national mass standards. Six are kept here in Paris, to be used as a check on the main kilogram.

Every few years, the members of the kilogram diaspora take turns to come home. Each country sends a senior scientist to take its national kilogram by plane, in his or her hand luggage, to the weighing room at the BIPM, where it is cleaned, checked and calibrated. The process is so exacting that air pressure has to be accounted for when comparing the cheaper stainless-steel masses with platinum-iridium ones.

“Platinum is very high in density, so one kilogram of it has a small volume,” says Dr Davis. “Stainless steel is maybe three times bigger in volume; it is much more sensitive to changes in air pressure.”

After weeks of measurements, it is time for the daughter kilogram to return, along with a very, very small number: the difference between its mass—which calibrates every experiment in its home country—and the mass of the kilogram itself. That number is supposedly a correction to make up for imperfect storage of the national kilograms—not to reflect imperfections in the Parisian one. Yet, as far as its guardians can tell, the kilogram has been systematically losing mass, at least in comparison with the kilograms it fathered—including those in Paris that have had virtually the same treatment. The difference between the kilogram and its heaviest daughter is now about 60 micrograms.

That is not much—a mere 0.000006% of the total. If an ant were to walk over the kilogram while it was being weighed, it would change the reading by 100 times that. Nevertheless, the scientists are puzzled. One theory is that it’s caused by trapped gas slowly diffusing out over centuries—although it is difficult to see why this would affect some kilograms more than others. Other possibilities include mercury absorption and contamination from the cleaning process. None of the explanations seems wholly satisfactory.

Back in the weighing room, currently occupied by the Croat kilo, Davis points at the door leading to the vault. “There it is, past the moat and the alligators.”

For an object that spends decades at a time hidden from view, the kilogram has a strangely charismatic presence. Like a mafia don on the run, it operates through its lieutenants, the daughter kilograms that maintain its rigid hegemony over the world’s weights and measures. Only on the very rare occasions when it emerges to be weighed do they receive new instructions. Then it goes back into hiding for several more decades. The first of those weighings was in 1946-50, the second in 1988-92; the most recent came this summer, after my visit. Security remains a serious business. As one scientist put it, “If anyone took the kilogram, we might as well not turn up the next day.”

After this November’s meeting, though, it could be that talking about stealing the kilogram would be as absurd as talking about stealing the speed of light.

Of the seven si units, the kilogram is the last to retain its definite article. “A” metre still exists in this Parisian laboratory. A rod of platinum-iridium, it was once The metre. But in 1960 it was redefined as 1.65m times the wavelength of light produced by a transition in krypton. Then, in 1983, it was re-redefined as the distance travelled by light in a vacuum in 1/299,792,458 of a second. These days, however much they may agree in reality, the metal version is just an approximation of the true metre, which exists as a pure concept in the Platonic ideal of SI units.

The second, too, has lost its intuitive definition. For most of chronometric history, time has been understood in terms of a division of the period between midday and midday: 24 hours, 1,440 minutes, 86,400 seconds. Looked at in this way, clockmaking is the process of producing better mechanical approximations of the Earth’s rotation. But, around the middle of the last century, we produced a clock that was a million times more accurate than the planet. Ever so slightly, the Earth is slowing. Each ebb and flow of the tides is energy coming out of its spin; in the time of the dinosaurs, the day was several hours shorter. With the creation of an atomic clock that could spot that slowing, the rotation of our planet became an inferior pendulum by which to set the global time standard.

These days, a second is instead defined as 9.2 billion oscillations of a microwave beam when tuned to the frequency required to excite a caesium atom. Because the Earth has slowed further since this value was fixed, there are now slightly more than 86,400 of these new seconds in a day. So it is that roughly once a year, in the atomic clocks that control the world’s markets and navigation systems, we have a 61-second minute.

As the other tangible SI standards fell like rarefied dominoes, the kilogram evaded redefinition, remaining the best-protected, best-defined lump of metal in the world. The kilogram as a concept had been forged in the fires of the French revolution. An enlightened country could not have a system in which weights and measures might vary, so a committee was convened to devise a replacement. At first those forges were meta­phorical: in 1795, the gram was defined as “the absolute weight of a volume of pure water equal to the cube of the hundredth part of the metre, and at the temperature of melting ice”—a cubic centimetre of water at freezing point. A kilogram, correspondingly, became a litre of water at freezing point. With the metre itself fixed as one ten-millionth of the distance of an arc from the equator to the North Pole, at last there was a system that could be used without confusion from London to Cape Town.

When the practicalities of using ice and undulating ground proved tricky, the committee opted to produce an artefact after all. The royal jeweller was called back to Paris from exile and set to work. The upshot, in 1799, was the Kilogram des Archives, a national mass standard that would last until the creation, 90 years later, of the even more exacting kilogram we know now.

A century and a quarter later, in laboratories around the world, scientists are working once more to unshackle the kilogram from the physical and create a new definition. But what is the quantity that is to the kilogram what the speed of light is to the metre? There are two answers: the Planck constant and the Avogadro constant. Both share the important quality that they are, in theory at least, invariant.

At the National Physical Laboratory in Teddington, west London, Dr Ian Robinson has devoted his career to creating the new kilogram. Almost 40 years ago, in the place that produced the atomic clock that precipitated the second’s existential crisis, a new kind of weighing scale was proposed: the watt balance.

“It’s a very simple system,” Robinson begins, with the misplaced optimism of a CERN physicist launching into yet another metaphor to describe the Higgs in layman’s terms. Physicists like to compare the watt balance to the classic weighing scale. On the right-hand side, you have whatever you want to measure. On the left, instead of counterweights, you have a big horizontal coil through which a current is passing, itself in a magnetic field. If you make the scales balance, you can relate mass to current and magnetic field. Perform another experiment by measuring the voltage when you move the coil at a set speed, use some equations whose development last century earned two Nobel prizes, and you can describe the whole thing in terms of the fundamental constant of quantum physics, Planck’s constant. As Robinson says, simple.

Less so in practice. “These things are murderously difficult to measure,” Robinson goes on. “The aim of all this work is to get to about one part in a hundred million.” When a watt balance is calibrated, you have to take account of altitude—at sea level the gravitational pull is greater—and latitude: as the world spins faster at the equator, the centripetal force counteracts gravity. The instrument is so sensitive that even the height difference between separate parts of its mechanism must be accounted for, as well as the position of the Moon.

As the readings from the world’s watt balances converge, Robinson believes the technology is now at the stage where a new definition of mass is possible. “Of course it’s all difficult,” he says, “but there’s a difference between difficult and practically impossible.”

One side effect is that if it’s successful, Planck’s constant too will be fixed. At present, partly because it is determined by the kilo rather than the other way round, in theory it fluctuates slightly. This bothers physicists. “It’s a fundamental constant,” Robinson argues. “It should be constant. Why is it changing?”

At Versailles in November, this will be the crucial decision for the world’s leading metrologists: can we at last set a fixed value for Planck’s constant, and go ahead and retire the kilogram?

There’s more. A wholly different standard must also produce agreement: a set of silicon balls called Avogadro spheres. There is a permanent test version in the BIPM, and, like the obelisk in “2001: A Space Odyssey”, these small black spheres are unnervingly perfect. Spin one, and you can’t tell it is moving. Walk around it, and your eye gets befuddled, unable to focus. It is a crystal of silicon, cut and measured by lasers to ensure a precise volume. Its purpose is to measure the Avogadro constant: a value that relates to the quantity of carbon-12 atoms in 12 grams of carbon. To achieve this, the scientists plan to count the number of atoms in a fist-sized object. Via a pincer movement of fundamental constants, this will give us another route to the Planck constant and hence to the kilogram.

Leaving the Avogadro sphere, we pass the vault again. If pushed to make a prediction, Davis says it is unlikely the kilogram will be changed at this conference. But he does not expect the physical kilogram to outlast the next conference, likely to be in 2018.

Isn’t this a shame? By eliminating it we may gain a few decimal points of accuracy—corresponding to a mass even our ant would consider barely significant—but do we not lose something bigger when mass is just a concept? Davis might have been the guardian of the kilogram, but he is unsentimental about its future. “My view has always been that we need to get rid of this system as soon as possible. I appreciate what a tremendous job people did in the 19th century. They have served us well. But when something better comes along, you use it.”

Over 200 years ago, a group of scientists envisaged a worldwide measurement system that could be described to anyone scientifically literate, recreated by any sufficiently advanced laboratory and, crucially, applied without recourse to any object—whether a lump of metal or a monarch’s body part. It has taken longer than anyone imagined, but we are almost there. The metric revolution is nearly complete.