Beautiful Realization

“Whaddaya mean, Sy, ‘charge and resistance and voltage all playing beautiful together‘? How’s that beautiful?”

“It is when they play together in a Kibble Balance, Vinnie. That beautifully-designed device solved the realization problem for two of the revised fundamental standards of measurement. Here’s the one for electricity.”

“That’s odd. It says ‘electric current’ but the number’s about charge. And I don’t see anything in there about voltage or resistance.”

“True. The electronic charge e is one of our universal constants. It and the speed of light and Planck’s constant h are the same on Mars as they are here on Earth. Take a cesium-based laser from Earth to Mars and its frequency doesn’t change. That’s why the revisions are measure-anywhere standards, no need to carry something to Paris to compare it to a physical object.”

“This is another one of those definition tricks, isn’t it? Like the cesium frequency — we defined the second by saying it’s the time required for so-and-so many waves of that light beam. Here, it’s not like someone measured the charge in coulombs, it’s we’re gonna make the coulomb exactly big enough so when we do measure an electron it’ll match up.”

“You’re not wrong, Vinnie, but it’s not quite that arbitrary. Lots of people did measure the electron against the old standard. This number represents the most accurate estimate across all the measurements. The standards board just froze it there. It’s the same strategy they took with the other six fundamental standards — each of them sits on top of a well-known constant.”

“Like Newton’s gravitational constant?”

“Sorry, Al, not that one. It’s universal, alright, but it’s only known to four significant figures, nowhere near the 8-or-better level the metrologists demand.”

“So tell us about the beauty part, Sy.”

I grab some paper napkins from the dispenser at our table. Al gives me a look. In his opinion Vinnie uses way too many of those and he doesn’t want it to spread. “Just using what I need to make a point, Al. Vinnie, I know you like pictures better than algebra but bear with me.”

“Yeah, you went through the kilogram thing pretty quick what with the garlic and all.”

“Oooh, yeah.” <scribbling on the first napkin> “Well anyway, here’s a sketch of the Kibble Balance rigged for weighing but let’s just pay attention to the parts in the dark blue oval. That zig-zag line labeled RK is a resistor that exploits the quantum Hall effect. Quantum math says its resistance is given by RK=h/e2. That’s exactly 25812.80756 ohms.”

“That a lot more digits than gravity.”

“Nice catch, Al. Now the second component in the oval is a quantum voltmeter. If you put a voltage V across it, the Josephson junction inside passes an alternating current whose frequency is f=V/CJ, where CJ=h/2e.” <scribbling on the second napkin> “Put another way. the frequency tells you the voltage from V=f×CJ and that’s the same as V=f×h/2e.” <scribbling on the third napkin> “The current iW going through RK is V/RK and that’s going to be iW=(f×CJ)/(RK)=f×(CJ/RK)=f×(h/2e)/(h/e2)=(f/2)×e. You with me?”

“Gimme a minute… You’re saying that the current is going to be half some frequency, which we can measure, times the charge on an electron. Yeah, that makes sense, ’cause the current is electrons and you got us counting electrons. Hey, wait, what happened to the h?”

“Canceled out in the fraction, just the way that e canceled out in the fraction for the kilogram.”

“Cute.”

“Better than cute, it’s beautiful. The same equipment, the Kibble Balance plus a gravimeter, gives you the realization of a kilogram depending only on h, AND the realization of the ampere depending only on e. Once you know the standards for time, which depends only on that cesium frequency, and for length, which depends only on time and the speed of light, you can get standards for mass and electric current in the NIST lab here on Earth or up on Mars or anywhere.”

“Almost anywhere.”

“What’s your exception?”

“In space, where there’s no gravity.”

“Einstein covered that with his Equivalence Principle.”

~~ Rich Olcott

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Revenge of The Garlic Calzone

“So what’s the next two steps?” Vinnie asks.

“I’m thinking a dose of the pink stuff and a glass of milk. That garlic calzone’s just not giving up.”

“Nah, we were talking about the new mass standard and how it uses a Kibble Balance protocol you said had three steps but you only got to the gravity-measuring step. You wanna talk to take your mind off your gut, do some more of that.”

“<burp-sigh> OK, assume we did an accurate measurement of gravity’s acceleration g right next to the Balance.” <pulling Old Reliable from its holster...> “Here’s the device in the protocol’s second step, ‘weighing mode’. Bottom to top we’ve got a permanent magnet A and a coil of wire B that’s hooked up to some electronics. The coil floats in the magnetic field because it’s carrying an electric current from that adjustable power source C. The balance’s test pan D rides on the coil and supports our target mass E. Up top, laser interferometer F keeps track of the test pan’s position. Got all that?”

“Mass goes in the pan, got it.”

“Good. You adjust the current through the coil until the interferometer tells you the test pan is floating motionless. Here’s where the electronics come into play. The same current goes through resistor RK, a quantum Hall effect device chilling in a magnetic field and a bath of liquid helium. Quantum math says its resistance is h/e², where e is the charge on an electron and h is Planck’s constant. Those’re both universals like Einstein’s lightspeed c. RK comes to 25812.807557 ohms. You remember the V-I-R diagram?”

“Once Ms Kendall drills it into your brain it’s there forever. Volts equals current in amps times resistance in ohms.”

“Yep. In the Kibble Balance we evaluate the coil’s balancing current by measuring the voltage drop across RK. The voltmeter uses a Josephson junction, another quantum thingie. At a voltage V the junction passes a small alternating current whose frequency is f=V/CJ, where CJ=h/2e. Count the frequency and you can calculate the voltage. DivideV by RK to get the current iW going through the resistor. Everything here meets the count-based, stable, reproducible-anywhere standard.”

“I suppose the w suffixes mean ‘weigh mode’ and m in the bottom equation is the mass. Makes sense that heavier masses need more current to float them. What’s G?”

“Hold on, I got another burp coming … <bo-o-o-O-O-ORP!>”

“Impressive.”

“Thanks, I suppose. G rolls up all those geometry factors — size, shape and power of the magnet and so forth — that you complained about when I said ‘motor-generator.’ We take care of that in the third step. Here’s the diagram for that.”

“Looks pretty much the same.”

“We took out the target mass and the power source, and see, there’s v-subscripts for ‘velocity mode.’ We move the coil vertically while
the atomic clock ticks and the interferometer tracks the pan’s position. That lets us calculate speed s. The coil moving through the magnetic field generates a voltage V=fvCj=sG. Because the geometry factor G is identical between modes, the linkage between coil speed and output power is exactly the same as the linkage between current and input power. That’s the middle equation — velocity-mode voltage divided by speed equals weighing-mode force divided by current.”

“That’s weird.”

“But true, and so elegant. Every variable in that equation save the mass comes from a high-accuracy, high-precision reproducible standard. That makes mass a measure-anywhere dimension, too. But wait, there’s more.”

“Too much math already.”

“Just a little more. Plug all these equations together and you get the bottom one. That’s exciting.”

“Doesn’t look exciting to me.”

“It goes back to the universal constants thing. The first factor in th middle is a ratio of count-derived quantities. Plug the quantum definitions into the second factor and you get CJ²/RK=(h²/4e²)(e²/h)=h/4. What that says is mass is expressible in units of Planck’s constant. That’s deep stuff! What’s exciting is that the standards people used that result in defining the kilogram.”

“Well, blow me down. And one more of your garlic burps or any more math just might.”

~~ Rich Olcott

The Case of The Garlic Calzone

I’m on an after-lunch hike through the park, trying to digest one of Pizza Eddie’s roasted garlic calzones. Vinnie’s walking a path that joins mine. “Hey, Sy. Whoa, lemme get upwind of you. You did the garlic calzone again, huh?”

“Yeah, and this time Eddie went two cloves over the line and didn’t roast them enough. Talk to me, take my mind off it, OK?”

“Sure. Uhhh… Let’s get back to kilograms which I got started on from a magazine article saying they’re chucking the old kilogram for something better. We were talking about that but got sidelined with measuring time and distance. So what’s the better thing?”

“They weren’t really sidelines, Vinnie, they were setting-up exercises. The technical world needs a set of measurement standards that are stable and precisely reproducible anywhere, any time. The old kilogram, the IPK, isn’t any of that. It’s a polished cylinder of platinum-iridium alloy in a Paris vault. You can’t reproduce it exactly, just very close. All you can do is bring a candidate object to Paris, measure the mass difference between it and the IPK, and then carry your newly-certified junior standard home to calibrate other masses on down the line. And hope you don’t scratch yours or get fingermarks on it en route.”

“But if we’re talking mass, why did time and distance standards even come into the conversation?”

“Several becauses. High-accuracy time measurement is fundamental to all the modern standards; much of the laser technology that supports the new time standard also plays into the other revised standards; and the time standard is the simplest one to describe and implement. No matter where you are, you can build a cesium-atom maser and fire it up. Start counting peaks in the maser beam and when you reach the defined number you’ve been counting for exactly one second. <burp> Excuse me.”

“You’re ‘scused. Yeah, the distance thing is pretty simple, too, now they’ve defined the speed of light as a standard. Is the mass standard that simple?”

“Nowhere near. In fact, it’s easier to describe the technique than to explain why it meets the requirements. It depends upon an apparatus called the Kibble Balance, named in honor of the late Bryan Kibble who devoted two decades of his life to perfecting the machine. Like with the spring balance we talked about, you estimate an object’s mass by comparing the force of gravity on it to some opposing force that you can quantify. The object in question goes on the Balance’s test pan. The opposing ‘pan’ is essentially a motor-generator, just a permanent magnet and a moving coil of wire.”

“Alright, I know enough about motors to see that’s complicated. To figure the balance of forces you gotta know the magnet’s strength and geometry, the coil’s resistance and geometry and speed, the voltage across it, the current through it… They’re none of them exact numbers. And you gotta account for how gravity can be different somewhere else like on Mars. Hard to see how that’s much of an improvement.”

“That’s the beauty of it. Kibble’s machine and measurement protocol are designed so that many of the finicky quantities drop out of the calculation. What’s left is high-accuracy counting-type numbers.”

“Measurement protocol? It’s not just ‘load the test pan and read a dial’?”

“Nope, it’s a three-step process. First step is to measure g, the acceleration of gravity in the Kibble room. Galileo showed all masses accelerate the same so any mass will do. National standards labs can’t just take a value from a book. At their level of rigor g has measurably different values on different floors of the building. You need a high-accuracy gravimeter — a vertical evacuated pipe with a laser interferometer pointing up from the bottom. Drop a mirrored test mass down the pipe while an atomic clock records exactly when the falling mass passes each of hundreds of checkpoints. Two adjacent distance-time pairs gives you one velocity, two adjacent velocity-time pairs gives you one acceleration, average them all together. <BURP!> You got any antacid tablets?”

“Do I look like somebody with a first aid kit in my purse? Don’t answer that. Here.”

“Thanks. No more garlic calzones, ever.”

~~ Rich Olcott