We all know what a kilogram is, right? It’s the mass of a bag of sugar. Thank goodness for the bag of sugar. Without it we’d be forced to imagine 1/7000th of an African bull elephant or 1/14560th of a double decker bus or God only knows what fraction of the weight of Wales.
Having a clear visualisation of the kilogram is important for all sorts of reasons, not least because it’s one of the seven SI units, the fundamental alphabet of symbols which can be combined in a variety of ways to express any physical quantity. Speed, for instance, is measured in metres per second, whereas force can be expressed in terms of kilogram metres per second squared.
The kilogram was accepted into this metrological pantheon alongside the metre 125 years ago today, when the value of both units was defined at the first General Conference on Weights and Measures organised by the BIPM. As a consequence of that meeting, three identical kilograms were cast by the firm Johnson Matthey out of a mass of platinum-iridium alloy. This alloy was chosen because of its density and chemical stability, meaning that the kilograms would be both small and resistant to rust. One of the kilograms was kept at the BIPM offices in Sevres, and two were sent for safekeeping in America. Rumours that a further three were subsequently distributed to the elven-kings under the sky have no foundation in truth.
The Paris Kilogram, incidentally, known colloquially as le Grand K (although never, for some reason, as Special K) is today kept under some of the most secure conditions on the planet. The small metallic cylinder is stored in three bell jars inside a specially-designed basement vault, and is only ever removed for the ceremonial weighings.
These take place around once every forty years, and like all family gatherings provide an opportunity for all the kilograms around the world to come back home and measure themselves against their more famous sibling. This is a fascinating procedure which has now inspired a very timely film called 1001 grams.
Fascinating though these occasions are, these cumbersome weighing sessions encapsulate all that is wrong with the current definition of the kilogram as opposed to that of all other SI units. Take the metre, for instance, which according to the 1889 treaty was also defined against a physical object. Over the intervening 125 years, however, a far less arbitrary definition has been reached thanks to the speed of light. Given that this is a universal constant, any laboratory around the world with sufficiently accurate timing equipment is now able to independently reach the same value for the fundamental SI unit of length.
But is it putting on weight?
A definition of the kilogram in terms of natural constants would not only make these Paris trips redundant, but would also improve the accuracy of the kilogram itself. At the moment, despite the intense protocols in place to keep it safe from tampering and the use of the ludicrously expensive but exceptionally stable platinum-iridium alloy, the grand K has actually been gaining and losing weight. Just to put in perspective how crazy this is, this would be like finding out that the letter A has been slowly transforming into B when nobody’s looking. Crazier still, of course, is the realisation that The Kilogram will always weigh exactly one kilogram no matter how much mass it loses or gains.
While the reasons for the sporadic weight gain are not yet known for certain, the most popular theory is that the annual handling process may be responsible in some way. Whatever the cause, subsequent weighings have shown that our fundamental unit of mass can fluctuate by as much as 50 micrograms, written in scientific notation as 50 μg. Now, this is a fairly abstract number to get one’s head around, so Matt decided to carry out a little experiment to work it out:
What exactly weighs 50 μg?
Right. Matt here. To visualise what this 50 μg weight loss looks like I went to our lab where we have a 5 decimal point balance which, according to its sticker, was calibrated 6 months ago.
Now we had a way of showing what weighed around 50 μg, we needed things that did. And our first thoughts turned to hair. Human hair is always used as a demonstrator of things that are small, so we assumed that their mass would be suitably tiny.
Also, we fortunately had a very abundant supply of different types and lengths of hair in the lab: my head. So Keir, PJ and I donned our PPE and set about doing a well-documented and thorough investigation of things that weighed 50 μg.
One of the hairs from my head — gracefully plucked by Keir — weighed a lot more than I thought it would at 900 μg, so we had to go for something shorter…
A beard hair came in at 580 μg. This is still more than 10 times more than the mass difference of Le Grand K after handling.
This was AN AWFUL IDEA: kudos goes to camera operator PJ for predicting my expletive and stopping filming just before. The secondary conclusion we took from today’s experiment is that pulling moustache hairs out with tweezers is really REALLY painful. Also, sort of a pointless experiment because they still weighed 490 μg and we clearly needed something a LOT shorter.
Daintily plucked by PJ Saini, my eyebrow hair (specifically from my mono-brow, I figured I could kill two birds with one stone and do science as well as come out looking good) came in at under 10 μg — the lower limit of the balance. As a result the scale kept flipping the last digit between 1 and 0, so we’ve decided to call the mass of the eyebrow hair ~5 μg. We then thought about getting a hair somewhere in length between an eyebrow hair and a moustache hair…
But then thought better of it.
So, here we have it: the mass difference between the Le Grand K and its replicas over the course of half a century is on average about the same as 5-10 eyebrow hairs, and is never more than half a moustache hair.
But is this accurate enough?
Now, (Gilead here again) that might strike you as being really pretty accurate. After all, scaled up to a human being, the relative weight difference is akin to Matt shaving off a third of an eyebrow (or a sixth of a monobrow, for those keeping score). For the sadists amongst you, imagine throwing a toddler off the Empire State Building.
But even this incredible accuracy is just not good enough. The current requirements for an SI unit prototype include accuracy to 8 decimal places, which means the Grand K just won’t cut it.
Scientists have been working on a replacement definition for years, and it now looks as though we may be just a few years away from chucking the whole platinum-iridium business altogether. There are two major techniques currently hoping to score the kill shot:
The Silicon Ball. As this great clip from Veritasium demonstrates, this is an almost perfect sphere of silicon atoms whose volume can be very accurately determined. By relating this volume to the dimensions of an individual silicon atom, Avogadro’s constant can be used to obtain an accurate value for the mass of the whole.
The Watt balance. An incredibly sophisticated piece of equipment, the Watt balance acts like an old-fashioned apothecary’s scale, balancing the downward force of the object’s weight with the upward force of the magnetic field generated by an electrical current. With a sufficiently accurate measurement of electrical current, the exact definition of the kilogram can be indirectly obtained.
Some of the leading research in these two areas is being carried out at NPL, the UK’s National Physical Laboratory in Teddington, just outside London. Recent breakthroughs lead them to believe this may well be the kilogram’s last major birthday. If they are right, it would at least provide long-lived couples of the future with an appropriate name for their 125th year together – the platinum-iridium anniversary.