The Currant Affair

Al has a new sign up at his coffee shop, “Scone of the day — Current.” He chuckles when I quietly point out the spelling error. “I know how to spell currant, Sy. I’m just gonna enjoy telling people that whatever I’m taking from the oven is the current flavor.” I’m high-fiving him for that, just as Vinnie slams in and yells out, “Hey, Al, you got your sign spelled wrong. Got any cranberry ones in there?”

Al gives me a look. I shrug. Vinnie starts in on me. “Hey, Sy, that was pretty slick what that Kibble guy did. All the measurements and calculations had the mass standard depending on three universal constants but then suddenly there was only two.”

Al pricks up his ears. “Universal constants, Sy?”

“We think so. Einstein said that the speed of light c is the same everywhere. That claim has withstood a century of testing so the International Bureau of Weights and Measures took that as their basis when they redefined the meter as the standard of length. Planck’s constant h is sometimes called the quantum of action. It shows up everywhere in quantum-related phenomena and appears to be fundamental to the way the Universe works. Bryan Kibble’s team created a practical way to have a measure-anywhere standard of mass and it just happens to depend only on having good values for c and h.”

“What’s the one that Vinnie said dropped out?”

“I knew you’d ask that, Al. It’s e, the charge on an electron. The proton and every other sub-atomic particle we’ve measured has a charge that’s some integer multiple of e. Sometimes the multiplier is one, sometimes it’s zero, sometimes it’s a negative, but e appears to be a universal quantum of charge. Millikan’s oil drop experiment is the classic example. He measured the charge on hundreds of ionized droplets floating in an electric field between charged plates. Every droplet held some integer multiple between 1 and 150 of 1.6×10-19 Coulomb.”

“That’s a teeny bit of electricity. I remember from Ms Kendall’s class that one coulomb is one ampere flowing for one second. Then a microampere flowing for a microsecond is, uhh, 6 million electrons. How did they make that countable?”

“Ah, you’ve just touched on the ‘realization problem,’ which is not about getting an idea but about making something real, turning a definition into a practical measurement. Electrical current is a good example. Here’s the official definition from 60 years ago. See any problems with it, Vinnie?”

“Infinitely long wires that are infinitely thin? Can’t do it. That’s almost as goofy as that 1960 definition of a second. And how does the force happen anyway?”

“The force comes from electrons moving in each wire electromagnetically pushing on the electrons in the other wire, and that’s a whole other story. The question here is, how could you turn those infinities into a real measurement?”

“Lemme guess. In the 1960 time standard they did a math trick to model a fake Sun and based the second on how the fake Sun moves. Is this like that, with fake wires?”

“Nice shot, Vinnie. One of the methods worked like that — take a pair of wires with a known resistance, bend them along a pair of parabolas or some other known curve set close together, apply a voltage and measure the force. Then you use Maxwell’s equations to ‘correct’ the force to what it would have been with the infinite wires the right distance apart. Nobody was comfortable with that.”

“Not surprised — too many ways to do it wrong, and besides, that’s an awfully small force to measure.”

“Absolutely. Which is why there were so many competing standards, some dating back to the 1860s when we were still trying to figure out what electricity is. Some people used a standard resistor R and the voltage V from a standard chemical cell. Then they defined their standard current I from I=V/R. Some measured power P and calculated I2=P/R. Other people standardized charge from the electrostatic force F=q1q2/r2 between two charged objects; they defined current as charge passed per second. It was a huge debate.”

“Who won?”

“Charge and R and V, all playing together and it’s beautiful.”

~~ Rich Olcott

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