Category: Physics

A Non-political Polarizing Topic

On By rolcottIn Astronomy: Techniques, Physics: Black Holes and Relativity, Physics: Waves, UncategorizedLeave a comment

Vinnie gets the deck next, but first thing he does is plop a sheet of paper onto the table. “Topic is black holes, of course. Everybody’s seen this, right?”

“Sure, it’s the new view of the Milky Way’s super-massive black hole with the extra lines. So deal already.”

“Hold your horses, Cal.” <Vinnie starts dealing.> “I’m looking for explanations. Where’d those lines come from? They swirl across the accretion disk like so much rope, right? Why aren’t they just going straight in orderly‑like? The whole thing just don’t make sense to me.”

Susan bets a few chips. “I saw a similar pop‑sci article, Vinnie. It said the lines trace out polarization in the light waves the Event Horizon Telescope captured. Okay, radio waves — same thing just longer wavelength. Polarized radio waves. I’ve measured concentrations of sugar and amino acid solutions by how much the liquid rotates polarized light, but the light first went through a polarizing filter. How does a black hole make polarized waves?”

Kareem matches Susan’s bet. “Mm‑hm. We use polarized light passing through thin sections of the rocks we sample to characterize the minerals in them. But like Susan says, we don’t make polarized light, we use a filter to subtract out the polarization we don’t want. You’re the physicist, Sy, how does the black hole do the filtering?”

Plane‑polarized electromagnetic wave
 Electric (E) field is red
 Magnetic (B) field is blue
(Image by Loo Kang Wee and Fu-Kwun Hwang from Wikimedia Commons)

My hand’s good so I match the current ante. “It doesn’t. There’s no filtering, the light just comes out that way. I’d better start with the fundamentals.” <displaying Old Reliable> “Does this look familiar, Vinnie?”

“Yeah, Sy, you’ve used it a lot. That blue dot in the back’s an electron, call it Alice, bobbing straight up and down. That’s the polarization it’s puttin’ on the waves. The red lines are the force that another electron, call it Bob, feels at whatever distance away. Negative‑negative is repelling that so Bob goes down where the red line goes up but you get the basic idea.”

“The blue lines are important here.”

“I’m still hazy on those. They twist things, right?”

“That’s one way to put it. Hendrik Lorentz put it better when he wrote that Bob in this situation experiences one force with two components. There’s the red‑line charge‑dependent component, plus the blue‑line component that depends on the charge and Bob’s motion relative to Alice. If the two are moving in parallel—”

“The same frame, then. I knew frames would get into this somehow.”

“It’s hard to avoid frames when motion’s the subject. Anyway, if the two electrons are moving in parallel, the blue‑line component has zero effect. If the two are moving in different directions, the blue‑line component rotates Bob’s motion perpendicular to Alice’s red‑line polarization plane. How much rotation depends on the angle between the two headings — it’s a maximum when Bob’s moving perpendicular to Alice’s motion.”

“Wait, if this is about relative motion, then Bob thinks Alice is twisting, too. If she thinks he’s being rotated down, then he thinks she’s being rotated up, right? Action‑reaction?”

“Absolutely, Vinnie. Now let’s add Carl to the cast.”

“Carl?”

Alice and Bob’s electromagnetic interaction
begets motion that generates new polarized light.

“Distant observer at right angles to Alice’s polarization plane. From Carl’s point of view both electrons are just tracking vertically. Charges in motion generate lightwaves so Carl sees light polarized in that plane.”

Cathleen’s getting impatient, makes her bet with a rattle of chips. “What’s all this got to do with the lines in the EHT image?”

“The hole’s magnetic field herds charged particles into rotating circular columns. Faraday would say each column centers on a line of force. Alice and a lot of other charged particles race around some column. Bob and a lot of other particles vibrate along the column and emit polarized light which shows up as bright lines in the EHT image.”

“But why are the columns twisted?”

“Orbit speed in the accretion disk increases toward its center. I’d bet that’s what distorts the columns. Also, I’ve got four kings.”

“That takes this pot, Sy.”

~~ Rich Olcott

No Symphony on Mars

On By rolcottIn Astronomy: Planetary Science, Physics: Waves, Uncategorized2 Comments

“Evening, Jeremy, a scoop of your pistachio gelato, please. What’re you reading there?”

“Hi, Mr Moire. It’s ‘A City on Mars‘ by Kelly and Zach Weinersmith. One of my girlfriends read it and passed it along to me. She said it’s been nominated for a Hugo even though it’s non‑fiction and it argues against the kind of go‑to‑Mars‑soon planning that Mr Musk is pushing.”

“Is she right about the argument?”

“Pretty much, so far, but I’m not quite done. You get a clue, though, from the book’s subtitle — ‘Can we settle space, should we settle space, and have we really thought this through?‘ Here’s your gelato.”

“Thanks. Not just Mars, space also?”

“That’s right. It’s about the requirements and implications for people living in space and on the Moon and on Mars. The discussion starts with making and raising babies.”

“That first part sounds like fun.”

“Well, you’d think so, but apparently you need special equipment. Hard to stay in contact if there’s no gravity to key on. But that’s only the start of a problem cascade. Suppose the lady gets pregnant. The good news is in zero gravity it’s easy for her to move around. The bad news is we don’t know whether Earth gravity’s important for making babies develop the way they’re supposed to. Also, delivering a baby isn’t the only medical procedure that’d be a real challenge in zero‑g where you need to keep fluid droplets from bouncing around the cabin and into the air system.”

“Whoa. Hmm, never thought about it in this context before, but babies leak. Diapers can help, but babies burp up stuff along with the air. Yuck! Tears they cry in space would just stay on their eyes instead of rolling down cheeks. So … we’d need OB/GYN clinics and nurseries somewhere down a gravity well.”

“For sure, although no‑one knows whether even the Moon’s 1/6‑g is strong enough for good development. I know my little cousins burn up a lot of energy just running around. Can’t give a toddler resistance bands or trust it on a treadmill.”

“So we need an all‑ages gym down there, too, with enough room for locals and visiting spacers.”

“You’re coming round to the Weinersmiths’ major recommendation — don’t go until you can go big! Don’t plan on growing from a small colony, plan on starting with a whole city that can support everything you need to be mostly self‑sufficient.”

“So you’re young, Jeremy. Are you looking forward to being a Mars explorer?”

“I’ll admit all that rusty landscape reminds me of Navajoland, but I think I’d rather stay here. On Mars I’d be trapped in tunnels and domes and respirators and protective coveralls. I wouldn’t be able to just go out and run under the sky the way I was brought up to do.”

“Wouldn’t be able to do a lot of things. Concerts would sound weird, according to a paper I just read.”

“Sure, wind instruments wouldn’t work with bubble helmets. We could still have strings, percussion and electronics, though, right?”

“Sure you could have them. But it’s worse than that. Mars atmosphere is very different from Earth’s. Its temperature measured in kelvins is 25% colder. The pressure’s 99% lower. Most important, molecule for molecule Mars’ mostly‑CO2 atmosphere’s is 50% heavier than Earth’s N2‑O2 mixture. Those differences combine to muffle sounds so they don’t carry near as far as they would on Earth. Most sounds travel about 30% more slowly, too, but that’s where a CO2 molecule’s internal operation makes things weird.”

“Internal? I thought molecules in sound waves just bounced off each other like little billiard balls.”

“That’s usually the case unless you’re at such high pressures that molecules can start sticking to each other. CO2 under Mars conditions is different. If there’s enough time between bounces, CO2 can convert some of its forward kinetic energy into random heat. The threshold is about 4 milliseconds. A sound wave frequency longer than that travels noticeably slower.”

“Four milliseconds is 250 Hertz — that’s a middle B.”

“Mm-hm. Hit a cymbal and base drum simultaneously, your audience hears the cymbal first. Terrible acoustics for a band.”

~~ Rich Olcott

Marconi Would Be Proud

On By rolcottIn General: Fun Stuff, Physics: Quantum Mechanics, UncategorizedLeave a comment

A warmish Spring day.  I’m under a shady tree by the lake, waiting for the eclipse and doing some math on Old Reliable.  Suddenly there’s a text‑message window on its screen.  The header bar says 710‑555‑1701 . Old Reliable has never held a messaging app, that’s not what I use it for, but the set-up is familiar. I type in, Hello?

Hello, Mr Moire. Remember me?

Of course I do.  That sultry knowing stare, those pointed ears.  Hello, Lieutenant Baird.  It’s been a year.  What can I do for you?

Not Lieutenant any more, I’m back up to Commander, Provisional.

Congratulations. Did you invent something again?

Yes, but I can’t discuss it on this channel. I owe you for the promotion. I got the idea from one of your Crazy Theories posts. You and your friends have no clue but you come up with interesting stuff anyway.

You’re welcome, I suppose. Mind you, your science is four centuries ahead of ours but we do the best we can.

I know that, Mr Moire. Which is why I’m sending you this private chuckle.

Private like with Ralphie’s anti‑gravity gadget? I suggested he add another monitoring device in between two of his components. That changed the configuration you warned me about. He’s still with us, no anti‑gravity, but now he blames me.

Good ploy. Sorry about the blaming. Now it’s your guy Vinnie who’s getting close to something.

Vinnie? He’s not the inventor type, except for those maps he’s done with his buddy Larry. What’s he hit on?

His speculation from your Quantum Field Theory discussion that entanglement is somehow involved with ripples in a QFT field, ripples that are too weak to register as a particle peak. He’s completely backwards on entanglement, but those ripples—

Wait, what’s that about entanglement?

Entanglement is the normal state for quantized particles. Our 24th‑Century science says every real and virtual particle in the Universe is entangled with every other particle that shares the same fields. It’s an all‑embracing quantum state. Forget your reductionist 20th‑Century‑style quantum states, this is something … different. Your Hugh Everett and his mentor John Archibald Wheeler had an inking of that fact a century before your time, though of course they didn’t properly understand the implications and drew a ridiculous conclusion. Anyway, when your experimenting physicists say they’ve created an entangled particle pair, they’ve simply extracted two particles from the common state. When they claim to transmit one of the particles somewhere they’re really damping out the local field peak linked to their particle’s anti‑particle’s anti‑peak at the distant location and that puts an anti‑anti‑particle‑particle peak there. Naturally, that happens nearly instantaneously.

I don’t follow the anti‑particle‑anti‑peak part. Or why it’s naturally instantaneous.

I didn’t expect you to or else I wouldn’t have told you about it. The Prime Directive, you know. Which is why the chuckle has to be private, understand?

I won’t tell. I live in “the city that knows how to keep its secrets,” remember?

Wouldn’t do you any good if you did tell and besides, Vinnie wouldn’t think it’s funny. Here’s the thing. As Vinnie guessed, there are indeed sub‑threshold ripples in all of the fundamental fields that support subatomic particles and the forces that work between them. And no, I won’t tell you how many fields, your Standard Model has quite enough complexity to <heh> perturb your physicists. A couple hundred years in your future, humanity’s going to learn how to manipulate the quarks that inhabit the protons and neutrons that make up a certain kind of atom. You’ll jiggle their fields and that’ll jiggle other fields. Pick the right fields and you get ripples that travel far away in space but very little in time, almost horizontal in Minkowski space. It won’t take long for you to start exploiting some of your purposely jiggled fields for communication purposes. Guess what a lovely anachronism you’ll use to name that capability.

‘Jiggled fields’ sounds like communications tech we use today based on the electromagnetic field — light waves traveling through glass fibers, microwave relays for voice and data—

You’re getting there. Go for the next longer wavelength range.

Radio? You’ll call it radio?

Subspace radio. Isn’t that wonderful?

~~ Rich Olcott

Fields of Dreams

On By rolcottIn Cosmology, Physics: Quantum Mechanics, Physics: Waves, Uncategorized1 Comment

Vinnie takes a slug of his coffee. “So the gravitational field carries the gravitational wave. I suppose Einstein would blame sound waves on some kind of field?”

I take a slug of mine. “Mm-hm. We techies call it a pressure field. Can’t do solar physics without it. The weather maps you use when plotting up a flight plan — they lay three fields on top of the geography.”

“Lessee — temp, wind … and barometer reading. In the old days I’d use that one to calibrate my altimeter. You say those are fields?”

“In general, if a variable has a value at every point in the region of interest, the complete set of values is a field. Temperature and pressure are the simplest type. Their values are just numbers. Each point in a wind field has both speed and direction, two numbers treated as a single value, so you’ve got a field of vector values.”

“Oh, I know vectors, Sy. I’m a pilot, remember? So you’re saying instead of looking at molecules back‑and‑forthing to make sound waves we step back and look at just the pressure no matter the molecules. Makes things simpler, I can see that. Okay, how about the idea those other guys had?”

“Hm? Oh, the other wave carrier idea. Einstein’s gravitational waves are just fine, but the Quantum Field Theorists added a collection of other fields, one for each of the 17 boxes in the Standard Model.”

“Boxes?”

<displaying Old Reliable’s screen> “Here’s the usual graphic. It’s like the chemist’s Periodic Table but goes way below the atomic level. There’s a box each for six kinds of quarks; another half‑dozen for electrons, neutrinos and their kin; four more boxes for mediating electromagnetism and the weak and strong nuclear forces. Finally and at last there’s a box for the famous Higgs boson which isn’t about gravity despite what the pop‑sci press says.”

“What’s in the boxes?”

“Each box holds a list of properties — rest mass, spin, different kinds of charge, and a batch of rules for how to interact with the other thingies.”

“Thingies, Sy? I wouldn’t expect that word from you.”

“I would have said ‘particle‘ but that would violate QFT’s tenets despite the graphic’s headline.”

“Tenets? That word sounds more like you. What’s the problem?”

“That the word ‘particle‘ as we normally use it doesn’t really apply at the quantum field level. Each box names a distinct field that spreads its values and waves all across the Universe. There’s an electron field, a photon field, an up‑quark field, a down‑quark field, and so on. According to QFT, what we’d call a particle is nothing more than a localized peak in its underlying field. Where you find a peak you’ll find all the properties listed in its box. Wherever the field’s value is below its threshold, you find none of them.”

“All or none, huh? I guess that’s where quantum comes in. Wait, that means there could be gazillions of one of them popping up wherever, like maybe a big lump of one kind all right next to each other.”

“No, the rules prevent that. Quarks, for instance, only travel in twos or threes of assorted kinds. The whole job of the gluons is to enforce QFT rules so that, for instance, two up‑quarks and a down‑quark make a proton but only if they have different color charges.”

“Wait, color charge?”

“Not real colors, just quantum values that could as easily have been labeled 1, 2, 3 or A, B, C. There’s also an anti- for each value so the physicists could have used ±1, ±2, ±3, but they didn’t, they used ‘red’ and ‘anti‑red’ and so forth. And ‘color charge‘ is a different property from electric charge. Gluons only interact with color charge, photons only interact with electric charge. The rules are complicated.”

“You said ‘waves.’ Each of these fields can have waves like gravity waves?”

“Absolutely. We can’t draw good pictures of them because they’re 3‑dimensional. And they’re constantly in motion, of course.”

“How fast can those waves travel?”

“The particles are limited to lightspeed or slower; the waves, who knows?”

“Ripples zipping around underneath the quantum threshold could account for entanglement, ya’ know?”

“Maybe.”

~~ Rich Olcott

A Million Times Weaker Than Moonlight

On By rolcottIn Cosmology, Gravitational astronomy, Physics: Waves, UncategorizedLeave a comment

Big Vinnie’s getting downright antsy, which is something to behold. “C’mon, Sy. We get it that sonication ain’t sonification and molecules bumping into each other can carry a sound wave across space if the frequency’s low enough and that can maybe account for galaxies having spiral arms, but you said the Cosmic Hum is a sound, too. That’s a gravity thing, not molecules, right?”

“Not quite what I said, Vinnie. The Hum’s sound‑related, but it’s not ‘sound’ even by our extended definition.”

“Then what’s the connection?”

“Waves.”

“Not frames like always?”

“Not frames, for a change.”

“So it’s waves, but they go though empty space. Can’t happen like sound waves from molecules bumping into each other ’cause molecules are too small to have enough gravity do that when they’re so far apart. What’s carrying the waves?”

“Good question. Einstein figured out one answer. A whole cohort of mid‑20th‑century theoreticians came to a slightly different conclusion.”

“Okay, I’ll bite. What was Einstein’s answer?”

“Relativity, of course. Gravity’s the effect we see from mass deforming nearby space. Moving a mass drives corresponding changes in the shapes of space where it was and where it has moved to. The shape‑changes generate follow‑on gravitational effects that propagate outward over time. Einstein even showed that the gravitational propagation speed is equal to lightspeed.”

“Gimme a sec … Okay, that black hole collision signal LIGO picked up back in 2015, the holes lost a chunk of their combined mass all of a sudden. Quick drop in the gravity thereabouts. You’re saying it took time for the missing gravity strength to get noticed where we’re at. If I remember right, the LIGO people said the event was something like a billion lightyears away so that tells me it happened about a billion years ago and what the LIGO gadget picked up was space waves, right?”

“Right, but it wasn’t just the mass loss, it was the rapid and intense waggles in the gravitational field as those two enormous bodies, each 30 times as massive as the Sun, whirled around each other multiple times per second. The ever‑faster whirling shook the field with a frequency that swept upward to the ‘POP‘ when your mass‑loss happened. LIGO eventually picked up that signal. Einstein would say there’s no ‘action at a distance‘ in the collision‑LIGO interaction, because the objects acted on the gravitational field which acted on the LIGO system.”

“Like using a towel to pop someone in the locker room. The towel’s just transmi– ulp.”

“An admission of guilt if I ever heard one. Yes, like that, except a towel pop carries all the initial energy to its final destination. Gravitational waves spread their energy across the surface of an expanding sphere. The energy per unit area goes down as the square of the distance.” <keying a calculation on Old Reliable> “Suppose the collision releases 10 solar masses worth of energy, we’re a billion lightyears away, and the ‘POP‘ signal is delivered in a tenth of a second. We’d see a signal power … about a millionth as strong as moonlight.”

“Not much there.”

“Right, which is why LIGO and its kin have been such pernickety instruments to build and run. LIGO’s sensors are mirrors roughly a meter across. You get a million times more power sensitivity if your detector’s diameter is a mile across. That was part of the NANOGrav team’s strategy, but they went much bigger.”

“Yeah, that’s the multi-telescope thing, so NANOGrav faked a receiver the size of the Earth, like the Event Horizon Telescope.”

“Much bigger. Their receiver is the entire Milky Way. Instead of LIGO’s mirrors, NANOGrav’s signal generators are neutron stars a dozen or more miles wide scattered across the galaxy.”

“Gotcha, Sy. Two ways. Neutron stars are billions heavier than a LIGO mirror so they’d be less power‑sensitive, not more. Then, power is about moving stuff closer or farther but if I got you right these space waves don’t really do that anyway, right?”

“Right and right, Vinnie, but not relevant. What NANOGrav’s been watching for is pulsar beams being twitched by a gravitational wave. A waltzing black hole pair should generate years‑long or decades‑long wavelengths. NANOGrav may have found one.”

~~ Rich Olcott

Sounds, Harsh And Informative

On By rolcottIn Astronomy: Techniques, Chemistry, Physics: Waves, UncategorizedLeave a comment

Vinnie’s frowning. “Wait, Sy. I get how molecules bumping into each other can carry a sound wave across space if the frequency’s low enough and that can maybe account for galaxies having spiral arms. So what’s that got to do with the Sonication Project?”

Now Jeremy’s frowning. “What’s sonication got to do with Astronomy? One of my girl friends uses sonication in Biology lab when she’s studying metabolism in plant cells.”

“Whoa! Sonification, not sonication — they could have called it soundify‑cation but sonification‘s classier. ‘Sonication‘ uses high‑intensity ultrasound to jiggle a sample so roughly that cell walls can’t take the stress. They break open and spill the cell’s internal soup out where your friend’s probes can get to it. Tammy, the chemist down the hall from my lab, uses sonication, too.”

“Whoa, Susan, wouldn’t sonication break up molecules?”

“Depends on the frequency and intensity, Vinnie. Sonication can mess up big floppy proteins and DNA, but chemists who play with little peptides and such don’t care. Tammy does solid‑state chemistry. She’s looking for superconductors and she actually does want to break things. The field’s hot category these days is complex copper oxides doped with other metals. You synthesize those compositions by sintering a mix of oxide powders. To maximize contact for a good reaction you need really fine‑grained powders. Sonication does a great job of shattering brittle oxide grains down to bits just a few‑score atoms wide. But Tammy’s technique is even more elegant than that.”

“Elegant sneezes from the powder?”

Susan wallops my shoulder. “No, Sy, the powders are so small they’d be a lung hazard and some of them are toxic. Everything’s done behind respiratory protection.” <Susan doesn’t joke about lab safety.> “There’s evidence that some of these materials are only superconductive if they have the right kind of layered structure. Turns out that if Tammy has her sonicator setup just right when she preps a sample for sintering, the sound wave peaks and valleys inside the machine make the shattered particles settle out in interesting layers.”

“Like Chladni figures.”

“Oh, you know about them.”

“Yeah, I wrote about them a few years ago. Waves do surprising things.”

The Bullet Cluster (1E 0657-56)
Sonification Credit: NASA/CXC/SAO/K.Arcand,
SYSTEM Sounds (M. Russo, A. Santaguida), based on X-Ray image by NASA/CXC/CfA/M.Markevitch,
Optical and lensing map: NASA/STScI, Magellan/U.Arizona/D.Clowe,
Lensing map: ESO WFI

Vinnie’s getting impatient. “So what’s sonification then?”

Tinkly music bursts from Cathleen’s tablet. “This one’s listenable, Susan, and it’s a nice demonstration of what sonification’s about and how arbitrary it can be. You start with complicated multi‑dimensional data and use some process to turn it into audible signals. The process algorithm can use any sound characteristics you like — loudness, pitch, timbre, whatever. This example started with the famous Bullet Cluster image that most people accept as the first direct confirmation of dark matter. All the white‑ish thingies are galaxies except for the ones with pointy artifacts — those are stars. The pink haze is X‑ray light from the same region. The blue haze comes from a point‑by‑point assessment of how badly the galaxy images have been distorted by gravitational lensing — that’s an estimate of the dark matter mass between us and that region of sky. Got all that?”

“And that vertical line is like a scan going across the picture?”

“It’s not like a scan, it is a scan. Imagine a collection of tiny multi‑spectral cameras arranged along a carrier bar. As the bar travels across the picture, each camera emits three signals proportional to the amount of white, pink and blue light it sees. If you look close, just to the right of the line, you’ll see moving white, red and blue line‑charts of the respective signals.”

“That’s fine, but what’s with the sound effects?”

“The Project’s sonification processing generated hiss and rumble sounds whose loudness is proportional to the red and blue signals. Each white‑ish peak became a ping whose pitch indicates position along that bar.”

“Why go to all that trouble?”

“The sounds encode the picture for vision‑challenged people. Beyond that, the Project participants hope that with the right algorithms, their music will reveal things the pictures don’t.”

“They should avoid screamy sounds.”

~~ Rich Olcott

Galaxies Sing In A Low Register

On By rolcottIn Astronomy, Physics: Waves, UncategorizedLeave a comment

Jeremy gets a far‑away look. ”It’s gotta be freakin’ noisy inside the Sun.” just as our resident astronomer steps into Cal’s Coffee.

“Wouldn’t bet that, Jeremy. Depends on where you are in the Sun and on how you define noise.”

Vinnie booms, quietly. ”We just defined it, Cathleen. Atoms or molecules bumping each other in compression waves. Oh, wait, that’s ‘sound,’ you said ‘noise.’ Is that different?”

Susan slurps the last of her chocolate latte. ”Depends on your mood, I guess. All noise is sound, but some sound can be signal. Some people don’t like my slurping so for them it’s noise but Cal hears it as an order for another which makes him happy.”

“Comin’ up, Susan. Hey, Cathleen, maybe you can slap down Sy. He said spiral galaxies have something to do with sound which don’t make sense. Set him straight, okay?”

“Sy, have you all settled that sound isn’t limited to what humans hear?”

“Sure. Everybody’s agreed that infrasound and ultrasound are sound, and that Bishop Berkeley’s fallen tree made a sound even though nobody heard it. That’s probably what got Jeremy thinking about sound inside the Sun.” Jeremy nods.

“Then Vinnie’s definition is too limited and Sy’s statement is correct. Probably.”

That gets a reaction from everyone, though mine is a smile. ”Let ’em have it, Cathleen.”

“Okay. Let’s take Jeremy’s idea first and then we’ll get to galaxies.” <fetches her tablet from her purse and a display on her tablet> “Here’s a diagram of the Sun I did for class. If you restrict ‘sound‘ to mean only coherent waves borne by atoms and molecules, there’s no sound in the innermost three zones. The only motion, if Sy grants I can call it that, is photons and subnuclear particles randomly swapping between adjacent nuclei that are basically locked into position by the pressure. Not much actual atomic motion until you’re up in the Convection Zone where rising turbulence is the whole game. Even there most of the particles are ions and electrons rather than neutral atoms. Loud? You might say so but it’d be a continuous random crackle‑buzz, not anything your ears would recognize. Sound waves as such don’t happen until you reach the atmospheric layers. Up there, oh yes, Jeremy, it’s loud.”

Geologist Kareem is a quiet guy, normally just sits and listens to our chatter, but Cathleen’s edging onto his turf. ”How about seismic waves? If there’s a big flare or CME up top, won’t that send vibrations all the way through?”

“Good point, Kareem. Yes, the Sun has p and s waves just like Earth does, but they travel no deeper than the Convection Zone. A different variety we may not have, g waves, would involve the core. Unfortunately, theory says g waves are so weak that the Convection Zone’s chaos swamps them. Anyway, the Sun’s s, p and g waves wouldn’t contribute to what Jeremy would hear because their frequencies are measured in hours or days. Can I get to galaxies now?”

“Please do.”

A Hubble view of NGC 5457, the Pinwheel Galaxy. Credit: NASA, ESA.

“Thanks.” <another display on her tablet> “Here’s a classic spiral galaxy. Gorgeous, huh? The obvious question is, is it winding in or spraying out? The evidence says ‘No‘ to both. The stars are neither pulled into a whirlpool nor flung out from a central star‑spawner. By and large, the stars or clusters of them are in perfectly good Newtonian orbits around the galactic center of gravity. So why are they collected into those arms? Here’s a clue — most of the blue stars are in the arms.”

“What’s special about blue stars?”

“In general, blue stars are large, hot and young. Our Sun is yellow, about halfway through a 10‑million‑year lifetime. The blue guys burn through their fuel and go nova in a tenth of that time. Blue stars out there tell us that the arms serve as stellar nurseries. It’s not stars gathering into arms, it’s galaxy‑wide rotating waves of gas birthing stars there. There’s argument about whether the wave rotation is intrinsic or whether there’s feedback as each wave is pulled along by star formation at the leading edge and pushed by novae at the trailing edge. Sy’s point, though, is that an arm‑dwelling old red star would experience the spinning gas density pattern as a basso profundo sound wave with a frequency even lower than the million‑year range. Right, Sy?”

“As always, Cathleen.”

~~ Rich Olcott

  • More thanks to Alex.

Screams And Thunders

On By rolcottIn Astronomy: Techniques, Physics: Waves, UncategorizedLeave a comment

Coffee time. I step into Cal’s shop and he’s all over me. ”Sy, have you heard about the the NASA sonification project?”

Susan puts down her mocha latte. “I didn’t like some of what they’ve released. Sounds too much like people screaming.”

Jeremy looks up from the textbook he’s reading. ”In space, no-one can hear you scream.”

Vinnie rumbles from his usual table by the door. “Any of these got anything to do with the Cosmic Hum?”

“They have nothing to do with each other, except they do. Spiral galaxies, too.”

“Huh?”
 ”Huh?”
  ”Huh?”
   ”Huh?”

“A mug of my usual, Cal, please, and a strawberry scone.”

“Sure, Sy, here ya go, but you can’t say something like that around here without you tellin’ us how come.”

“Does the name Bishop Berkeley ring a bell with anyone?”

Vinnie’s on it. ”That the ‘If a tree falls in the forest…‘ guy, right? Claimed there’s no sound unless somebody’s there to hear it?”

“And by extension, no sound outside human hearing range.”

“But bats and them use sound we can’t hear.”
 ”So do elephants and whales.”

“Well there you go. So are we agreed that he was wrong?”

“Not quite, Mr Moire. His definition of ‘sound‘ was different from one you’d like. He was a philosopher theorizing about perception, but you’re a physicist. You two don’t even define reality the same way.”

Vinnie’s rumble. ”Good shot, Jeremy. Sound is waves. Sy and me, we talked about them a lot. One molecule bangs into the next one and so on. The molecules don’t move forward, mostly, but the banging does. Sy showed me a video once. So yeah, people listening or not, that tree made a sound. There’s molecules up in space, so there’s sound up there, too, right, Sy?”

“Mmm, depends on where you are. And what sounds you’re equipped to listen for. The mechanism still works, things advancing a wave by bouncing off each other, but the wave’s length has to be longer than the average distance between the things.” <drawing Old Reliable, pulling up display> “Here’s that video Vinnie saw. I’ve marked two of the particles. You see them moving back and forth over about a wavelength. Suppose a much shorter wave comes along.”

“Umm… Each one would get a forward kick before they got back into position. They wouldn’t oscillate, they’d just keep moving in that direction. No sound wave, just a whoosh.”

“Right, Jeremy. Each out‑of‑sync interaction converts some of the wave’s oscillating energy into one‑way motion. The wave doesn’t get energy back. A dozen wavelengths along, no more wave. So the average distance between particles, we call it the mean free path, sets limits to the length and frequency of a viable wave. Our ears would say it filters out the treble.”

“Space ain’t quite empty so it still has a few atoms to bump together. What kinds of limits do we get out there?”

“Well, there’s degrees of empty. Interplanetary space has more atoms per cubic meter than interstellar which is more crowded than intergalactic. Nebulae and molecular clouds can be even less empty. Huge range, but in general we’re talking wavelengths longer than a million kilometers. Frequencies measured in months or years — low even for your voice, Vinnie.”

Jeremy gets a look on his face. ”One of my girlfriends is a soprano. We tested her in the audio lab and she could hit a note just under two kilohertz, that’s two thousand cycles per second. My top screech was below half that. I could scream in space, but I guess not low enough to be heard.”

“Yeah, keep that spacesuit helmet closed and be sure your radio intercom’s working.”

“Wait, what about screaming over the radio?”

“Radio operates with electromagnetic waves, not bumping atoms. Mean free path limits don’t apply. Radio’s frequency range is around a hundred megahertz, screeching’s no problem. Your broadcast equipment’s response range would set your limits.”

“Sy, those screamy sounds I objected to — you say they can’t have traveled across space as sound waves. Was that a radio transmission?”

“Maybe, Susan. From what I’ve read, we’ve picked up beaucoodles of radio sources, all different types and all over the sky. Each broadcasts a spectrum of different radio frequencies. Some of them are constant radiators, some vary at different rates. You may have heard a recording of a kilohertz variable source.”

<shudder> “All nasty treble, no bass or harmony.”

~~ Rich Olcott

  • Thanks to Alex, who raised several questions.

Shapes And Numbers

On By rolcottIn Mathematics: Spherical Harmonics, Physics: Quantum Mechanics, UncategorizedLeave a comment

I’m nursing my usual mug of eye‑opener in Cal’s Coffee Shop when astronomer Cathleen and chemist Susan chatter in and head for my table. Susan fires the first volley.

“Sy, those spherical harmonics you’ve posted don’t look anything like the atomic orbitals in my Chem text. Shouldn’t they?”
 ”How do you add and multiply shapes together?”
  ”What does the result even mean?”
   ”And what was that about solar seismology?”

The angular portion of the lowest‑energy spherical harmonics.
Adapted from work by Inigo.quilez, under CCA SA 3.0 license

“Whoa, have you guys taken interrogation lessons from Mr Feder? One at a time, please. Let’s start with the basics.” <sketching on a paper napkin> “For example, the J2 zonal harmonic depends only on the latitude, not on the longitude or the distance from the center, so whatever it does encircles the axis. Starting at the north pole and swinging down to the south pole, the blue line shows how J2 varies from 1.0 down to some negative decimal. At any latitude, whatever else is going on will be multiplied by the local value of J2.”

“The maximum is 1.0, huh? Something multiplied by a number less than 1 becomes even smaller. But what happens where J2 is zero? Or goes negative?”

“Wherever Jn‘s zero you’re multiplying by zero which makes that location a node. Furthermore, the zero extends along its latitude all around the sphere so the node’s a ring. J2‘s negative value range does just what you’d expect it to — multiply by the magnitude but flip the product’s sign. No real problem with that, but can you see the problem in drawing a polar graph of it?”

“Sure. The radius in a polar graph starts from zero at the center. A negative radius wouldn’t make sense mixed in with positives in the opposite direction.”

“Well it can, Cathleen, but you need to label it properly, make the negative region a different color or something. There are other ways to handle the problem. The most common is to square everything.” <another paper napkin> “That makes all the values positive.”

“But squaring a magnitude less than 1 makes it an even smaller multiplier.”

“That does distort the shapes a bit but it has absolutely no effect on where the nodes are. ’Nothin’ times nothin’ is nothin’,’ like the song says. Many of the Chem text orbital illustrations I’ve seen emphasize the peaks and nodes. That’s exactly what you’d get from a square‑everything approach. Makes sense in a quantum context, because the squared functions model electron charge distributions.”

“Thanks for the nod, Sy. We chemists care about charge peaks and nodes around atoms because they control molecular structures. Chemical bonds and reactions tend to localize near those places.”

“I aim for fairness, Susan. There is another way to handle a negative radius but it needs more context to look reasonable. Meanwhile, we’ve established that at any given latitude each Jn is just a number so let’s look at longitudes.” <a third paper napkin> “Here’s the first two sectorial harmonics plotted out in linear coordinates.”

“Looks familiar.”

“Mm‑hm. Similar principles, except that we’re looking at a full circle and the value at 360° must match the value at 0°. That’s why Cm always has an even node count — with an odd number you’d have -1 facing +1 and that’s not stable. In polar coordinates,” <the fourth paper napkin> “it’s like you’re looking down at the north pole. C0 says ‘no directional dependence,’ but C1 plays favorites. By the way, see how C1‘s negative radii in the 90°‑270° range flip direction to cover up the positives?”

“Ah, I see where you’re going, Sy. Each of these harmonics has a numeric value at each angle around the center. You’re going to tell us that we can multiply the shapes by multiplying their values point by point, one for each latitude for a J and each longitude for a C.”

“You’re way ahead of me as usual, Cathleen. You with us, Susan?”

“Oh, yes. In my head I multiplied your J2 by C0 and got a pz orbital.”

“I’m impressed.”
 ”Me, too.”

“Oh, I didn’t do it numerically. I just followed the nodes. J2 has two latitude nodes, C0 has no longitude nodes. There it is, easy‑peasy.”

~~ Rich Olcott

A Pencil In Space

On By rolcottIn Astronomy: Planetary Science, Mathematics: Spherical Harmonics, Physics: Newton and Gravity, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“I have a question I think you’ll find interesting, but it’s best we talk in person. Care for pizza?”

“If you’re buying.”

“Of course. Meet me at Eddie’s, twenty minutes. Bring Old Reliable.”

“Of course.”

Tall fellow, trimmed chevron mustache, erect bearing except when he’s leaning on that cane. “Moire?”

“That’s me. Good to meet you, Mr … ?”

“No names. Call me … Walt.”

We order, find a table away from the kitchen. “So, Walt, what’s this interesting question?”

“Been following this year’s Jupiter series in your blog. Read over the Kaspi paper, too, though most of that was over my head. What I did get was that his conclusions and your conclusions all come from measuring very small orbit shifts which arise from millionths of a g of force. Thing is, I don’t see where any of you take account of the Sun’s gravity. If the Sun’s pull holds Jupiter in orbit, it ought to swamp those micro-g effects. Apparently it doesn’t. Why not?”

“Well. That’s one of those simple questions that entail a complicated answer.”

“I’ve got time.”

“I’ll start with a pedantic quibble but it’ll clarify matters later on. You refer to g as force but it’s really acceleration. The one‑g acceleration at Earth’s surface means velocity changes by 980 meters/second per second of free fall. Drop a one kilogram mass, it’ll accelerate that fast. Drop a 100 kilogram mass, it’ll experience exactly the same acceleration, follow?”

“But the second mass feels 100 times the force.”

“True, but we can’t measure forces, only movement changes. Goes all the way back to Newton defining mass in terms of force and vice‑versa. Anyway, when you’re talking micro‑g orbit glitches you’re talking tiny changes in acceleration. Next step — we need the strength of the Sun’s gravitational field in Jupiter’s neighborhood.”

“Depends on the Sun’s mass and Jupiter’s mass. No, wait, just the Sun’s mass because that’s how it curves spacetime. The force depends on both masses.”

I’m impressed. “And the square of the very large distance between them.” <tapping on Old Reliable’s screen> “Says here the Sun’s field strength out there is 224 nano‑g, which is pretty small.”

“How’s that compare to what else is acting on Juno?”

<more tapping> “Jupiter’s local field strength crushes the Sun’s. At Juno’s farthest point it’s 197 micro‑g but at Juno’s closest point the field’s 22.7 million micro‑g and the craft’s doing 41 km/s during a 30-minute pass. Yeah, the Sun’s field would make small adjustments to Juno’s orbital speed, depending on where everybody is, but it’d be a very slow fluctuation and not the rapid shakes NASA measured.”

“How about side‑to‑side?”

“Good point, but now we’re getting to the structure of Juno’s orbit. Its eccentricity is 98%, a long way from circular. Picture a skinny oval pencil 8 million kilometers long, always pointed at Jupiter while going around it. It’s a polar orbit, rises above Jupiter on the approach, then falls below going away. The Sun’s effect is greatest when the orbit’s at right angles to the Sun‑Jupiter line. The solar field twists the oval away from N‑S on approach, trues it back up on retreat. That changes the angle at which Juno crosses Jupiter’s gravitational wobbles but won’t affect how it experiences the zonal harmonics.”

“Tell me about those zonal things.”

“A zone is a region, like the stripes on Jupiter, that circles a sphere at constant latitude. Technically, zonal harmonic Jn is the nth Legendre polynomial in cos(θ)—”

“Too technical.”

“Gotcha. Okay, each Jn names a shape, a set of gravitational ripples perpendicular to the polar axis. J0‘s a sphere with no ripples. Jupiter’s average field looks like that. A bigger n number means more ripples. Kaspi’s values estimate how much each Jn‘s intensity adds to or subtracts from J0‘s strength at each latitude. The Sun’s field can modify the intensity of J0 but none of the others.”

Walt grabs his cane, stands, drops a C‑note on the table. “This’ll cover the pizza and your time. Forget we had this conversation.” And he’s gone.

“Don’t mention it.”

~~ Rich Olcott

  • Thanks to Will, who asked the question.