The Search for a More Perfect Kilogram

October 4, 2011 8:12 AM

The official SI definition of a kilogram is "equal to the mass of the international prototype," a cylinder of nine-tenths platinum and one-tenth iridium, forged in the 1880s. "Le Grand K," as the prototype is affectionately known, is the basis not only for the measurement of mass and volume, but of force, energy, and luminosity—and since the 1940s, Le Grand K has been losing weight. Now scientists are trying to redefine the kilogram in terms of fundamental constants—and in doing so, perhaps fulfill the 18th-century promise of a universal, fundamental system of measurement "for all people, for all time."
posted by Zozo (58 comments total)

why did it only start losing weight in the 40's?
posted by carlodio at 8:19 AM on October 4, 2011

Mid-life crisis.
posted by run"monty at 8:21 AM on October 4, 2011 [15 favorites]

You don't have to explain outgassing to me.
posted by Splunge at 8:23 AM on October 4, 2011 [4 favorites]

But surely they can't define all units in terms of fundamental constants, where the values of those constants is known only in terms of units also defined in terms of other constants (or the same constants in other relations), right? Otherwise how would you ever get started? They'd all just be interdefined.
posted by kenko at 8:26 AM on October 4, 2011

So, I haven't been gaining weight, the standard has just been shrinking. That still doesn't explain why my old pants don't fit anymore.
posted by VTX at 8:27 AM on October 4, 2011 [6 favorites]

Relative to the témoins and to the national standards, Le Grand K has been losing weight—or, by the definition of mass under the metric system, the rest of the universe has been getting fatter.
...
No one can say for sure why the prototype and its brethren are drifting apart.

Maybe I'm overly cautious, but if you don't know why the standard is changing, maybe you shouldn't "fix" it. Otherwise what's the point of having the standard?

...the erratic behavior of the master kilogram shows that a system of measurement based on a physical artifact can’t be trusted.

I'm also very wary of any system that separates the standard from the system used to measure it. If you want to define a mass, you really need to use mass to do it. Otherwise you will forever have the question of whether the thing you are really measuring is actually linked to mass at all.
posted by DU at 8:27 AM on October 4, 2011

E.g., "The meter, for example, was redefined 30 years ago as the distance traveled by light in a given fraction of a second." How is a second defined? I guess we have atomic clocks for that, are they independent from other units? Or do you have to have a given mass of (radioactive element) for such a clock to work?
posted by kenko at 8:28 AM on October 4, 2011

How is a second defined?

Since 1967, the second has been defined to be 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 caesium 133 atom.
posted by Zozo at 8:29 AM on October 4, 2011

Yeah, that was the advantage of Le Grand K - it's a thing that you can just measure and boom, there's your kilogram. I mean, we've already got an empirical way to measure out a kilogram of mass - 1,000 cubic centimeters of water, kept at just under four degrees C. But then you have to define a centimeter, and it all goes to hell.
posted by Holy Zarquon's Singing Fish at 8:29 AM on October 4, 2011 [1 favorite]

a universal, fundamental system of measurement "for all people, for all time."

B-but it's metric!

/ducks
posted by chavenet at 8:30 AM on October 4, 2011

I guess we have atomic clocks for that, are they independent from other units?
Yes. A cesium atom oscillates between two states at what, as far is we know, is the same frequency anywhere, anywhen, under any conditions. So that frequency serves as a suitably "grounded" basis for defining a unit of time.
posted by Wolfdog at 8:30 AM on October 4, 2011

Ok!
posted by kenko at 8:31 AM on October 4, 2011

This reminds me of the episode of the John Larroquette Show in which the man who was officially carrying around "the" inch - as in, the "inch" that people refer to when measuring things in inches - had his inch accidentally broken in a briefcase.

Haywire ensued until the inch was fixed, after which point they received even more upsetting news: in the process of fixing the inch, they had discovered that the inch hadn't really ever been exactly an inch long, so now all the rulers in the US would have to be recalibrated.
posted by Sticherbeast at 8:37 AM on October 4, 2011

if you don't know why the standard is changing, maybe you shouldn't "fix" it

Implicitly you would be using something else as the standard, and without tying the value to a constant the standard can only be some arbitrary physical object on earth. What if my scale differs from yours by 0.000001%? Which of us is right? We could say that the scale you have in your lab is correct by definition and is the standard against which all others should be calibrated, but that's no improvement over the Parisian lump of metal definition.

he shows me several graphs charting his never-ending struggle against vibration. He points out the rumbling of earthquakes half a world away and the burbling of liquid helium boiling off in the adjoining room. “For every improvement you make you get better signal-to-noise, but then you see something else,” he says.

For once, an experiment that really would benefit from being conducted in space.
posted by justsomebodythatyouusedtoknow at 8:39 AM on October 4, 2011

why did it only start losing weight in the 40's?

In a more serious vein. By current definition, the International Prototype Kilogram cannot lose mass, because it defines one kilogram, so it doesn't matter how many platinum and iridium atoms are in the prototype -- it is exactly 1kg.

Having said that, what we've noticed is that the other standards are "increasing" in mass. In 1884, forty copies of the IPK were made to act as national standards. They weren't perfectly the same mass, even to 1884 standards, so they're documented with an offset. The K20 copy, which is documented as 1kg - 39μg, is the primary mass standard in the US.

All the copies gain mass from contamination, and a big step in making an official comparison to them (or for them to be compared to the IPK) is cleaning them to remove that contamination. But it quickly comes back -- about 4μg in the first three months, then 1μg/year thereafter.

It is clear that the IPK is diverging from the 40 copies made in 1884. It's common to say that it is losing mass, compared to those 40, but it might be that the other 40 are gaining mass, and the far less frequently used IPK isn't.

The US has another standard -- K4 -- that is quite clearly losing mass compared to both K20 and the IPK. This isn't a mystery, K4 is the Check Standard for the US, and is used to calibrate the test standards used by NIST to certify public test standards. Because of this, it is handled more often than K20 or the IPK, and that causes wear. The last number a quick google finds is that K4 was originally delivered measuring 1kg-75μg, and in 1999, was found by comparison to several other prototypes to be 1kg-116μg, a loss of 41 micrograms.

This is a big problem, and there are a lot of smart people at the various national standards institutes trying to come up with a way to tie the kilogram to a natural, and thus repeatable, standard. Orginally, the meter was defined as one ten-millionth of the distance between the north pole and equator, at the longitude of Paris, but since that was a PITA to work out, it was actually implemented via a prototype -- a platinum bar exactly 1m long. That was hard to measure, so it was replaced with a platinum-iridium (90%Pt-10%Ir) bar with two marks on it, the distance between those marks defined 1m.

In 1960, that changed, and the meter became defined as a multiple of the wavelength of light emitted by an isotope. IIRC, it was Kr-86. Then, finally, we defined the speed of light as 299,792,458 meters per second, which implicitly defined the meter as the distance light travels in a vacuum in 1/299,792,458 of a second.

Set standards are a hard problem -- and finding a natural standard for the kilogram would make things much easier.
posted by eriko at 8:46 AM on October 4, 2011 [33 favorites]

This is totally fascinating, especially since the hallowed meter is a completely arbitrary measurement as well. The old definition, before it was redefined, was the one ten millionth the length of the earth's meridian along a quadrant (on preview thanks eriko), but they got it wrong. The earth's circumference is actually 40,007,863 meters. Eventually they discovered their mistake but it was too late - the bar was the standard.

So while it is clearly repeatable standard, its actually length is just as arbitrary as the foot (perhaps more so, as the foot was designed with human proportions in mind). Just some food for thought.

An interesting blog post on the use of the foot and the meter in architectural design can be found here.
posted by daniel striped tiger at 8:56 AM on October 4, 2011 [1 favorite]

Wait, I know this story. I turns out Le Grand K hasn't actually been losing weight at all, but every night a bitter rival sneaks into his apartment and slightly adjusts his scale, to gaslight him into believing that he's losing his marketable weighing-exactly-a-kilogram skills and thereby drive him into suicidal depression.
posted by cortex at 9:02 AM on October 4, 2011 [7 favorites]

I like the idea of defining the kilogram by first defining the exact numeric value of Avogadro's constant. Some background, including the suggestion to define Avogadro's constant as exactly N_A = 214 194 554 987 427 447 486, "the number of atoms in a cubically cut 60 carat diamond with 42,223,446 atoms on an edge" are in this paper[pdf].

Of course, if the more easily constructible artifact turns out to be Si²⁸, then the rationale for that precise number is gone.
posted by jepler at 9:03 AM on October 4, 2011

...a universal, fundamental system of measurement "for all people, for all time."

Sounds like some serious New World Order talk there, buddy. I bet I can get the talk-radio looks up in-arms over this.
posted by Thorzdad at 9:04 AM on October 4, 2011

Maybe I'm overly cautious, but if you don't know why the standard is changing, maybe you shouldn't "fix" it. Otherwise what's the point of having the standard?

That seems completely ridiculous. The whole point of a standard is that it doesn't change. Why does it matter what's causing the change? It just has to do with the properties of whatever metal they used to make it, not some issue with physics itself. "Le Grand K" is just a lump of metal like any other. The only reason it's special is because people decided to make it special.

Having a standard that changes over time is the opposite of caution.

In a more serious vein. By current definition, the International Prototype Kilogram cannot lose mass, because it defines one kilogram, so it doesn't matter how many platinum and iridium atoms are in the prototype -- it is exactly 1kg.

No, that's backwards. The standard is losing mass. The definition of mass has nothing to do with the kilogram. If you want to be hyper-technical you could say the mass of the kilogram prototype is always 1000 grams, but a 2011 gram is lighter then a 1980 gram.

Also, looking at wikipedia they have an article about the current and proposed changes. It looks like, once they change the kilogram all the base units will be based on physical constants. In this case the second will be defined by the Cesium atom's frequency. The Meter will be defined by the speed of light, the Kilogram will be defined by the Plank constant, and the Ampere will be defined by the elementary charge of an electron.

So, you could run into problems only if the plank constant, the speed of light, or elementary charge change (or the cesium atom's properties)
posted by delmoi at 9:05 AM on October 4, 2011

An accurate determination of the Avogadro constant by counting the atoms in a 28Si crystal [2010]
posted by jepler at 9:11 AM on October 4, 2011

Has it been losing weight or has it been losing mass?
posted by shakespeherian at 9:15 AM on October 4, 2011

I read this a couple days ago, it was a great article. I had no idea I was so interested in weights and measures.

"They'd all just be interdefined."

Pretty sure the whole universe is interdefined. :) But seriously, at a certain point you just have to pick something arbitrary and go with it. And the article has some interesting history of "how they got started," which you can then follow up with googling. There's nothing particularly important about the Cesium-133 defining the second; it's just a natural constant that's, conveniently, about one second, and we were already using seconds.
posted by Eyebrows McGee at 9:16 AM on October 4, 2011

There's something I've always wondered: why is the second defined in terms of a cesium atom specifically? Presumably there are other atoms that emit radiation at some high frequency; why this one?

I also have the same question about the old definition of the meter, which used to be defined as "1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum." -- why krypton-86, and why that particular line? (Now the meter is defined by fixing the speed of light and the length of the second.)
posted by madcaptenor at 9:28 AM on October 4, 2011

There is actually something special about cesium 133 which makes it ideal for atomic clockery -- my layman's understanding is that it has to do with the transition of the energy state of a single electron.

This link and this link describe the clever physics a bit.
posted by RobotVoodooPower at 9:35 AM on October 4, 2011

That seems completely ridiculous. The whole point of a standard is that it doesn't change. Why does it matter what's causing the change?

Yeah, but the whole question is whether or not the standard is actually changing or whether the other stuff you're comparing it to is changing. We assume that if most things are getting heavier compared with the standard then the standard is probably losing mass somehow, but short of counting atoms, there's no way of knowing that for sure.
posted by straight at 9:36 AM on October 4, 2011

It is clear that the IPK is diverging from the 40 copies made in 1884. It's common to say that it is losing mass, compared to those 40, but it might be that the other 40 are gaining mass, and the far less frequently used IPK isn't.

If the rate of divergence is a known quantity, can't the SI folks extrapolate back to what the standard once was, from where we are now?
posted by Blazecock Pileon at 9:56 AM on October 4, 2011

the hallowed meter is a completely arbitrary measurement as well. The old definition, before it was redefined, was the one ten millionth the length of the earth's meridian along a quadrant (on preview thanks eriko), but they got it wrong. The earth's circumference is actually 40,007,863 meters. Eventually they discovered their mistake but it was too late - the bar was the standard.

So while it is clearly repeatable standard, its actually length is just as arbitrary as the foot (perhaps more so, as the foot was designed with human proportions in mind). Just some food for thought.

I bit off some of that food some time ago...

Consider: the finer the resolution (or smaller the scale) at which you're measuring the earth's circumference, the longer you will discover it to be. This is what happened between the first definition and the revistited statement: they measured more closely.

But more importantly: what was actually said at that meeting in the National Assembly, during the Revoltution, when Talleyrand suggested that they needed to institute a new basic measure? "We will institute the meter, and it shall be defined as the 40millionth part of the earth's circumference."? But: why not 20millionth? Or 100millionth? It seems obvious that the will to have a new measure was accompanied by an approximate idea of what that measure should be, as defined by very plain, immediately obvious "natural" terms (as, say, the ell, or the foot had been); a handy, practical measure. There will have been someone in the meeting who will have said: "It should be about this long (holding arms outstretched a comfortable distance), like, uhm, like a baguette."
And only then the astronomers/geometers were sent off to corroborate this baguette-length with some more scientific correspondent measure - setting scientists off on the endless search for just such a chimerical value. The true origin remains: the decision. (And the baguette.)
posted by progosk at 9:57 AM on October 4, 2011 [1 favorite]

B-but it's metric!

Everyone uses the metric system now. Even US manufacturers now primarily use the metric system. Measurements and sizes of products are sold as US standard weights and measurements only as a convenience to the public, but nearly every manufacturer now works entirely in metric behind the scenes.

Seriously, grab the consumer product nearest you and read the label. Unless it's a 128 oz gallon jug of something, chances are good that the given volume in metric is an even number, while the US standard measurement is some odd-numbered decimal-pointed number.

Sure, many US cars still offer US standard bolts and fasteners, but if you go back to the internal design documents I'll bet you lunch that it's measured in millimeters.
posted by loquacious at 10:32 AM on October 4, 2011

SI UNITS!!!!

It's fascinating how much effort is put into maintaining standards. I visited the Irish standards lab years ago. Apparently, the whole building sits on springs to isolate it from vibration. What sticks in my memory most was...
The Room Where They Keep The Volt
Racks and racks of gear all centered around a couple of zener diodes.

Ohms are kept in temperature controlled baths of silicone oil.
And speaking of temperature, the wonderful glass "sculptures" where water was kept at it's triple point. And I seen the actual National kg whilst it was being compared to other kilos.

(I regularly laugh at the irony that US standards are all now defined in terms of SI Units (as mentioned in previous posts))
posted by Homemade Interossiter at 12:25 PM on October 4, 2011

Sure, many US cars still offer US standard bolts and fasteners, but if you go back to the internal design documents I'll bet you lunch that it's measured in millimeters.

If only this were so. Fasteners, metal stock, piping, lumber are all frustratingly sold in imperial units in North America. The reason is that these all depend on decades old standards documents (ANSI, ASME, ASTM) written in the US. Newer revisions of these have metric notation as well, ("2 by 4"s are occasionally spec'd as 38 x 89 mm), but they only round evenly in imperial.

There are metric-based standards in other countries, notably Germany and Japan, but the old imperial standards are enshrined in law in the US and Canada. In Canada, we have to be fluent in both :(
posted by Popular Ethics at 12:32 PM on October 4, 2011 [1 favorite]

No, L- , not everybody uses the metric system. Don't get me wrong, I'm not saying this this as an advocate, but the imperial system is still in use in aviation, shipping, and many manufacturing processes. I'd love to hear from people who know more specifics.

I don't know about the auto industry, but as far as nuts and bolts go, it's either one or another. Fractional measures don't translate well into decimal.
posted by Steakfrites at 12:33 PM on October 4, 2011 [1 favorite]

Seriously, grab the consumer product nearest you and read the label. Unless it's a 128 oz gallon jug of something, chances are good that the given volume in metric is an even number, while the US standard measurement is some odd-numbered decimal-pointed number.

Of the products near me (standard cupboard - graham crackers, peanut butter, salt, other crackers, marmalade, crisco, etc) most are even imperial units.
The ones that aren't are things that have been hit by the grocery shrink-ray (chocolate chip bag going from 12oz to 11.63oz) or products that originated abroad (125g of dutch cocoa).

I don't know what they are doing on the backend, but customer facing, they seem to have stuck with imperial for the most part.

Also, I am now hungry...
posted by madajb at 12:45 PM on October 4, 2011

The story I always heard for the meter is that it was originally supposed to be the length of a pendulum with period two seconds (and therefore half-period one second). This has the effect that the acceleration due to gravity, g = 9.81 m/s², is numerically very close to π². I wrote about this in a blog post years ago, which got linked to on Reddit, and a lot of people there thought I was kind of stupid because of course that's a coincidence. That's when I discovered Reddit, I think, and also when I started to lose faith in it.
posted by madcaptenor at 1:06 PM on October 4, 2011 [2 favorites]

madcaptenor: more meter details here.
posted by progosk at 1:19 PM on October 4, 2011 [1 favorite]

g on earth varies quite a bit, though, so it wouldn't be a very accurate way to measure length.
posted by delmoi at 1:23 PM on October 4, 2011

Well, yeah. I'm not sure if it was known at the time that g varied on Earth, though.
posted by madcaptenor at 1:30 PM on October 4, 2011

Steakfrites: "No, L- , not everybody uses the metric system. Don't get me wrong, I'm not saying this this as an advocate, but the imperial system is still in use in aviation, shipping, and many manufacturing processes."

Transportation in the both the US and Canada primarily uses pounds.
posted by Chrysostom at 2:39 PM on October 4, 2011 [1 favorite]

The U.S. customary system is different from the imperial system and predates it. They are both derived from previous English units.
posted by grouse at 3:51 PM on October 4, 2011

You don't need a fancy metal block.

All you need is water. 1 ml of H20 = 1 cc of H20 = 1 g of H20. One liter of pure H20 will always have a mass of 1 kg.

The more you know (cue star!)
posted by Renoroc at 3:52 PM on October 4, 2011

All you need is water. 1 ml of H20 = 1 cc of H20 = 1 g of H20. One liter of pure H20 will always have a mass of 1 kg.

Even if the kg were still defined that way (it's not), then you'd need to get your hands on some Vienna Standard Mean Ocean Water.
posted by partylarry at 4:20 PM on October 4, 2011

One liter of pure H20 will always have a mass of 1 kg.

No, the density of water changes depending on temperature, pressure, and who knows what else. At 4 °C and 1 atm of pressure, 1 L of water has a mass of 0.999720 kg. That's a small number of significant figures, and it's hard to make sure things are exactly 4 °C, 1 atm, that the water is exactly the right composition, that you have exactly 1 L of it, and so on.
posted by grouse at 4:22 PM on October 4, 2011

Eriko, I applaud for you an awesome, substantive and non-lulzy comment. Good stuff, sir. If only yours was the fifth comment in the thread.
posted by smoke at 5:02 PM on October 4, 2011 [1 favorite]

Good stuff, sir.

I was about to point out that "eriko" is likely a female Japanese name.

But then I checked, and it turns out eriko is a guy named Erik.
posted by madcaptenor at 5:43 PM on October 4, 2011

In the US, aviation (as in the Federal Aviation Regulations) uses a baffling mix of units: distances are measured in nautical miles (so speed is in knots, nm/hr); altitudes are in feet (but climbs/descents are in feet-per-minute); angles are in degrees; and pressures are in inches of mercury. But temperatures are now in celsius.

(Nautical miles are cool because 1 minute of latitude is almost exactly one nm. Also 1 knot is very close to 100 feet per minute. This makes mental arithmetic feasible while flying.)
posted by phliar at 6:15 PM on October 4, 2011

Oh yes, and mass is in pounds.
posted by phliar at 6:16 PM on October 4, 2011

I will continue to consider this 'problem' to be primarily one of excess rectal astringency - until someone creates a standard for how much precision is enough.

We've got a world in which millions of people are starving, and someone gets paid to fret over a speck of dust? Clearly the 'urgency' is more commercial than humanitarian in nature. Philosophically, too, it's a bit mad in a universe in which -everything- is continually in flux to -hope- to establish bastions of permanence ... then lock them up and guard them like precious jewels. But hey, be my guest.
posted by Twang at 6:22 PM on October 4, 2011

since the 1940s, Le Grand K has been losing weight

What's its secret, dammit?
posted by anothermug at 6:24 PM on October 4, 2011

Seriously, grab the consumer product nearest you

I'm at my desk, surrounded by stationery, and it's pretty much all inches. Binder clips, envelopes, paper (its own size and the distance between the lines), binders — all inches. The tip of my pen is measured in millimeters, though.

(If I did this exercise in my kitchen, yeah, metric would win hands down.)
posted by stebulus at 8:35 PM on October 4, 2011

The Fahrenheit scale of temperature originally ranged from the freezing point of water (aka 0) to the body temperature of a human being (aka 100). This system worked well enough until the advent of Global Cooling, when human body temperatures were downgraded to 98.6°.
posted by twoleftfeet at 8:47 PM on October 4, 2011

The Room Where They Keep The Volt

Having read this, I will no longer sneer at plots where supervillains plot outrageous, carefully themed heists. Because now I know that the temptation to do so is all too real.
posted by No-sword at 9:05 PM on October 4, 2011 [1 favorite]

For the idea of using water for the kilogram, you need it under a defined pressure. Pressure is force/area. The standard unit of force is the Newton. The Newton is defined as one kg m/s^2. So you end up defining the kilogram in terms of itself.

I suppose you could define force in terms of charge by defining the exact number of electrons in the Coulomb which would then give you a definition of the ampere, which could then give a measure of force. But there isn't an exact number of electrons in the Coulomb, only an approximation. So we're back to measuring numbers of particles, at which time we might as well just build the silicon sphere.
posted by Hactar at 7:34 AM on October 5, 2011

So you end up defining the kilogram in terms of itself.

It could still work, though. We're not saying "the kilogram is equal to one kilogram". Still, you end up having to solve a system of equations, which is never fun.
posted by madcaptenor at 8:09 AM on October 5, 2011

We've got a world in which millions of people are starving, and someone gets paid to fret over a speck of dust?

We've got a world in which millions of people are starving and someone is spending money to be self-righteous ass on the internet?

These are very real problems that affect our ability to conduct commerce. It may seem trivial now, but if you're buying something that is sold by weight and very expensive (like gold at $1.6M per kilogram), you damn well want to be sure that the measurements are accurate.

Moreover, they're even more important when we're doing basic science. Do you want the LD50 of a particularly finicky drug calculated using wonky measurements? A few grams can make the difference between a life-saving treatment and a fatal overdose.
posted by chrisamiller at 8:24 AM on October 5, 2011 [2 favorites]

And when you are building MRI machines or rocket nozzles or boring subway tunnels or building bridges or building chip factories, you need to make sure the designers are speaking exactly the same language as the builders as the sub contractors as the quality inspectors.
Any collaborative endeavor requires precise communicable parameters, and the more technologically advanced, the finer precision is typically needed.
posted by Catfry at 12:07 PM on October 5, 2011

The Fahrenheit scale of temperature originally ranged from the freezing point of water (aka 0) to the body temperature of a human being (aka 100).

Water freezes at 32F. 0F is the temperature that a mix of stuff (googling: water, ice, and ammonium chloride) equilibrates to, at least for a while.

ISTR that back in the day, this mixture gave the coldest reliable temperature then achievable, so it got to be zero.
posted by ROU_Xenophobe at 2:24 PM on October 5, 2011

0-100 on the Fahrenheit scale also maps very closely to the highest and lowest temperatures in most habitable parts of the world.
posted by straight at 4:49 PM on October 5, 2011

if you go back to the internal design documents I'll bet you lunch that it's measured in millimeters.

Definitely not true in electronics. In circuit board design, some components have pin spacing specified in millimeters, others in inches. For the stuff I design, it seems to be about 50/50. I just round everything to 0.01 mm and go from there. I suppose this could get you into trouble with big high-density components, but I avoid those for other reasons.
posted by ryanrs at 7:02 PM on October 5, 2011