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ARTICLE: Self-referential Problems with the Electronic Kilogram
From Greg Lloyd, R&D Engineer
Spokane, Washington, USA
glloyd48@comcast.net


I read this evening about the apparent 50 microgram loss over the last 100 years in the kilogram standard maintained by the Bureau International des Poids et Mesures in France. I calculate this is equal to an average loss of about four-trillion atoms per day. This would upset anyone who maintains precise standards. May I suggest cross checking the mass standards more often that once per century?
But trying to improve on this inadequacy by using a watt balance to measure the kilogram in terms of the electrical current required to lift a mass against gravity seems like the wrong way to go. As your article mentions, it requires a precise knowledge of the strength of gravity at each lab (which is a variable even at one particular location and would be a challenge to measure to the required precision in its own right); and second, I believe it creates a self-referential definition.


I read that one of the reasons the density of water was abandoned as a basis for the mass standard was because it required that water's density be measured at exactly one standard atmosphere (101.325 kPa).
Water has a small bulk modulus effect so it is important, in precise work, to make the measurements at a reproducible pressure. However, I read that since the definition of pressure has the kilogram as one of its terms, the water-based mass standard was abandoned, in part, because its definition was self-referential. So how can you now seriously consider expressing the kilogram in terms of electrical current? Is this not self-referentially too? The absolute definition of the ampere is a unit of force, the newton. And one of the terms in the absolute definition of the newton is the kilogram!


I can't overlook the inescapable double standard of this logic. At least with water as the standard, the effect of small errors in pressure was divided down into a VERY small difference in density due to water's high bulk modulus. The old water-based definition may have been technically self-referential, but the effect was negligible after only one circle. In the case of a watt balance where you express the kilogram as an electrical current, the self-referential effect is exactly unity!


The more I think about it, the more I'm attracted to the notion of just tallying-up a quantity of gold atoms. Gold makes so much sense. It's effectively impossible to oxidize and has only one naturally occurring isotope (which whips silicon hands down). All you have to do is two things: define Avogadro's number, and redefine the mole. Avogadro's number can simply be defined at the latest CODATA value of 6.022 141 99E+23 atoms per mole. Then the mole would be redefined as being equal
to 0.196 966 55 kg of gold rather than 0.012 kg of carbon 12. Then, all any lab in the world has to do to make their own kilogram standard is to make a wad of gold comprising, by definition, 3.057 444 012 701 649 087 116 569E+24 atoms (or as close as possible to this quantity).


And what do you do if you don't take good care of your gold mass standard article? If you suspect you might have lost an average of four-trillion atoms per day over that last few years, all you have to do is stick your wad of gold back in your machine and measure-out a new one. Granted, this is no trivial endeavor. If you were to truly COUNT gold atoms, then even at 10 terahertz, you'd be at it for nearly 97 centuries to make a single kilogram. But if a way can't be found to count atoms really, REALLY fast, then I'm sure a clever group of researches can figure out a way to measure the rate of deposition with the required precision and without succumbing to self-referential definitions (as would be required when measuring the amperes of current required to neutralize a stream of gold ions). Maybe there's a slick way of reducing the rate of deposition to a frequency, mixing in a reference frequency standard, and counting the heterodyne pulses. If you can design a machine that outputs nine-billion heterodyne pulses per kilogram, you'd have about as much precision as the current record-holding definition: a second's-worth of time.



Go to NIST Plans To "Stabilize" Kilogram



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Jaren Green, Editor
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