Cube Roots

Cathleen steps into at Al’s for her morning coffee-and-scone.  “Heard you guys talking neutrinos so I’ll bet Al got you started with something about IceCube.  Isn’t it an awesome project?  Imagine instrumenting a cubic kilometer of ice, and at the South Pole!”

“Ya got me, Cathleen.  It knocked me out that anyone would even think of building it.  Where did the idea come from, anyhow?”

“I don’t know specifically, but it’s got a lot of ancestors, going back to the Wilson Cloud Chamber in the 1920s.”

“Oh, the cloud chamber!  Me and my brother did one for the Science Fair — used dry ice and some kind of alcohol in a plastic-covered lab dish if I remember right, and we set it next to one of my Mom’s orange dinner plates.  Spooky little ghost trails all over the place.”

“That’s basically what the first ones were.  An incoming particle knocks electrons out of vapor molecules all along its path.  The path is visible because the whole thing is so cold that other vapor molecules condense to form micro-droplets around the ions.  Anderson’s cloud chambers were good enough to get him a Nobel Prize for discovering the positron and muon.  But table-top devices only let you study low-energy particles — high-energy ones just shoot through the chamber and exit before they do anything interesting.”

“So the experimenters went big?”

“Indeed, Sy, massive new technologies, like bubble chambers holding thousands of gallons of liquid hydrogen or something else that reacts with neutrinos.  But even those experiments had a problem.”

“And that was…?”

FirstNeutrinoEventAnnotated 2

Adapted from public domain image
courtesy of Argonne National Laboratory

“They all depended on photography to record the traces.  Neutrino-hunting grad students had to measure everything in the photos, because neutrinos don’t make traces — you only find them by finding bigger particles that were disturbed just so.  The work got really intense when the astrophysicists got into the act, trying to understand why the Sun seemed to be giving off only a third of the neutrinos it’s supposed to.  Was the Sun going out?”

“Wait, Cathleen, how’d they know how many neutrinos it’s supposed to make?”

“Wow, Vinnie, you sure know how to break up a narrative, but it’s a fair question.  OK, quick answer.  We know the Sun’s mostly made of hydrogen and we know how much energy it gives off per second.  We’ve figured out the nuclear reactions it must be using to generate that energy.  The primary process combines four hydrogen nuclei  to make a helium nucleus.  Each time that happens you get a certain amount of energy, which we know, plus two neutrinos.  Do the energy arithmetic, multiply the number of heliums per second by two and you’ve got the expected neutrino output.”

“So is the Sun going out?”

“As usual, Al cuts to the chase.  No, Al, it’s still got 5 billion years of middle age ahead of it.  The flaw in the argument was that we assumed that our detectors were picking up all the neutrinos.”

“My mutations!”

“Yes, Vinnie.  Our detector technology at the time only saw electron neutrinos.  The Sun’s reactions emit electron neutrinos.  But the 93-million mile trip to Earth gave those guys plenty of time to oscillate through muon neutrino to tau neutrino and back again.  All we picked up were the ones that had gone through an integer number of cycles.”

“We changed technology, I take it?”

“Right again, Sy.  Instead of relying on nuclear reactions initiated by electron neutrinos, we went so spark chambers — crossed grids of very fine electrified wire in a box of argon gas.  Wherever a passing neutrino initiated an ionization, zap! between the two wires closest to that point.  Researchers could computerize the data reduction.  Turns out that all three neutrino flavors are pretty good at causing ionizations so the new tech cleared up the Solar Paradox, but only after we solved a different problem — the new data was point-by-point.  Working back from those points to the traces took some clever computer programming.”

“Ah, I see the connection with IceCube.  It doesn’t register traces, either, just the points where those sensors see the Cherenkov flashes.  It’s like a spark chamber grown big.”

“Cubic-kilometer big.”

~~ Rich Olcott


Einstein’s Revenge

Vinnie’s always been a sucker for weird-mutant sci-fi films so what Jennie says gets him going.  “So you got these teeny-tiny neutrinos and they mutate?  What do they do, get huge and eat things?”

“Nothing that interesting, Vinnie — or uninteresting, depending on what you’re keen on.  No, what happens is that each flavor neutrino periodically switches to another flavor.”

“Like an electron becomes a muon or whatever?”

“Hardly.  The electron and muon and tau particles themselves don’t swap.  Their properties differ too much —  the muon’s 200 times heaver than the electron and the tau’s sixteen times more massive than that.  It’s their associated neutrinos that mutate, or rather, oscillate.  What’s really weird, though, is how they do that.”

“How’s that?”

“As I said, they cycle through the three flavors.  And they cycle through three different masses.”

“OK, that’s odd but how is it weird?”

“Their flavor doesn’t change at the same time and place as their mass does.”Neutrino braid with sines

“Wait, what?”

“Each kind of neutrino, flavor-wise, is distinct — it reacts with a unique set of particles and yields different reaction products to what the other kinds do.  But experiments show that the mass of each kind of neutrino can vary from moment to moment.  At some point, the mass changes enough that suddenly the neutrino’s flavor oscillates.”

“That makes me think each mass could be a mix of three different flavors, too.”

“Capital, Vinnie!  That’s what the math shows.  It’s two different ways of looking at the same coin.”

“The masses oscillate, too?”

“Oh, indeed.  But no-one knows exactly what the mass values are nor even how the mass variation controls the flavors.  Or the other way to.  We know two of the masses are closer together than to the third but that’s about it.  On the experimental side there’s loads of physicists and research money devoted to different ways of measuring how neutrino oscillation rates depend on neutrino energy content.”

“And on the theory side?”

“Tons of theories, of course.  Whenever we don’t know much about something there’s always room for more theories.  The whole object of experiments like IceCube is to constrain the theories.  I’ve even got one I may present at Al’s Crazy Theory Night some time.”

“Oh, yeah?  Let’s hear it.”

“It’s early days, Al, so no flogging it about, mm?  Do you know about beat frequencies?”

“Yeah, the piano tuner ‘splained it to me.  You got two strings that make almost the same pitch, you get this wah-wah-wah effect called a beat.  You get rid of it when the strings match up exact.”  He grabs a few glasses from the counter and taps them with a spoon until he finds a pair that’s close.  “Like this.”

“Mm-hmm, and when the wah-wahs are close enough together they merge to become a note on their own.  You can just imagine how much more complicated it gets when there are three tones close together.”

I see where she’s going and bring up a display on Old Reliable —an overlay of three sine waves.   “Here you go, Jennie.  The red line is the average of the three regular waves.”Three sines on Old Reliable“Thanks, Sy.  Look, we’ve got three intervals where everything syncs up.  See the new satellite peaks half-way in between?  There’s more hidden pattern where things look chaotic in the rest of the space.”

“Yeah, so?”

“So, Vinnie, my crazy theory is that like a photon’s energy depends on its wave frequency in the electromagnetic field, a neutrino is a combination of three weak-field waves of slightly different frequency, one for each mass.  When they sync up one way you’ve got an electron neutrino, when they sync up a different way you’ve got a muon neutrino, and a third way for a tau neutrino.”

I’ve got to chuckle.  “Nothing against your theory, Jennie, though you’ve got some work ahead of you to flesh it out and test it.  I just can’t help thinking of Einstein and his debates with Bohr.  Bohr maintained that all we can know about the quantum realm are the averages we calculate.  Einstein held that there must be understandable mechanisms underlying the statistics.  Field-based theories like yours are just what Einstein ordered.”

“I could do worse.”Neutrino swirl around Einstein

~~ Rich Olcott

The Neapolitan Particle

“Welcome back, Jennie.  Why would anyone want to steer an ice cube?

“Thanks, Jeremy, it’s nice to be back..  And the subject’s not an ice cube, it’s IceCube, the big neutrino observatory in the Antarctic.”

“Then I’m with Al’s question.  Observatories have this big dome that rotates and inside there’s a lens or mirror or whatever that goes up and down to sight on the night’s target.  OK, the Hubble doesn’t have a dome and it uses gyros but even there you’ve got to point it.  How does IceCube point?”

“It doesn’t.  The targets point themselves.”


“Ever relayed a Web-page?”


“Guess what?  You don’t know where the page came from, you don’t know where it’s going to end up.  But it could carry a tracking bug to tell someone at some call-home server when and where the page had been opened.  IceCube works the same way, sort of.  It has a huge 3D array of detectors to record particles coming in from any direction.  A neutrino can come from above, below, any side, no problem — the detectors it touches will signal its path.”

IceCube architecture

Adapted from a work by Francis Halzen, Department of Physics, University of Wisconsin

“How huge?”

“Vastly huge.  The instrument is basically a cubic kilometer of ultra-clear Antarctic ice that’s ages old.  The equivalent of the tracking bugs is 5000 sensors in a honeycomb array more than a kilometer wide.  Every hexagon vertex marks a vertical string of sensors going down 2½ kilometers into the ice.  Each string has a couple of sensors near the surface but the rest of them are deeper than 1½ kilometers.  The sensors are looking for flashes of light.  Keep track of which sensor registered a flash when and you know the path a particle took through the array.”

icecube event 3“Why should there be flashes? I thought neutrinos didn’t interact with matter.”

“Make that, they rarely interact with matter.  Even that depends on what particle the neutrino encounters and what flavor neutrino it happens to be at the moment.”

That gets both Al and me interested.  His “Neutrinos come in flavors?” overlaps my “At the moment?”

“I thought that would get you into this, Sy.  Early experiments detected only 1/3 of the neutrinos we expected to come from the Sun.  Unwinding all that was worth four Nobel prizes and counting.  The upshot’s that there are three different neutrino flavors and they mutate.  The experiments caught only one.”

Vinnie’s standing behind us.  “You’re going to tell us the flavors, right?”

“Hoy, Vinnie, Jeremy’s question was first, and it bears on the others.  Jeremy, you know that blue glow you see around water-cooled nuclear fuel rods?”

“Yeah, looks spooky.  That’s neutrinos?”

“No, that’s mostly electrons, but it could be other charged particles.  It has to do with exceeding the speed of light in the medium.”

“Hey, me and Sy talked about that.  A lightwave makes local electrons wiggle, and how fast the wiggles move forward can be different from how fast the wave group moves.  Einstein’s speed-of-light thing was about the wave group’s speed, right, Sy?”

“That’s right, Vinnie.”

“So anyhow, Jeremy, a moving charged particle affects the local electromagnetic field.  If the particle moves faster than the surrounding atoms can adjust, that generates light, a conical electromagnetic wave with a continuous spectrum.  The light’s called Cherenkov radiation and it’s mostly in the ultra-violet, but enough leaks down to the visible range that we see it as blue.”

“But you said it takes a charged particle.  Neutrinos aren’t charged.  So how do the flashes happen in IceCube?”

“Suppose an incoming high-energy neutrino transfers some of its momentum to a charged particle in the ice — flash!  Even better, the flash pattern provides information for distinguishing between the neutrino flavors.  Muon neutrinos generate a more sharp-edged Cherenkov cone than electron neutrinos do.  Taus are so short-lived that IceCube doesn’t even see them.”Leptons

“I suppose muon and tau are flavors?”

“Indeed, Vinnie.  Any subatomic reaction that releases an electron also emits an electron-flavored neutrino.  If the reaction releases the electron’s heavier cousin, a muon, then you get a muon-flavored neutrino.  Taus are even heavier  and they’ve got their own associated neutrino.”

“And they mutate?”

“In a particularly weird way.”

~~ Rich Olcott