Author: rolcott

Born and raised in Chicago, schooled in WI and NJ and WI (again), one-time Chem professor, one-time Massage Therapist, one-time mainframe Performance Analyst, one-time husband of Val, two-time Daddy and two-time Grampa, long-time enthusiast of Science and careful thinking.

A High-contrast Image

On By rolcottIn Cosmology, Physics: Black Holes and Relativity, UncategorizedLeave a comment

Vinnie clomps into my office. “Morning, Sy. I knew you weren’t busy ’cause there’s music playing.”

“Well, you’re right, I am between assignments. Yesterday another client called to say they’re cancelling my contract because their Federal grant was cut off. They had to let three grad students go, too. That was a project with good prospects for generating a couple of successful businesses. These zealots are eating our seed corn, Vinnie, and they’re burning down the silo.”

“I know the feeling, Sy. There’s a lot less charter flying to do these days. Nobody wants to do meetings when they don’t know what the rules will be next week.”

<deep sigh>
 <deep sigh>

“Oh, yeah, Sy. Why I came up here — what’s with white holes? Cal asked me about ’em ’cause a little squib in one of his astronomy magazines didn’t tell us much so now I’m curious.”

“Okay, tell me something you know about black holes.”

“We can’t see one, but we can see light from its accretion disc.”

“Fair enough. Something else.”

“A black hole’s what you get when a right‑size star collapses.”

“I like that ‘right‑size’ qualification. Too small or too big doesn’t work. White holes almost certainly can’t happen from a star collapse. What else?”

“I heard that ‘almost.’ Uhh… once you pass inside the Event Horizon, you can’t get out.”

“You can’t get inside a white hole’s Event Horizon.”

“Okay, that’s weird. Like it’s got a hard crust like black holes don’t?”

“Nope. A white hole’s Event Horizon’s a mathematical abstraction just like a black hole’s. Not a hard surface, just a boundary where time starts playing games.”

“Wait, we talked about time and the Event Horizon some time ago. If I remember right, we worked out that cause‑and‑effect runs parallel to time. Outside the Event horizon time’s not locked to any specific orientation in space. We can cause things to happen in any direction. Inside the Event Horizon’s sphere, both time and cause‑and‑effect point further in. You can’t make anything happen further out than wherever you are in there which is why light can’t escape, right?”

“Mostly. Anything inside the Horizon is bound to spiral inward toward the singularity. The journey could be slow or fast. There’s some disagreement on how long it would take, though — could be forever, could be forever near enough. Some current models say the Horizon’s geometric center is the infinitely distant future. Other models say, no, for a stellar‑collapse black hole it’s only beyond the age of the Universe.”

“Why not … oh, because the real black hole was born at a definite time so it can’t have an infinite future.”

“That’s about the size of it — both directions either finite or infinite. Physicists love to propose symmetries like that but I’m not willing to bet either way.”

“Black hole/white hole sounds like symmetry.”

“In a way it isn’t, in a way it is. Both varieties are solutions for Einstein’s equation about spacetime under—”

“Hold it, no equations, you know I hate those things. Anyway, how can two different holes solve one equation?”

“Solve x=√9.”

“Gotta be x=3.”

“Or minus‑3. They’re both right answers, right?”

“Mmm, yeah. Okay, that was arithmetic, not an equation, but why’d you give it to me at all?”

“To demonstrate plus‑or‑minus symmetry. Einstein’s equation tells how mass warps spacetime. The answers relate to square‑roots of summed squares like Pythagoras’ c=√(a²+b²). If you pick positive square roots the warping describes a black hole. The negative square roots give the warping for a white hole which behaves differently. Both kinds depend on intense gravitational fields arising from a singularity but a white hole’s cause‑and‑effect arrow points outward.”

“So that’s why you’re locked out? You can’t cause anything further in than you are?”

“Exactly. But it gets deeper. A black hole’s singularity, the one you can’t avoid if you’re inside its Event Horizon, is in the distant future. A white hole’s singularity, the one you can’t get to anyway, is in the distant past.”

“That’s why you said they can’t come from star collapses — the stars died too recent.”

“Mm-hm. If white holes exist at all, they probably were born in the Big Bang.”

~ Rich Olcott

A Carefully Plotted Tale

On By rolcottIn Cosmology, Physics: Quantum Mechanics, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“Hello, Mr Moire. Remember me?”

“Yes, I do, Walt. I hope your people were satisfied with what you brought them from our last meeting.”

“They were, which is why I’m calling. Buy you pizza at Eddie’s, fifteen minutes?”

“Make it twenty.”

We’re at the rear‑corner table, Walt facing both doors, naturally. “So, what’s the mysterious question this time?”

“Word on the street is that the CPT Law’s being violated. We want to know who’s involved, and what’s their connection with ChatGPT.”

Good thing I’ve just bit into my pizza so I can muffle my chuckle in my chewing. “What do you know about anti‑matter?”

“Inside‑out atoms — protons outside whizzing around electrons in the nucleus.”

“Common misconception. One proton has the mass of 1800 electrons. An atom built as you described would be unstable — the thing would fly apart. You’ve got anti‑matter’s charges arranged right but not the particles. Anti‑matter has negative anti‑protons in the nucleus and positrons, positive electrons, on the outside.”

<writing rapidly in his notebook> “You can do that? Just flip the sign on a particle?”

“No, positrons and such are respectable particles in their own right, distinct from their anti‑partners. Electric charge comes built into the identity. What’s important is, an anti‑atom behaves exactly like a normal atom does. Maxwell’s Equations and everything derived from them, including quantum mechanics, work equally well for either charge structure.”

“There’s a bit of Zen there — change but no‑change.”

“Nice. Physicists call that sort of thing a symmetry. In this case it’s charge symmetry, often written as C.”

“The C in CPT?”

“Exactly.”

“What about the P and T?”

“When someone says something is symmetrical, what do you think of first?”

“Right side’s a reflection of left side. Symmetrical faces look better but they’re usually less memorable.”

“Interesting choice of example. Anyway, reflection symmetry is important in common physical systems.”

“Classical Greek and Cambodian architecture; the Baroque aesthetic without the decorative frills.”

“I suppose so. Anyway, we call reflection symmetry Parity, or P for short.”

“And T?”

“Time.”

“Time’s not symmetrical. It’s always past‑to‑future.”

“Maybe, maybe not. In all our physical laws that deal with a small number of particles, you can replace t for time with –t and get the same results except for maybe a flipped sign. Newton’s Laws would run the Solar System in reverse just as well as they do forward.”

“But … Ah, ‘small number of particles,’ that’s your out. If your system has a large number of particles, you’re in chaos territory where randomness and entropy have to increase. Entropy increase is the arrow for one‑way time.”

“Good quote.”

“I’ve been in some interesting conversations. You’re not my only Physics source. So CPT is about Charge AND Parity AND Time symmetries. But you can’t simply add them together.”

“You multiply them. Technically, each of them is represented by a mathematical operator—”

“Step away from the technically.”

“Understood. This’ll be simpler. If a system’s atoms have positive nuclei, set C=1, otherwise set C=–1. If the system’s naturally‑driven motion is counterclockwise set P=1, otherwise P=–1. If time is increasing, set T=1, otherwise set T=–1. Okay?”

“Go on.”

“You can summarize any system’s CPT state by multiplying the prevailing symmetry values. The product will be either +1 or –1. The CPT Law says that in any universe where quantum mechanics and relativity work, one CPT state must hold universe‑wide.”

“Make it real for me.”

“You know the Right-hand Rule for electromagnetism?”

“Grab the wire with your right hand, thumb pointing along the current. Your fingers wrap in the direction of the spiraling magnetic field.”

“Perfect. Suppose C*P*T=+1 for this case. Now reverse the charge, making C=–1. What happens?”

“Ssss… The magnetic spin flips orientation. That’s a reflection operation so P=–1. The C*P*T calculation is (+1)*(–1)*(–1)=+1, no change.”

“The CPT Law in action. The CPT violation you’ve heard about is only observed in rare weak‑force‑mediated radioactive decays of a carefully prepared nucleus. That was a 1956 Nobel‑winning discovery, though the right person didn’t win it.”

“1956. Decades before A.I.”

“Yup, ChatGPT is off the hook. For that.”

“Bye.”

“Don’t mention it.”

~ Rich Olcott

  • Thanks to Caitlin, the hand model.

Why A Disk?

On By rolcottIn Astronomy: Stellar Science, Cosmology, UncategorizedLeave a comment

Late Summer is quiet time on campus and in my office. Too quiet. I head over to Cal’s coffee shop in search of company. “Morning, Cal.”

“Morning, Sy. Sure am glad to see you. There’s no‑one else around.”

“So I see. No scones in the rack?”

“Not enough traffic yet to justify firing up the oven on such a hot day. How about a biscotti instead?”

“If it’s only the one it’s a biscotto. Pizza Eddie’s very firm on that. Yeah, I’ll have one.”

“Always learning. By the way, a photo spread in one of my astronomy magazines got me thinking. How come there’s so much flat out there?”

“Huh? I know you’re not one of those flat‑Earthers.”

“Not the planets, I mean the way their orbits go all in the same plane. Same for most of the asteroids and the Kuiper belt, even. Our Milky Way galaxy’s basically flat, too, and so are a lot of the others. Black hole accretion disks are flat. You’d think if some baby star or galaxy was attracting stuff from everywhere to grow itself, the incoming would make a big globe. But it’s not, we get flatness. How come?”

“Bad aim and angular momentum.”

“What’s aim got to do with it?”

“Suppose there’s only two objects in the Universe and they’re closing in on each other. If they’re aimed dead‑center to each other, what happens?”

“CaaaRUNCH!!!”

“Right. Now what if the aim’s off so they don’t quite touch?”

“Oh, I know that one … it’ll come to me … yeah, Roche’s limit, it was in an article a few months ago. Whichever’s less dense will break up and all the pieces go like Saturn’s rings. Which are also flat, by the way.”

“In orbit around the survivor, mm‑hm. The pieces can’t fall straight down because they still have angular momentum.”

“I know about momentum like when you crash a car if you go too fast for your brakes. Heavier car or faster speed, you get a worse crash. How does angle fit into that — bigger angle, more angular momentum?”

“Not quite. In general, momentum is mass multiplied by speed. It’s a measure of the force required to stop something or at least slow it down. You’ve described linear momentum, where ‘speed’ is straight‑line distance per time. If you’re moving along a curve, ‘speed’ is arc‑length per time.”

“Arc‑length?”

“Distance around part of a circle. Arc‑length is angle in radians, multiplied by the circle’s radius. If you zip halfway around a big circle in the same time it took me to go halfway around a small circle, you’ve got more angular momentum than I do and it’d take more force to stop you. Make sense?”

“What if it’s not a circle? The planet orbits are all ellipses.”

“It’s still arc‑length except that you need calculus to figure it. That’s why Newton and Leibniz invented their methods. A falling something that misses a gravity center keeps falling but on an orbit. Whatever momentum it has acts as angular momentum relative to that center. There’s no falling any further in without banging into something else coming the other way and each object canceling the other’s momentum.”

“Or burning fuel if it’s a spaceship.”

“… Right. … So anyway, suppose you’ve got a star or something initially surrounded by a spherical cloud of space junk whirling around in all different orbits. What’s going to happen?”

“Lots of banging and momentum canceling until everything’s swirling more‑or‑less in the same direction and closer in than at come‑together time. But it’s still a ball.”

“Gravity’s not done. Think about northern debris. It’s attracted to the center, but it’s also attracted to the southern debris and vice-versa. They’ll meet midway and build a disk. The ball‑to‑disk collapse isn’t even opposed by angular momentum. Material at high latitudes, north and south, can lose gravitational potential energy by dropping straight in toward the equator and still be at the orbitally correct distance from the axis of rotation.”

“That’d work for stuff collecting around a planet, wouldn’t it?”

“It’d even work for stuff collecting around nothing, just a clump in a random density field. That may be how stars are born. Collapsing’s the hard part.”

~ Rich Olcott

The Beaming Beacon

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

“So, Vinnie, that first article’s bogus. Blobs in M87’s supermassive black hole’s jet don’t travel faster than light. Your second article — is it also about M87*?”

M87* image – Credit EHT Collaboration

“Yeah, Cathleen. It’s got this picture which a while ago Sy explained looks like a wrung‑out towel because that’s the way the thing’s magnetic field forces electrons to line up and give off polarized light.”

“As always, Vinnie, your memory impresses.”

“Thanks, I work at it. Anyhow, this one‑paragraph article says they figured out from the picture that everything’s spinning around as fast as it’s possible to spin. How fast is that, and how’d they get the spin speed if they only used one frequency so redshift/blueshift doesn’t apply?”

Cathleen’s been poking at her tablet. “HAH! Found the real paper behind your pop‑sci article, Vinnie. Give me a minute…” <pause, with mumbling> “Wow, not much there in the disk. They estimate even at the crowded innermost orbit, they call it ISCO, the density’s about 10-14 kg/m3 which would be one nanopascal of pressure. Most labs consider that ultrahigh vacuum. They get angular momentum from something called ‘Doppler beaming’, which I’m not familiar with.” <passes tablet to me> “Your turn, Sy.”

“ISCO’s the Innermost Stable Circular Orbit. ISCO’s radius depends on the black hole’s mass and spin.” <pause, with mumbling> “Doppler beaming’s a velocity‑dependent brightness shift from outbound to inbound sides of ISCO. They connected brightness range within the images to ISCO velocity, multiplied that by ISCO radius and the black hole’s mass to get the disk’s angular momentum, J. The lightspeed rotation angular momentum Jmax comes from theory. The paper puts a number to M87*’s J/Jmax.“

“My article says it’s near 100%.”

“That’s not what the paper says, Vinnie. ‘…our value of 0.8 would appear to be a lower limit,’ in other words, something above 80% but definitely not 100%. Like I said, pop‑sci journalism. So what’s Doppler beaming, Sy?”

“Classical Doppler shifts happen when a wave source moves relative to us. Motion toward us crams successive wave peaks into decreasing distance. Motion away increases wavelength. The same principle applies to light waves, sound waves, even ocean waves.”

“Blueshifting.”

“Mm‑hm. By contrast, beaming is about how a source’s motion affects the photon count we receive per second. Imagine a beacon steadily sending us photons as it whips at near‑lightspeed around M87*. When the beacon screams towards us its motion crams more photons into one of our seconds than when it dashes away.”

“More blueshifting.”

“Not quite. Photon‑count compression sort‑of resembles the blueshifting process but wavelength isn’t relevant. It combines with the other part of beaming, Special Relativity space compression, which concentrates a moving beacon’s photons in the direction of motion. It’s like focusing a fancy flashlight, narrowing the beam to concentrate it. The faster the beacon travels in our direction, the greater proportion of its photons are sent towards us.”

Vinnie looks up and to the left. “If ISCO’s going near lightspeed, won’t the disk’s inertia drag on the black hole?”

“Sure, within limits. M87* and Sagittarius-A* both have magnetic fields; most black holes probably do. Accretion disk plasma must be frozen into the field. The whole structure would rotate like a spongy wheel with a fuzzy boundary. The lightspeed limit could cut in at the wheel’s rim, much farther out than the Event Horizon’s sphere.”

Count on Vinnie to jump on vagueness. “Spongy? Fuzzy?”

“Because nothing about a black hole’s extended architecture is rigid. It’s a messy mix of gravitational, electric and magnetic fields, all randomly agitated by transients from inbound chunks of matter and feeding outbursts from inside ISCO. The disk’s outer boundary is the raggedy region where the forces finally give way as centrifugal force works to fling particles out into the Universe. I don’t know how to calculate where the boundary is, but this image suggests it’s out about 10 times the Horizon’s radius. The question is, how does the boundary’s speed limit affect spin?” <tapping rapidly on Old Reliable’s screen>

“And the answer is…?”

“Disk particles driven close to lightspeed do push back. They lightly scramble those mushy fields but much too feebly to slow the central spin.”

~ Rich Olcott

Look, Look Again, Then Think

On By rolcottIn Astronomy, UncategorizedLeave a comment

Cathleen and I are sharing scones and memories when Vinnie trundles up to our table. “Glad I got you two together. I just ran across a couple news items and I need some explanations.”

“Astronomy AND Physics in the same news items? Do tell.”

“They’re only one paragraph each and read like someone wrote ’em before their morning coffee. They’re both about that big black hole they’ve been taking pictures of.”

“The one in our galaxy or the M87* supermassive black hole in the Messier‑87 galaxy?”

“The second one, Cathleen. This item says it shot out a jet traveling faster than light.”

<sigh> “Pop‑sci journalism at its worst, right, Sy? I know the work that’s based on and the academic reports don’t say that. Good observations leading to less flamboyant conclusions.”

“Maybe it was supposed to be a bigger article but the editors cut it down badly. That happens. I’m sure it’s not really a superluminal jet—”

“Superluminal’s faster‑than‑light, right?”

“Right, Vinnie. Sorry to get technical. Anyway, it’s an illusion.”

“Ah geez, it’ll be frames again, right?” <eyes suddenly open wide> “Wait, I got it! I betcha it’s about the time difference. Take a blob in that jet, it’s flying out at near lightspeed. Time dilation happens when relativity’s in the game, me and Sy talked about that, so blob‑frame seconds look like they take longer than ours do. We see the blob cramming a lightsecond of distance traveled into less than one of our seconds and that’s superluminal. Am I right, Sy?”

“Right answer to a different question, I’m afraid. You’re straight on the time dilation but it doesn’t apply to this situation. Something happening within the blob’s frame, maybe a star blowing up or something weird metabolizing in there, Special Relativity’s time distortion hijinks would show us that action taking place in slow motion. But this superluminal blob claim hinges on how the blob’s whole frame moves relative to ours. That motion isn’t superluminal but it can look that way if conditions are right. As I understand it, the M87* jet qualifies. Your bailiwick rather than mine, Cathleen.”

“Actually it is a frames thing, Vinnie, but timeframes, not spacetime. Those blobs move too slowly in our sky to watch in real time. We take snapshot A and then maybe a few years later we take snapshot B and compare. Speed is the ratio of distance to time. We need the A‑B distance in 3‑D space to compare to the known time between snapshots. But we can’t see the blob’s trajectory in 3‑D. All we can capture is its 2‑D arc C‑B across an imaginary spherical shell we call the sky. If the M87* jet were perpendicular to our line of sight the C‑B image on the sky‑sphere would match the 3‑D path. Multiply the image’s angle in radians by the distance to M87* and we’re done.”

“We’re not done?”

“Nope. This jet points only 20° away from our direct line of sight. I’ll spare you the trigonometry and just say that distance A‑B is about 3 times longer than C‑B.”

“So we measure C‑B, triple the angle and multiply by the M87* distance. No problem.”

“Problem. That tripling is what makes the blob’s A‑B journey appear to go faster than light. Three times 0.4c equals 1.2c. But you missed something important. Your arithmetic assumed you could use a simple ‘M87* distance’. Not in this case, because the blob moves towards us at close to lightspeed. Visualize two concentric sky‑spheres. The outer one’s radius runs from us to the blob’s location at A‑time. The inner sphere’s radius runs to the blob’s location at B‑time. The B‑sphere is our reference frame. The light we saw at A‑time had to travel from the outer sphere to the inner one before we could register the C‑B image.”

“Can’t be very far.”

“We’re talking years at lightspeed, so lightyears, so significant. A properly illusion‑free A‑B travel calculation must include the A‑C travel time in the denominator of the distance/time ratio. The true kilometers per second come out well below lightspeed. Oh, and relativity’s not involved.”

“Dang, Cathleen, it was such a cool illusion.”

~ Rich Olcott

Not Even A Sneeze in A Hurricane

On By rolcottIn General: Fun Stuff, Physics: Newton and Gravity, Space Travel, UncategorizedLeave a comment

Quite a commotion at the lakeshore this morning. I walk over to see what’s going on. Not surprised at who’s involved. “Come away from there, Mr Feder, you’re too close to their goslings.” Doesn’t work, of course, so I resort to stronger measures. “Hey, Mr Feder, any questions for me?”

That did the trick. “Hey, yeah, Moire, I got one. There’s this big problem with atomic power ’cause there’s leftovers when the fuel’s all used up and nobody wants it buried their back yard and I unnerstand that. How about we just load all that stuff into one of Musk’s Starships and send it off to burn up in the Sun? Or would that make the Sun blow up?”

“Second part first. Do you sneeze?”

“What kinda question is that? Of course I sneeze. Everyone sneezes.”

“Ever been in a hurricane?”

“Oohyeah. Sandy, back in 2012. Did a number on my place in Fort Lee. Took out my back fence, part of the roof, branches down all over the place—”

“Did you sneeze during the storm?”

“Who remembers that sort of thing?”

“If you had, would it have made any difference to how the winds blew?”

“Nah, penny‑ante compared to what else was going on. Besides, the storm eye went a couple hundred miles west of us.”

“Well, there you go. The Sun’s surface is covered by about a million granules, each about the size of Texas, and each releasing about 400 exawatts—”.

“Exawha?”

“Exawatt. One watt is one joule of energy per second. Exa– means 1018. So just one of those granules releases 400×1018 joules of energy per second. By my numbers that’s about 2300 times the total energy that Earth gets from the Sun. There’s a million more granules like that. Still think one of our rockets would make much difference with all that going on?”

“No difference anybody’d notice. But that just proves it’d be safe to send our nuclear trash straight to the Sun.”

“Safe, yes, but not practical.”

“When someone says ‘practical’ they’re about to do numbers, right?”

“Indeed. How much nuclear waste do you propose to ship to the Sun?”

“I dunno. How much we got?”

“I saw a 2022 estimate from the International Atomic Energy Agency that our world‑wide accumulation so far is over 265 000 tonnes, mostly spent fuel. Our heaviest heavy‑lift vehicle is the SpaceX Starship. Maximum announced payload to low‑Earth orbit is 400 tonnes for a one‑way trip. You ready to finance 662 launches?”

“Not right now, I’m a little short ’til next payday. How about we just launch the really dangerous stuff, like plutonium?”

“Much easier rocket‑wise, much harder economics‑wise.”

“Why do you say that?”

“Because most of the world’s nuclear power plants depend on MOX fuel, a mixture of plutonium and uranium oxides. Take away all the plutonium, you mess up a significant chunk of our carbon‑free‑mostly electricity production. But I haven’t gotten to the really bad news yet.”

“I’m always good for bad news. Give.”

“Even with the best of intentions, it’s an expensive challenge to shoot a rocket straight from Earth into the Sun.”

“Huh? It’d go down the gravity well just like dropping a ball.”

“Nope, not like dropping a ball. More like flinging it off to the side with a badly‑aimed trebuchet. Guess how fast the Earth moves around the Sun.”

“Dunno. I heard it’s a thousand miles an hour at the Equator.”

“That’s the planet’s rotation on its own axis. My question was how fast we go taking a year to do an orbit around the Sun. I’ll spare you the arithmetic — the planet speeds eastward at 30 kilometers per second. Any rocket taking off from Earth starts with that vector, and it’s at right angles to the Earth‑Sun line. You can’t hit the Sun without shedding all that lateral momentum. If you keep it, the rules of orbital mechanics force the ship to go faster and faster sideways as it drops down the well — you flat‑out miss the Sun. By the way, LEO delta‑v for SpaceX’s most advanced Starship is about 7 km/s, less than a fifth of the minimum necessary for an Earth‑to‑Sun lift.”

~ Rich Olcott

The Phase Rue

On By rolcottIn General: Fun Stuff, Uncategorized2 Comments

Stepping past the fourth wall again. You may have noticed that some of my recent posts have included A.I.‑generated illustrations. The creation process has been fun and often frustrating. Sometimes I’ve gone through half‑a‑dozen or more iterations, refining and re‑refining a prompt until I got the effect I wanted. Or not.

A couple of times I just gave the beast the text of the post and was delighted with the results (see in particular this one and this one). I used prompts for most of the space scenery in the “Sulfur on Io” series; on the whole they came out well. For some posts (for instance this one) I had to haul out my toolkit and tinker with the generated image. Other times I simply gave up and went back to my trusty digital artsy processes. I had to do that when I turned the A.I. loose on one of the “Phase Rule” posts:

The title (which I hadn’t asked for) was almost too good, but the column headings (“Thiogy”? “Presture”?) definitely went off the deep end.

Then there’s the following image, the final unfortunate result of an extended series of prompts I went through trying to illustrate a post about the three-body problem. So many issues:

  • The mise-en-scène just isn’t my visualization of Pizza Eddie’s place and I couldn’t get the A.I. to adjust it properly.
  • That “clock” has only ten, or maybe 9½, numbers. Besides, it’s in a stupid place, at the ceiling above the crown molding.
  • Vinnie’s holding a pizza fragment but neither pizza in front of him has been touched.
  • Eddie has no flour dust on his apron.
  • Sy’s right shoulder is too hyper‑developed for an office worker who doesn’t bowl or do archery. He’s the kind of guy who would wear a sport jacket any time he’s out of the house. Finally, in all of my prompts I had him facing the other two. Sy may be a shy person, but he’s not one to avoid the camera.

And then I watched John Oliver’s harangue about “A.I. slop.” As usual, he’s on‑target. The tech is fundamentally unfair because it has been built using work from real live working artists with whom it now competes. Moreover, A.I. is gleefully being abused by rapacious click‑harvesters who flood the internet with rubber‑stamp crap*, generally either political or cringey. Like the guy said, “It ain’t right.”

So in the future I’m going to avoid using A.I.‑generated images in favor of hand-made ones. Mostly.

* See Theodore Sturgeon’s First Law — “95% of everything is crap.” On recent evidence, that number’s probably too low these days.

[/rant]

~ Rich Olcott

Two’s Company, Three Is Perturbing

On By rolcottIn Mathematics, Physics: Newton and Gravity, Space Travel, UncategorizedLeave a comment

Vinnie does this thing when he’s near the end of his meal. He mashes his pizza crumbs and mozzarella dribbles into marbles he rolls around on his plate. Mostly on his plate. Eddie hates it when one escapes onto his floor. “Vinnie, you lose one more of those, you’ll be paying extra.”

“Aw, c’mon, Eddie, I’m your best customer.”

“Maybe, but there’ll be a surcharge for havin’ to mop extra around your table.”

Always the compromiser, I break in. “How about you put on less sauce, Eddie?”

Both give me looks you wouldn’t want.
  ”Lower the quality of my product??!?”
    ”Adjust perfection??!?”

“Looks like we’ve got a three‑body problem here.” Blank looks all around. “You two were just about to go at it until I put in my piece and suddenly you’re on the same side. Two‑way interaction predictable results, three‑way interaction hard to figure. Like when Newton calculated celestial orbits to confirm his Laws of Gravity and Motion. They worked fine for the Earth going around the Sun, not so good for the Moon going around the Earth. The Sun pulls on the Moon just enough to play hob with his two‑body Earth‑Moon predictions.”

“Newton again. So how did he solve it?”

“He didn’t, not exactly anyway.”

“Not smart enough?”

“No, Eddie, plenty smart. Later mathematicians have proven that the three‑body problem simply doesn’t have a general exact solution.”

“Ah-hah, Sy, I heard weaseling — general?”

“Alright, Vinnie, there are some stable special cases. Three bodies at relative rest in an equilateral triangle; certain straight‑line configurations; two biggies circling each other and a third, smaller one in a distant orbit around the other two’s center of gravity. There are other specials but none stable in the sense that they wouldn’t be disrupted by a wobbly gravity field from a nearby star or the host galaxy.”

A special-case solution
to the three-body problem
by MaxwellMolecule,
licensed under CC ASA 4.0

“So if NASA’s mission planners are looking at a four‑body Sun‑Jupiter‑Europa‑Juno situation, what’re they gonna do? ‘Give up’ ain’t an option.”

“Sure not. There’s a grand strategy with variations. The oldest variation goes back to before the Egyptian builders and everybody still uses it. Vinnie, when you fly a client to Tokyo, do you target a specific landing runway?”

“Naw, I aim for Japan, contact ATC Narita when I get close and they vector me in to wherever they want me to land.”

“How about you, Eddie? How do you get that exquisite balance in your flavoring?”

“Ain’t easy, Sy. Every batch of each herb is different — when it was picked, how it was stored, even the weather while it was growing. I start with an average mix which is usually close, then add a pinch of this and a little of that until it’s right.”

“For both of you, the critical word there was ‘close’. Call it in‑flight course adjustments, call it pinch‑and‑taste, everybody uses the ‘tweaking’ strategy. It’s a matter of skill and intuition, usually hard to generalize and even harder to teach in a systematic fashion. Engineers do it a lot, theoretical physicists work hard to avoid it.”

“What’ve they got that’s better?”

” ‘Better’ depends on your criteria. The method’s called ‘perturbation theory’ and strictly speaking, you can only use it for certain kinds of problems. Newton’s, for instance.”

“Good ol’ Newton.”

“Of course. Newton’s calculations almost matched Kepler’s planetary observations, but finagling the ‘not quite’ gave Newton headaches. More than 150 years passed before Laplace and others figured out how to treat a distant object as a perturbation of an ideal two‑body situation. It starts with calculating the system’s total energy, which wasn’t properly defined in Newton’s day. A perturbation factor p controls the third body’s contribution. The energy expression lets you calculate the orbits, but they’re the sum of terms containing powers of p. If p=0.1, p2=0.01, p3=0.001 and so on. If p isn’t zero but is still small enough, the p3 term and maybe even the p2 term are too small to bother with.”

“I’ll stick with pinch‑and‑taste.”

“Me and NASA’ll keep course‑correcting.”

~ Rich Olcott

Sharpening The Image

On By rolcottIn Astronomy: Stellar Science, Astronomy: Techniques, UncategorizedLeave a comment

“One coffee, one latte and two scones, Cal. Next time is Cathleen’s turn. Hey, you’ve got a new poster behind the cash register. What are we looking at?”

“You like it, Sy? Built the file myself from pics in my astronomy magazines, used the Library’s large‑format printer for the frameable copy. Came out pretty well, didn’t it, Cathleen?”

“Mm‑hm. Sy, you should recognize the pebbly-looking one. It’s granules at the bottom of the Sun’s atmosphere. The image came from the Inouye Solar Telescope at Haleakala Observatory on Maui, probably Earth’s best ground‑based facility for studying the Sun. I showed the image to your niece in that phone call. For scale, those granules of super‑heated rising gas are each about the size of Texas.”

“My magazine article didn’t mention Texas but it said there’s about ten million granules. What it was mostly about was the IST and its resolution. Those edges in the picture are as narrow as 18 miles across. It’s that good ’cause the beast has a 4‑meter mirror, which used to be amazing, but they made it even better with active and adaptive optics.”

“Hmm. It’s obvious that the bigger the mirror, the better it is for catching photons. If someone’s going to build a big mirror they’re going to put it behind a big aperture, which is important for resolving points that are close together. But what are ‘active and adaptive optics’ and why did you say that like they’re two different things?”

” ‘Cause they are two different things, Sy. Different jobs, different time‑scales. Gravity here on Earth can make a big mirror sag, and the sag changes depending on where the machine is pointed and maybe part of it gets the wrong temperature. Active optics is about keeping the whole mirror in the right shape to focus the photons where they’re supposed to go. There’s a bunch of actuators rigged up to give adjustable support at different points behind the mirror. The astronomer tells the system to watch a certain guide point and there’s a computer that directs each actuator’s pushing to sharpen the point’s image.”

“And adaptive optics?”

“That’s about solving a different problem. Stars twinkle, right, and the reason they twinkle is because of the atmosphere. One part refracts light one way, another part maybe warmer or with different humidity sends the light another way. Everything moves second to second. By the time a light‑wave gets down to us it’s been jiggled a lot. Adaptive optics is a small mirror, also with a lot of actuators, placed up in the light path after the primary mirror. Again with a guide point and a computer, the little mirror’s job is to cancel the jiggles so the scope’s sensors see a smooth wave. Adaptive works a lot faster than active, which sounds backwards, but I guess active came first.”

“The granules must be in the Sun’s disk somewhere. The other two images look like they’re on the edge.”

“That’s right, Sy. The bottom one is from the Solar Dynamic Observatory satellite a few years ago. That’s not visible light, it’s EUV—”

“EUV?”

“Extreme UltraViolet, light‑waves too short even for hydrogen so it’s mostly from iron atoms heated to millions of degrees. SDO had to be a satellite to catch that part of the spectrum because the atmosphere absorbs it. Of course, up there there’s no need for active or adaptive optics but imaging EUV has its own problems.”

“How tall is that photogenic tree?”

“It’s a prominence. The article said it’s about twenty times Earth’s diameter.”

“What about the pink one?”

“That’s new, Cathleen, from another Maui telescope. Adaptive optics were in play but there’s a problem. If you’re probing inside the corona there’s no fixed guide point. The team focused their adjustment system on corona features where they were a few seconds ago. The article said the process was ‘tricky,’ but look at the results. The loop is about the size of Earth, and those fine lines are about the width of Vancouver Island. They discovered details no‑one’s ever seen before.”

Top left: Schmidt et al./NJIT/NSO/AURA/NSF;
Top right: NSO/AURA/NSF under CC A4.0 Intl license;
Bottom: NASA/SDO

~ Rich Olcott

Snap The Whip

On By rolcottIn Astronomy: Stellar Science, Physics: Electromagnetism, UncategorizedLeave a comment

“You say Alfven invented a whole science, Sy, but his double‑layer structures in plasma don’t look like much compared with the real ground‑breakers like Herschel or Hubble.”

“Your Astronomy bias is showing, Cathleen. The double‑layer thing was only a fraction what he gave to magnetohydrodynamics. To begin with, he dreamed up a new kind of wave.”

“There’s more than light waves, sound waves and ocean waves?”

“Certainly. There’s dozens of different kinds — look up waves in Wikipedia some day. Some move, some make other things move; sometimes things move in the direction the wave does, sometimes crosswise to it. From a Physics perspective waves are about repetition. Something that happens just once, where do you go from there?”

“That used to be Astronomy’s problem — only one solar system with fewer than a dozen planets, only two galaxies we could inspect closely. Now our space telescopes and monster‑mirror ground‑based observatories have given us thousands of planets and billions of stars and galaxies. If we get our classifications right we can follow an object type through every stage of development. It’s almost like watching Chemistry happen.”

“I doubt Susan Kim would agree but I get your point. Anyhow, most waves have a common underlying process. Many systems have an equilibrium condition. Doing something energetic like plucking on a guitar string moves the system away from equilibrium. That provokes some force to restore equilibrium. For the guitar, tension in the wire pulls it straight. Usually the restoration overshoots so the restoring force turns around to act in the opposite direction. That’s when the repetition starts, right?”

“Mm-hm, that’s sound waves in a nutshell. Ocean waves, too, because gravity’s the restoring force fighting with the wind to pull things flat.”

“Same idea. Well, Alfven’s first trick was to demonstrate that in a plasma or any conducting medium, a magnetic field acts like that guitar string. The field’s equilibrium configuration is straight and smooth. If you perturb the medium somehow to put a bend or kink in the field, magnetic tension kicks in to restore equilibrium. Waves restored by magnetic fields are important enough that they’re now called Alfven waves in his honor.”

“First trick, mmm? There’s more?”

“Yup, an old one he borrowed from Maxwell — the flux tube. Maxwell worked before atoms were a conceptual thing. He thought about magnetism in terms of immaterial ‘lines of force’ that followed the rules laid out in his equations. Think of grabbing a handful of barely cooked spaghetti, still mostly stiff.”

“Yuck.”

“You’re wearing gloves, okay? The point is, you’ve got a more‑or‑less cylindrical bundle of parallel strands. Pretend each strand is a line of magnetic force. Maxwell’s rules say the number of lines of force, the total magnetic flux, coming out one end of the bundle exactly equals the flux that went in the other end. There’s no sourcing or destroying magnetic flux in between.”

“What if I squeeze real hard?”

“Nope. The flux per unit area intensifies — that’s called ‘the pinch effect’ and particle beam folks love it — but the total flux stays the same. Here’s where it gets interesting. Alfven showed that if the flux tube passes through a plasma or other conducting medium, the medium’s charged particles get frozen into the field. Waggle the field, you waggle the particles. Now put that together with his waves.”

“Oh, that’s what those guys have been talking about! There’s a slew of recent papers built on observations from the Parker Solar Probe mission. One of the biggest outstanding problems in solar physics is, how can the corona, the outermost layer of the Sun’s atmosphere, be millions of degrees hotter than the 6000‑degree photosphere beneath it? Well, PSP and other satellite missions have recorded many observations where the ambient magnetic field suddenly flipped from one direction to its near‑opposite. It’s like the probe had flown through a flux tube zig‑zag in space.”

“Those sharp angles indicate a lot of pent‑up magnetic tension.”

“Absolutely! Now imagine those zig‑zags in the crowded chaos inside the Sun’s atmosphere, colliding, criss‑crossing, disconnecting, reconnecting, releasing their magnetic flux energy into frozen‑in particles that aren’t frozen any more. What do you get, Sy?”

“Immense amounts of kinetic energy. Hot times, indeed”

~ Rich Olcott