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


For the VLA, Timing Is Everything

Eddie’s pizza is especially tasty after a long walk down a stairwell. Vinnie and I are polishing off the last of our crumbs when he says, “OK, so we got these incredibly accurate clocks. Two questions. What do we use them for besides sending out those BBC pips, and what do they have to do with the new kilogram standard?”

“Pips? Oh, the top-of-the-hour radio station beeps we used to depend upon to set our watches. Kept us all up-to-the-minute, us and the trains and planes — but we don’t need 10-digit accuracy for that. What we do get from high-quality time signals is the ability to create distributed instruments.”

“Distributed instruments?”

“Ones with pieces in different places. You know about the Jansky Very Large Array, that huge multi-dish radio telescope in New Mexico?”

Karl G. Jansky Very Large Array, photo by Mihaiscanu
via Wikimedia Commons licensed under Creative Commons

“Been there. Nice folks in Pie Town up the road.”

“Did you look around?”

“Of course. What I didn’t understand is why they got 27 dishes and they’re all pointed the same direction. You’d think one would be enough for looking at something.”

“Ah, that’s the thing. All of them together make one telescope.”

<sets smartphone to calculator mode> “Lessee … dish is 25 meters across, πD2/4, 27 dishes, convert square meters to… Geez, 3¼ acres! A single dish that size would be a bear to keep steady in the wind down there. No wonder they split it up.”

“That was one concern, but the total area’s not as important as the distance between the pairs.”

“Why’s that even relevant?”

“Because radio telescopes don’t work the way that optical ones do. No lens or mirror, just a big dish that accepts whatever comes in along a narrow beam of radio waves.”

“How narrow?”

“About the size of the full Moon.”

“That can cover a lot of stars and galaxies.”

“It sure can, which is why early radio astronomy was pretty low-resolution. Astronomers needed a way to pick out the signals from individual objects within that field of view. Turns out two eyes are better than one.”

“3D vision?”

“Kinda related, but not really. Our two eyes give us 3D vision because each eye provides a slightly different picture of close-by objects, say, less than about 5 yards away. For everything further, one eye’s view is no different from the other’s. You’d get the same effect if distant things were painted on a flat background, which is how come a movie set backdrop still looks real.”

“You’re saying that the stars are so far away that each dish gets the same picture.”


“So why have more than one?”

“They don’t get the picture at the same time. With an atomic clock you can take account of when each signal arrives at each dish. Here’s a diagram I did up on Old Reliable. It’s way out of scale but it makes the point, I think. We’ve got two dishes at the bottom here, and those purple dots are two galaxies. Each dish sees them on top of each other and can’t distinguish which one sent that peaky signal. What’s important is, the dish on the right receives the signal later. See that red bar? That’s the additional path length the signal has to travel to reach the second dish.”

“Can’t be much later, light travels pretty fast.”

“About 30 centimeters per nanosecond, which adds up. When the VLA dishes are fully spread out, the longest dish-to-dish distance is about 36 kilometers which is about 120 microseconds as the photon flies. That’s over a million ticks on the cesium clock – no problem tracking the differences.”

“Same picture a little bit later. Doesn’t seem worth the trouble.”

“What makes it worth the trouble is what you can learn from the total space-time pattern after you combine the signals mathematically. Under good conditions the VLA can resolve signals from separate objects only 40 milliarcseconds apart, about 1/45000 the diameter of the Moon. That’s less than the width of a dime seen from 50 miles away.”

“The time pattern is how the dishes act like a single spread-around telescope, huh? Without the high-precision time data, they’re just duplicates?”

“Atomic clocks let us see the Universe.”

~~ Rich Olcott