Redefining The Kilogram: The Ancient History Of New Measurements

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In this photo taken Wednesday, Oct. 17, 2018., a replica of the International Prototype Kilogram is pictured at the International Bureau of Weights and Measures, in Sevres, near Paris. The golf ball-sized metal cylinder at the heart of the world’s system for measuring mass is heading into retirement. Gathering this week in Versailles, west of Paris, governments on Friday Nov. 16, 2018, are expected to approve a plan to instead use a scientific formula to define the exact weight of a kilo. (AP Photo/Christophe Ena)ASSOCIATED PRESS

The big science-y news of last week was the vote to officially redefine of the kilogram– see the stories in Physics World and Physics Today for more detail–after decades of work by physicists on improving metrology technology. This removes the last of the physical artifact standards, a chunk of platinum-irridium alloy that fellow Forbes blogger Brian Koberlein called a magic rock.

This is a remarkable technological achievement, involving many years of exceedingly careful laboratory work to refine two techniques for making measurements, one based on a “watt balance” that matches a known magnetic force against the gravitational force on some mass, the other based on making ultra-pure spheres of silicon whose mass can be tied to the number of atoms they contain. At a more fundamental level, this changes the character of several numbers– Planck’s constant, Boltzmann’s constant, and Avogadro’s number– that had previously been empirically measured values with assigned uncertainties. Now, like the speed of light before them, these are officially defined as exact values.

At a deep level all of this traces back to the phenomenal precision with which we can measure time and frequency. With the speed of light defined as an exact value, the measure of length is converted to a measurement of time– one meter is 1/299792485th of the distance light travels in one second. The practical measurement of mass is now related to the force generated by an electric current, which is defined in terms of the number of electrons passing through a wire in one second. Of the common SI units, only the second has a definition related to a particular material object– it’s the time required for 9,192,631,770 oscillations of the light associated with the ground-state hyperfine transition in cesium-133 atoms.

(In a deep sense, you can probably trace the value of the kilogram back to the frequency associated with the rest energy of mass, thus tying together quantum physics and special relativity. The balance method is complicated and indirect enough as it is, though, and I don’t want to try to work through explaining how that plays out. I do reserve the right to use that philosophical association at a later date, though…)

In some sense, though, the most interesting thing about this is how little practical impact it has. That is, while there’s been a fundamental change in the underpinnings of the SI units, the new definitions of the various constants are carefully chosen so as not to upset the vast existing infrastructure based on the previous measurement standards. The kilogram is now defined in terms of Planck’s constant, but the ultimate value still matches the mass of the “magic rock” previously in use. The meter is now defined in terms of the speed of light, but still matches the distance between two marks scribed on a platinum-irridium bar back in the late 1800’s. The second is defined in terms of light emitted by cesium, but still equals the time it takes for an American to say “One Mississippi.”

Metal chrome exact weight on a dark background. Old style, sepiaGetty

The practical reason for doing this is obvious– in fact, it would be completely crazy, from a political and economic standpoint, to do anything else. In more philosophical terms, though, the process by which this happened is kind of fascinating. That is, all of our units have their origins in process that are remarkably arbitrary from the standpoint of physics, and yet we’ve steadily moved to anchor them to fundamental physical processes over the course of thousands of years. There’s a sort of bootstrapping nature to the whole business, with initial definitions used to test new processes, which then become the new definitions, which are used to test even newer processes, and so on.

It’s not an accident that our fundamental units are all conveniently human in scale. A second is not too far off the time of a typical heartbeat, a meter is a convenient separation between the hands of an adult human saying “about so big,” a kilogram is an easy mass to lift. In the case of the meter and the kilogram, these are not-accidentally close to older units defined in terms of particular people holding their hands apart or lifting handy objects.

The second, meanwhile, is a convenient human time interval, that’s then anchored to an astronomical one. For thousands of years, the most precise time measurements possible were astronomical in nature– using a sundial to track the motion of the sun across the sky, or using some visible markers to track stars at night– and necessarily involved long-ish times. Shorter intervals were measured via physical artifacts like water clocks, which marked time by the filling or emptying of some standard container.

roman style stone sundial in a gardenGetty

Of course, most of these processes are not perfectly consistent. A second is sort of close to a resting heartbeat, but of course, we’re not always at rest, and our heart rates change. Water clocks change their flow rate depending on the fill level and temperature. The length of a day changes over the course of the year, so a given change in the angle of the shadow cast by a sundial isn’t always the same total amount of time.

How do we get from these inconstant standards to the modern fundamental definitions? It’s the culmination of thousands of years of a kind of bootstrapping process: you establish that a new measurement technique is at least as good as the existing one, and then work out all the factors that might skew its results. Once you get those under control, you can get to a place where the new measurement is more reliable than the old, and it becomes a new standard that you can use to investigate variability of the old standard.

So, for example, the length of a mean solar day (noon on one day to noon on the next) is pretty good, but not perfect– it varies by a minute or so over the course of a year. You can use the mean solar day as a basis to test some shorter units– it’s two dozen re-fillings of a particular water clock, say– and then use that shorter standard to investigate the factors that change the behavior of the new standard. So, you build an identical clock, and test it with different fill levels, or fill it with hot water rather than cold, and figure out how all those factors change the behavior, and how to control them in a way that maximizes the reliability of your water clock. Once you’ve achieved the necessary level of reliability, you can use the new standard to make precise measurements of how the length of a day changes through the course of the year, and even the slow increase in the length of a day over the course of many years as the Earth’s rotation slows (which is why we add occasional “leap seconds” at midnight on December 31).

The passage tomb at Newgrange, outside Dublin (photo by Chad Orzel).Photo by Chad Orzel

This is a process that’s been going on for literally thousands of years. There are Egyptian water clocks from 1400BCE that are tapered in a way that reduces the effect of the changing water pressure as the level drops, and similarly ancient schemes for using an intermediate tank to ensure a more constant flow rate. A Chinese scholar in the tenth century CE used liquid mercury instead of water to remove the effects of temperature, and so on. While modern science has formalized refined these techniques to an extreme degree, there’s nothing particularly modern about the process, which is just the same thing humans have been doing since as far back as we have found traces of human activity.

A key step in the process of upgrading standards involves figuring out how and why the variability occurs, so you can know that you’re not missing something that undermines your reliability. That’s most of the job of the metrologists, and why it’s taken so long to replace the “magic rock” of the standard kilogram. Physicists have known that the standard kilogram was suboptimal for decades– it was a topic of concern when I was a grad student at NIST in the early 1990’s, and if I recall correctly Bill Phillips (my Ph.D. advisor) worked on an early version when he was first hired by NBS back in the 1970’s, with laser cooling as a side project. We’re only just getting around to redefining the kilogram in 2018 because it’s taken decades to characterize and control all the possible sources of uncertainty.

So, last week’s big vote on the redefinition of the kilogram is a remarkable achievement in more ways than one. It’s not just a cool bit of work by the scientists and engineers who developed and refined the new standard, it’s also a significant change in the philosophical basis of all our units. And, most importantly, it’s the culmination of a bootstrapping process that stretches back through thousands of years of human history.

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