Tags: kilogram | le grand k | plancks constant

Say, How Much Does a Kilogram Weigh?

Image: Say, How Much Does a Kilogram Weigh?
Physicist Richard Davis of the International Bureau of Weights and Measures, sits next to a copy of a 118-year-old cylinder that has been the international prototype for the metric mass, in his office in Sevres, southwest of Paris, Wednesday, Sept. 12, 2007. (AP Photo/Jacques Brinon)

By Lee Gruenfeld
Monday, 10 Jul 2017 11:22 AM Current | Bio | Archive

No, that’s not the start to one of those idiot jokes you used to tell in grade school. It’s actually a very serious question.

If you ask how long a second is, there’s an easy answer. It’s not simple, but it’s easy. A second is how long it takes for radiation to transition 9,192,631,770 times between the two hyperfine levels of the ground state of the cesium 133 atom.

I have no idea what that means. But what I do know is that it’s a definition of a second that can be duplicated with the proper equipment anywhere in the universe.

Same thing with a meter. Back in the day, it was one ten-millionth of the length of a line drawn from the equator through Paris to the North Pole. Not a bad idea, except that this distance isn’t constant, for a number of reasons, one of them being the distortions caused by the Earth’s rotation. Nowadays, the official definition of a meter is the distance traveled by light in a vacuum in 1/299,792,458 of a second. (The meter is surprisingly close to the length of a yard, itself originally defined by the length between the king’s nose and his outstretched middle finger, a sub-optimal strategy unless you don’t mind redefining a yard at every monarchial beheading or other form of succession.)

What ties the definitions of a second and a meter together is that they’re based on natural, fundamental physical constants that are unvarying and can be measured anywhere.

Which brings us back to the kilogram. What’s the official definition? Believe it or not, something weighs a kilogram if it weighs the same as a chunk of metal that’s been sitting in a box in a basement in Paris for the last 128 years.

I’m not making this up. There are no physical constants to hang our measuring hats on. The entire metric system of weights is dependent on a small cylinder of platinum and iridium kept under airtight lock and key at the Bureau International des Poids et Measures. It was crafted in 1889 and is referred to by standards geeks (they do exist) as "Le Grand K."

Now, as a practical matter, manufacturers can’t be taking Le Grand K out of its little hermetic home all the time to use in calibrating their machines and products, so there are duplicates, known as "witnesses," all over the world. And while this has been a happy arrangement for over a century, serious discontent is now brewing.

Why? It seems that Le Grand K is losing weight. Or, the witnesses are gaining some, maybe from contaminants, but nobody knows for sure. What they do know is that that there is a discrepancy between the big guy and the copies, which a few years ago got bad enough to require an embarrassing reissue of certificates by the U.S. government’s National Institute of Standards and Technology (NIST).

Even though the difference is only about 45 micrograms, roughly the weight of a flea’s leg, the implications are significant. As an example, standards for allowable pollutants or filter effectiveness are often expressed in micrograms, which can make life tough for those enforcing compliance when faced with an objection that goes something like, "You’re going to fine me when you can’t even tell me what a microgram is?"

So it’s time to consign Le Grand K and his witnesses to museums, and instead come up with a definition that can be independently applied in any lab by using fundamental physical constants that are the same everywhere.

Fortunately, there appears to be a way to do this, based on what is arguably the most fundamental property of all, Planck’s Constant. Named after one of the founders of quantum theory, Planck’s Constant actually puts the "quantum" in quantum physics, by defining the basic unit of atomic vibration. The constant is denoted by the symbol h, and while atoms can vibrate at h, or 2h, or 6h, they can’t vibrate at 3.5h, because vibrations are quantized in whole number multiples of h.

As it happens, there’s a way to use Planck’s Constant h to set the mass of a standard kilogram. That’s the good news. The bad news is, nobody knows exactly what the value of h is, because there’s never been a need to calculate it to the kinds of precision required to boot Le Grand K off its podium.

At a conference three years ago, a committee of scientists who worry about these kinds of things set out a challenge: If h could be determined by three different teams working independently, with two of those teams accurate to within 50 parts per billion (ppb) and the third within 20 ppb, the committee would use those values to redefine the kilogram.

Since that gauntlet was thrown, NIST spent 16 months using a special gadget called a Kibble balance, which uses electromagnets instead of weights, to come up with a value for Planck’s constant that was accurate to within 13 ppb. A Canadian team used the same device to also get below 20 ppb, and an international consortium did the same by calculating the number of atoms in a sphere of ultra-pure silicon.

This month, the committee is going to average the results, along with figures from other labs, to come up with a single value for Planck’s Constant. (Spoiler alert: It’s going to be 6.626069934 x 10−34 kg∙m2/s.) Next year, they’re going to draft a resolution to redefine the kilogram based on this number and retire Le Grand K after many years of service.

I’m personally hopeful that those of you who have been suffering acute anxiety over this crisis will now be able to relax.

(P.S. For those of you who have already started to denounce me on social media for treating a kilogram in terms of weight instead of mass: Yeah, yeah. I’ve got a general readership here so back off and ride this train for a few minutes.)

Lee Gruenfeld is a managing partner of Cholawsky and Gruenfeld Advisory, as well as a principal with the TechPar Group in New York, a boutique consulting firm consisting exclusively of former C-level executives and "Big Four" partners. He was vice president of strategic initiatives for Support.com, senior vice president and general manager of a SaaS division he created for a technology company in Las Vegas, national head of professional services for computing pioneer Tymshare, and a partner in the management consulting practice of Deloitte in New York and Los Angeles. Lee is also the award-winning author of fourteen critically-acclaimed, best-selling works of fiction and non-fiction. For more of his reports — Click Here Now.

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If you ask how long a second is, there’s an easy answer. It’s not simple, but it’s easy. A second is how long it takes for radiation to transition 9,192,631,770 times between the two hyperfine levels of the ground state of the cesium 133 atom.
kilogram, le grand k, plancks constant

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