Last November a group of scientists from Europe and the United States gathered in a meeting-room in Bern to discuss a deeply embarrassing problem. Among the 20 or so who took their seats around the horseshoe-shaped table were some who had spent most of their careers wrestling with it. Some had even thought they would never see a solution during their working lives.
Yet there was a sense of optimism among those present at the meeting that after years of struggle, they were now close to ridding science of its humbling little secret.
It is this: no-one knows what a kilogram really weighs.
Sure, everyone knows roughly what a kilogram weighs: about the same as a cauliflower, or a litre of beer, or a decent-sized Bible. But that is nowhere near good enough for scientists, for whom precision is everything. For over 200 years, they have been working on a set of standards for all the properties of matter: size, quantity, temperature, even its luminosity. And they have succeeded in finding perfect, universal standards for all of but one - which, by sheer bad luck, just happens to be the most important one of all: mass.
If you want to know the precise length of a metre, scientists can tell you: since 1983 they have defined it to be the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. If you want to know precisely how long that single second lasts, they can tell you that as well: it is the amount of time taken for 9 192 631 770 cycles of a specific form of radiation emitted by atoms of caesium-133.
But if you ask for a definition of a kilogram, the answer is - well, not so impressive. No references to cosmic concepts like rays of light in vacuum, no long strings of digits. Instead, since 1901 the kilogram has been officially defined as the mass of a small alloy object locked away in a safe near Paris.
Known as the International Prototype kilogram, the object takes the form of a 40-mm high cylinder made from platinum and iridium in 1889. Kept at the Bureau International des Poids et Mesures (BIPM) </enus/4_BIPM> in Sevres (GRAVE accent, first "e") under a series of special covers, it has a kind of enigmatic beauty - and the distinction of being the One True Kilogram In The Universe.
But it is a distinction that comes at a hefty price. For if someone were to drop it, lose it, steal it, or even touch it, that would be the end of the One True Kilogram - its pristine state lost for ever.
Not surprisingly, no-one is normally allowed anywhere near it. Instead, scientists have to content themselves with one of the 80-odd copies of the One True Kilogram that have been made over the last 100 years. Every few decades, all the copies are brought together and compared to the International Prototype, just to check that they are still in good condition.
The last comparison took place in the 1980s - and it revealed a disturbing fact. Some of the copies had mysteriously put on weight since they were last brought together in the 1940s. It was only around 20 millionths of a gram, but no-one could explain it.
Worse still, no-one could think of a reason why the International Prototype might not also have gained weight. Yet as its mass is always exactly one kilogram by definition, its mass must always be the same. It's a paradox: a fixed standard that could be changing all the time. And it is one that reveals that, deep down, no-one can really say what a kilogram weighs.
The scientists who gathered in Bern in November are leading the effort to put that right. They met at Metas, Switzerland’s Federal Office for Metrology and Accreditation, to discuss progress in a 30-year project aimed at making that shiny metal cylinder in Sevres redundant. They plan to replace it with a new standard kilogram which - in principle, at least - can be created by anyone, anywhere, and which never, ever changes.
But as Dr Philippe Richard of Metas explains, it has proved extraordinarily hard to find a replacement for that relic of 19th century science. "It’s possible to measure its mass with a very high level of accuracy - one part in a billion, or even ten billion", he says. "They did a very good job when they chose it all that time ago".
Even so, Dr Richard is one of the scientists at last November’s meeting who thinks a replacement has finally been found. It’s called the Watt Balance. Devised back in the mid-1970s by a scientist at the UK National Physical Laboratory (NPL) in Teddington, near London, the basic idea sounds simple enough. A mass is put on one arm of a kind of hyper-sophisticated set of weighing scales, which are brought into balance by applying electrical power. This power is measured in watts, giving the balance its name.
The amount of power required to achieve balance can be measured extremely accurately. Better still, it can be measured in terms of fundamental properties of the cosmos, including something called "Planck’s Constant", a universal quantity whose value is known with great precision.
So now the definition of the kilogram becomes the mass which gives the right value for Planck’s Constant when put on a Watt Balance gives - a definition that allows anyone, anywhere with the right equipment to have their own perfect, unchanging kilogram.
If only it were that simple. In practice, the Watt Balance is stunningly complex piece of equipment that requires a host of quantities to be measured all at the same time, and with extreme precision. The first prototype, constructed at the UK National Physical Laboratory (NPL) in Teddington, near London, proved incredibly temperamental, with even the tidal tug of the Moon affecting its precision. "It’s being replaced", says NPL kilogram group leader Dr Stuart Davidson, with a palpable sense of relief. "At the moment, only one person knows how to use it, and if he left, we’d be in trouble".
Those attending the Bern meeting know all too well the size of the challenge they face. The Watt Balance has been designed to reach a precision equivalent to measuring the distance between Zurich and Los Angeles to the nearest millimetre. Other national standards bodies in the US, France and even the BIPM at Sevres are confident enough of the technique to have begun work with their own Watt Balances. "We’re all making quite good progress", says Dr Ian Robinson of the NPL, who attended the meeting (and, incidentally, is that one person who knows how to work the NPL’s Watt Balance). "It’s still looking extremely promising".
By that, Dr Robinson means there is a real chance of the Watt Balance being turned into a device that routinely reaches the precision required to make the International Prototype redundant. They’re within a factor of 10 of that now, and could hit the target within a decade.
But does it really matter ? Do we really need to know the mass of the kilogram to such precision, any more than we need to know the number of millimetres separating Zurich from Los Angeles ? The scientists involved admit it probably won’t help anyone resolve a dispute with a grocer over the accuracy of his scales. Even so, they argue that the world deserves the most sophisticated measurement system science can possibly produce - and a metal cylinder in a safe can hardly be part of that. "It’s really the need for elegance that driving this", says the NPL’s Stuart Davidson.
Yet anyone who has seen the prototype Watt Balance would be hard-pressed to describe it as elegant. Surely there must be an easier way to define the kilogram. Over the years, scientists have come up with several alternatives, such as the number of silicon atoms in a precisely-made ball, or the mass of charged particles caught in a metal cup. None have them has proved as successful as the Watt Balance.
Even so, Dr Davidson admits he does sometimes wonder if there is some really clever method that the experts have somehow missed. Just in case, the NPL website explaining the intricacies of the Watt Balance ends with a simple request: "Any better ideas on a postcard please".