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I read that there is an effort to define a kilogram in terms that can exactly be reproduced in a lab. Why has it taken so long to get this done? It seems this would be fairly important.

Edit

Today I got around to finding the references.
You can see the international prototype of the kilogram IPK is the artifact whose mass defines at present the SI unit of mass here. You can also go here where you will see a link on the possible future revision to the SI. It sounds like this may happen in the next few years. I am not surprised that it takes years of R&D and millions of dollars to do this. Well that's peanuts compared to what was spent on LHC. I am not saying LHC was not worth the cost. It just seems we could have a modern definition of a kilogram by now if a few governments wanted to make it a priority. Does anyone here know if this effort has been given the investment that it deserves?

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I'm afraid it's not possible, in principle, to have a definition of a kilogram that can exactly be reproduced in a lab. –  Alfred Centauri Jul 16 '12 at 2:02
    
Relavent: constants in physics –  Argus Jul 16 '12 at 2:04
    
The first answer in the related question uses this basic understanding –  Argus Jul 16 '12 at 2:06
    
@AlfredCentauri: in principle? The mass of 1000/12 of a mole of carbon 12, in an atmosphere of 1 Pa Nitrogen. –  Jerry Schirmer Jul 16 '12 at 2:09
    
The wikipedia article on the kilogram explains that they recently considered a number of approaches, and have finally settled on one. I think mass is somehow inherently harder to define in this way than other units. –  Peter Shor Jul 16 '12 at 2:10

3 Answers 3

The kilogram is defined by a prototype (the "International Prototype Kilogram", IPK) -- basically, a kilogram is by definition the mass of a metal cylinder sitting in a vault in Paris. People have made a bunch of other metal blocks with almost exactly the same mass (as near as they could get), called "sister copies". To measure a mass extremely accurately in kilograms, you need to get your hands on either the IPK or one of its sister copies, and use it to calibrate your super-accurate balance.

There is an alternative approach which is planned to be used eventually. To measure a kilogram you would need a watt balance, calibrated by using the quantum hall effect and the Josephson effect, and also an accurate measurement of local gravitational acceleration.

The second approach seems more pleasing than the first, but is not [yet] used. Why? (1) The first approach actually allows significantly greater precision and reproducibility. Who would have thought that an old-fashioned balance could measure with so many significant figures, or that a metal cylinder could retain almost exactly the same mass over many years? (Well, it doesn't actually retain exactly the same mass, one of the reasons for an eventual switch.) But that's the case. It is so far impossible to make a watt balance with as many significant-figures of mass measurement precision as the prototype approach. (2) A watt balance is not just something any old lab can make, you need years of effort and millions of dollars. Even carrying a resistor down a hallway can change its resistance by enough to mess up the watt balance accuracy. When the watt balance standard is adopted, I doubt the number of places on earth where masses can be super-accurately measured will be any higher than it is today.

As far as I understand, the switched definition will allow super-precise electrical measurements to be much much easier. That benefit is supposed to outweigh the disadvantage that it becomes impossible to measure masses in kilograms as precisely as before.

I am not an expert, sorry for any mistakes.

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"Who would have thought that an old-fashioned balance could measure with so many significant figures" Yep. This kind of thing can be very surprising. I actually worked with a professor a few yeas ago who had a 19th century analytic balance that could measure as much as a two kilograms to 0.1 mg in a reproducible manner. Bloodly thing was good for seven significant figures! Beautiful piece of equipment. –  dmckee Jul 16 '12 at 13:56
    
+1 Nice post. I would daydream maybe someday it could be done by counting atoms, or maybe some kind of interference effect, where you could make a crystal of 1000 atoms, then make 9 more of those & put them together in precise alignment, etc., until you got a molar quantity. –  Mike Dunlavey Jul 16 '12 at 14:32
    
@MikeDunlavey - that's not far from some current attempts at redefining the kilogram. –  Emilio Pisanty Jul 16 '12 at 23:18
    
I have to say, though, that fixing the value of $\hbar$ is for some reason quite a bit more appealing to me than fixing Avogadro's number. –  Emilio Pisanty Jul 16 '12 at 23:19
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@Emilio: That silicon sphere is just begging to be put on a billiard table. –  Mike Dunlavey Jul 16 '12 at 23:50

Just to put some numbers in: as the wikipedia article states, the stability of the national kilogram standards is of roughly tens of micrograms over a century. This means that the relative stability is of the order of $10^{-11}\textrm{ yr}^{-1}$. This is pretty damn good (if short of the $10^{17}$ stabilities of the standard atomic clocks!) and to replace the International Prototype Kilogram as the SI standard you need a system for measuring mass that's at least that good at each national lab, and additionally can be used to compare national standards to that same accuracy, and can be used to calibrate across the whole range from micrograms to tonnes at an accuracy at least comparable to what the IPK and its sisters and derivative standards afford.

All in all this is a pretty tall order, and while there's probably a firm consensus$^\textrm{[citation needed]}$ that it's doable and worth doing, it does take some time to do it, and metrologists worldwide have also been busy setting up similar physical-constant-based standards for frequency, time, length, voltage, current, etc. I do get the feeling that mass is the next SI unit to get an overhaul, though.

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Kilogram is a measure of mass(remember, mass(direct mathematical representation) is not directly related to kilograms(A randomly chosen value with no scientific pattern))

One kilogram is a mass of a randomly chosen prototype ie a chunk of metal as the base unit.
Attempts to duplicate this "prototype" will lead to differences in accuracy relative to the original.

Background: Natural units , Physical constant

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This doesn't answer the question. And perhaps you could explain what you mean by "mass is not directly related to kilograms". –  Keith Thompson Jul 16 '12 at 17:50
    
Our ability to measure kilograms to any non arbitrary accuracies is extremely limited; therefore the determination of associated mass described in kilograms is innacurate. –  Argus Jul 16 '12 at 18:13
    
But you didn't mention that in your answer. You merely stated that "One kilogram is a mass of a randomly chosen prototype." without saying why (which was the question). And again, I don't understand what you mean by "mass is not directly related to kilograms". –  Keith Thompson Jul 16 '12 at 18:19
    
I thought you were asking for the defenition when I have more time this evening I will provide appropriate edits to my question in the links is were my statements stride. –  Argus Jul 16 '12 at 18:25

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