Tag: Walt

Luminous horned goat head surrounded by stars with one glowing red eye

A Mote in Capricorn’s Eye

On By rolcottIn Astronomy, Crazy Theories, UncategorizedLeave a comment

<bzzt, bzzt> “You again, Moire. What is it this time?”

“Better get over to my office, Walt. I’ve got some charts you’ll want to see, but you probably don’t want them spread all over.”

“Fifteen minutes. No, make that twenty. Bye.” <click>

Twenty minutes later on the dot, his cane taps my office doorpost. “Let’s see those charts.”

“Let me cast this video from Old Reliable to my wall screen. Watch it while I give you the background.”

Data from JPL’s Small Body Database

“I’ll need background to even read this thing.”

“I figured. Here’s a sketch for vocabulary. The big oval is a comet orbit, though they’re usually a lot skinnier than that, roughly ten times longer than wide. ‘Perihelion’ is Greek for ‘close to the Sun’. The word for its opposite point is ‘aphelion’. Your maybe‑incoming chunk of neutronium would be a quarter the Sun’s mass but far too small to see. Even so, I thought its gravity field could be enough to generate a signal made of long‑period comets kicked inward from the Oort cloud.”

“Ah, that’s why your chart’s doing aphelions. A comet at aphelion far from the Sun would be out in the Oort cloud and vulnerable to being kicked. Side‑to‑side in the chart is east‑west; up top is the Pole Star then down to the southern sky. So what you’re showing me is where in the sky each long‑term comet would be when it’s farthest from the Sun. The markers are pretty much everywhere each decade. What’s with the orange fringes?”

“They’re bar charts to summarize relative comet count in each 10‑degree slice of latitude or longitude. The biggest bar in each longitude set represents 4 comets; the biggest latitude bars represent 6. If comets are coming in randomly around the Equator, the summaries along the bottom would be essentially flat, like it shows for the 50 years starting in 1950.”

“This is the kind of map that stretches Greenland relative to Africa, isn’t it?”

“Mm-hm. The latitude lines are drawn parallel to each other although they actually converge on an spherical surface.”

“So I can correct for that by mentally squeezing distances between latitudes … I’d expect relatively few markers close to the poles compared to what’s near the Equator. Right, that’s roughly the latitude summary pattern given the small sample sizes. But what’s going on after 2010?”

“You noticed that red-dot cluster centered above the Equator at about –75°. It’s in the constellation Capricorn. I asked Old Reliable to select the group between –100° and –50° and chart where and when each comet was at its most recent aphelion. Here’s the result. By the way, the slope estimate is at the 75% confidence level. You don’t often see data as tight as that.”

“Whoa! Around 1100 A.D. something from beyond 200 a.u. in the general direction of Capricorn started knocking long‑period comets down from the Oort cloud. Every century that thing’s gotten 17 a.u. closer which gives us … about 400 years before planetary chaos breaks out. What’s an ‘a.u.’?

“Astronomical unit, essentially the radius of Earth’s orbit — 140 million kilometers. But here’s a plot of the same variables including all the long‑period comets reported since 1950. The red dots aren’t special; they behave like the general population. Feeling better?”

“Absolutely not. This looks like the entire Oort cloud is collapsing on us!”

“Relax. You’re looking at an observational artifact — a subtle one, the kind that scientists hate but they get their jollies from uncovering one. Especially if it’s someone else’s.”

“How is this an artifact? The dates and distances are right there.”

“The dates hide something deeper. We can’t see these guys at aphelion — they’re dark and far away. Our telescopes can only pick them up when they’re within 5 a.u. of the Sun, 10 a.u. at the most. Five a.u. is less than 3% of a 200‑a.u. orbit. Within a few percent, observation dates are perihelion dates in disguise. The chart’s horizontal axis is really perihelion‑to‑aphelion cycle time. We’ve known since Kepler’s time that more energetic comets fly farther and take longer to return.”

“Hmph. So your red dots are probably just a random eddy in the Oort cloud. Bye.”

~ Rich Olcott

Luminous horned goat head surrounded by stars with one glowing red eye

Neutronium Chill

On By rolcottIn Astronomy, Astronomy: Stellar Science, Crazy Theories, UncategorizedLeave a comment

<chirp, chirp> I recognize the caller’s number. “Afternoon, Walt. Weren’t you going to trash that phone?”

“Afternoon, Moire. I decided to keep it, just for you.”

“Aww.”

“Don’t get cute. My people have a follow-on question for you. The neutronium chunk that might or might not rearrange our Solar System — how much lead time do we have between when we detect it and when things go sour?”

“So many unknowns. The object’s size, its speed, what signal we’re monitoring, even what you mean by ‘go sour’.”

“Yes, yes, very uncertain. Make some assumptions.”

“Big assignment. I’ll start with size. The smallest neutron star we’ve ever seen is about 1.3 solar masses, but Oppenheimer’s calculations say smaller chunks could be stable. Suppose it’s near the theoretical minimum, say about a quarter of a solar mass, maybe 20‑25 kilometers in diameter.”

“A whole neutron star’s about that diameter. This chunk would be a small cast‑off.”

“No, the cast‑off could be wider than its parent. It’s only a fraction of the star’s mass, so there’d be less gravity squeezing its component particles together. Anyway, it’s a reasonable size for calculating the telescopic detection limit.”

“Walk me through that.”

“Sure. Our sharpest telescopes, the Hubble and the Webb, both use detectors that span about about 40 milliarcseconds per pixel‑width.”

” ‘Milli-‘ I get; that’s one one‑thousandth. ‘Arcseconds’?”

“Works like a clock. Sixty arcseconds to an arcminute, sixty arcminutes to a degree. While I’m at it, 360 degrees is full circle is 2π radians. Put it all together, one of those pixels covers about 0.2 microradian across the sky. Now visualize a triangle. One side spans the chunk; the angle opposite it is at Hubble’s detector.”

“A long, pointy triangle.”

“Pointy enough that the angle in radians is essentially equal to its sine and we can do trigonometry. Your question boils down to, how close does the chunk have to be so its light spans a Hubble pixel?” <keyboard clatter> “You’re not going to like this. A 20‑kilometer object casting a one‑pixel figure can’t be more than 180 million kilometers away. That’s already well inside the Solar System, closer to us than the Asteroid Belt. Just a one‑pixel ‘image,’ not a portrait, from our best telescope for visible light.”

“How about another part of the spectrum?”

“I wouldn’t bet on it. The chunk probably radiated X‑rays early on, but it’s had millions of years in interstellar space to cool off.”

“How is it millions? The Crab Nebula hosts a neutron star and its supernova looks pretty random to me. The Nebula could have flung a chunk at us and it’s only 6500 lightyears away.”

“The fastest interstellar traveler we’ve seen so far is 3I/Atlas, got here from who knows where with a base velocity of 58 kilometers per second. I’ll give you a factor of two — say the Crab flung your chunk at 120 km/sec. That’s still 2500 times slower than lightspeed. At that rate it’d take 16 million years to arrive here. The Crab supernova’s light got here only 970‑some years ago so no chance for an IR‑bright Crab chunk any time soon.”

“Neutrinos?”

“The IceCube Neutrino Observatory detects a million cosmic‑ray muons for every neutrino it sees. Tough odds.”

“Telescopic surveillance isn’t an option. Observing neutrinos is a crapshoot. How about gravitational messing with planet orbits?”

“Something subtler would appear first. Imagine a spherical shell where the inward pull of the Sun’s gravity just equals the outward pull of everything outside.”

“That’d be the outer edge of the Oort Cloud.”

Data from
wikipedia.org/wiki/List_of_long-period_comets

“Pretty much. The chunk will carry its own gravity sphere. Where the two spheres intersect, the opposing gravity fields fight. Some Oort objects fly outward, many drop inward to become long‑period comets. The chunk‑detection signal would be a drastic rise in long‑period comet sightings. Typical long‑period comets take hundreds of years to get down to where we can see them. Nonetheless, we’ve had an upward spike recently.”

“Because of improved technology?”

“Or improved financing. Congress is interested in finding Earth‑threatening asteroids. Look for asteroids, maybe find comets.”

“Lead time in centuries, opening bell may have rung. Bye”

Author’s conception of a neutronium fragment
being expelled from the Crab Nebula.

~ Rich Olcott

A Three Burdens Story

On By rolcottIn Astronomy: Stellar Science, Crazy Theories, Physics: Quantum Mechanics, UncategorizedLeave a comment

<bzzzt, bzzzt> “Who is this and how did you get this number?”

“Morning, Walt. It’s Sy Moire. Does hitting ‘Reply’ to your entry on my phone log count as spycraft?”

“Drat, another burner phone to trash. Oh well. Why the call?”

“Some history for your neutronium question, may make a difference.”

“Good difference or bad difference?”

“Depends on how you slant it, I suppose. The good news is that detecting that Earth‑threatening lump of neutronium would be easier than I thought. The bad news is that detecting it would be easier than I thought.”

“Forward and backward in the same statement. Unravel that.”

“It all goes back to Oppenheimer—”

“J Robert, the guy who ran the Manhattan Project?”

“The same, except before that he did theoretical Physics, not project management. Probably the most prominent physicist of the 1930s. He was active and influential in everything from molecular quantum mechanics and quantum field theory to astrophysics. He knew pretty much everyone who counted; everyone else knew of him. That made him a natural choice as a recruiter for the Project. I think many people were surprised when he turned out to be a good administrator.”

“Good for him and us. Why drag him into this?”

“He showed how neutron stars and black holes could happen. We’d known since 1915 that black holes were implicit in Einstein’s equations. Einstein himself didn’t think the Universe would allow matter to be that dense. In 1939 Oppenheimer showed how a star’s collapse could compress matter enough for the job. Actually, black holes were the easy part.”

“How could that be easy?”

“A star’s outer layers are supported by thermal pressure from the gas inside, right? When there’s not enough fuel to supply the heat, those outer layers come smashing inward like a roof when you knock out a load‑bearing wall. A big‑enough star would have plenty of gravitational potential energy to crush its core into black‑hole mode. Oppenheimer’s real challenge was explaining why the fall stopped partway for a smaller star. He used a tip from Fermi.”

“Enrico Fermi, the guy who built the nuclear reactor under the football field?”

“The same, except it wasn’t under the field, it was under the bleacher seats, but that’s another story. Anyway, Fermi had applied Pauli’s exclusion principle—”

“Out from the weeds, please.”

“Sorry. A couple of years prior, Fermi had worked out how a gas of quantum particles would behave under compression.”

“We’re talking electron or neutron gases?”

“Those among others. Squeeze a sparse quantum gas and measure the pressure it exerts at each decrease in volume. Pressure times volume is energy. For normal gases, pressure change times volume change at constant temperature is essentially constant. With quantum gases there’s a quantum‑limit pressure where the ΔP×ΔV energy goes nuts regardless of temperature. You need to input drastic amounts of energy to achieve even a small volume decrease. Technically, the limit’s called degeneracy pressure but I’d avoid that term in your report.”

“Because negative electron repels negative electron, naturally.”

“Nope, this is completely quantum, nothing to do with charge. It applies to neutrons just like it does to electrons although the limits are different. Try to cram too many quantum particles into a given volume and something has to give.”

“I see where you’re going. Does that energy limit depend on particle mass?”

“Indeed. Heavier particles have a higher limit.”

“Let me guess. White dwarf stars collapse to the electron limit, neutron stars to the neutron limit, pressure crushing beyond that makes a black hole. That’s what Oppenheimer calculated?”

“Mm‑hm. Better yet, he calculated minimum mass for each object type. That’s where the good‑news/bad‑news comes in. You need a lot of gravitational pressure to maintain a stable neutronium object. Below about a tenth of a solar mass, BLOOEY! If your nasty nova were to fling a too‑small chunk of neutronium at us, the chunk would disintegrate long before it could get this far.”

“So the good‑bad news is, a mass of neutronium could only get near us if it was more than a tenth of the Sun’s mass. Anything that heavy would make noticeable changes to planetary orbits long before we could see it. Bye.” <click>

~ Rich Olcott

Abstract cosmic composition with colorful swirling ribbons, organic forms, and stars

A Cosmic Trattoria

On By rolcottIn Astronomy: Multi-messenger, Crazy Theories, UncategorizedLeave a comment

Walt is not amused. ” ‘Not likely but probably’ — what kind of answer is that, Moire? You going for Pratchett’s ‘million-to-one chances crop up nine times out of ten’?”

“You asked me two questions, I gave you two answers. I won’t even bill you for one of them.”

“You know my opinion about lagniappes. We’ll pay for both, but only if we get value.”

“Your first question was, could a nova have flung a chunk of neutronium that’ll hit our Solar System?” <starts tapping on Old Reliable’s screen> “I assume your people are worried about protecting Earth.”

“I neither confirm nor deny that assumption.”

“Either way, by geometry alone the likelihood’s negligible. All our System’s planets and most of the satellites and asteroids and comets are within a few degrees of the Plane of the Ecliptic. Think of everything from Neptune’s orbit inward as a thin flat disk. From above, Earth’s cross‑section area is almost a trillionth of the disk’s area. Suppose your nova is 10 times as far away as our nearest star. Worst case is the nova hanging directly above the Ecliptic. Our disk would be a circular patch in the nova’s sky. If the nova throws a neutronium chunk, it can choose randomly from 20 billion patches the same size as ours; Earth is only a trillionth of one of them. Best case is the nova’s located edge-on to our disk; the odds of a hit would be far smaller. A neutronium chunk striking Earth is a framazillion times less likely than a hit from one of our own near‑Earth asteroids.”

“‘Framazillion.’ I’m going to quote you on that.”

“No extra charge. Now for your second question, whether we could detect a neutronium interloper. Yes, if we’re looking in the right direction with the right detectors.”

“Needs a full-sky survey, obviously, because we have no clue where it’s coming from. What kind of detectors? It’s got to be warmer than empty space. Infrared?”

“Mm-hm. The chunk’s free electrons would shine with black‑body radiation.at all wavelengths but IR’s your best choice.”

“Free electrons? I thought the thing was made of neutrons.”

“Sorry, that’s pop‑sci simplification. The neutrons in a neutronium object are stabilized by gravitational compression, but the gravity field tapers off near the surface. Deep inside you’ve got neutron soup, possibly superfluid, but the particles further up aren’t crowded quite as tightly and have ways of freezing up. There’s a slushy lower crust of nuclear pasta, then an atomic upper crust of iron and its transition‑metal relatives plus some hydrogen and helium. Finally there’s a free‑electron ‘atmosphere’.”

“Wait — nuclear pasta?”

“Technical term, believe it or not. Liquid water and ice make a slush, right, one ingredient occurring in two phases. Water has about 20 different phases—”

“Ice-nine, in Vonnegut’s book.”

“That’s a plot device, I’m talking real ice here. You get different ices at different temperatures and pressures because the microscopic‑level components re‑arrange. We think neutronium does the same. Near the top of a neutron star’s lower crust, the pressure’s low enough that neutrons and protons can clump together as monster nuclei with a high neutron/proton ratio. Theorists depict them as ‘gnocci‘ (or ‘meatballs’) floating in the uncrystallized neutron phase. Down below where the pressure’s higher, the gnocci phase breaks up to form long thin strands of ‘spaghetti.’ Even further down you get sheets of ‘lasagna’ and so on. Physicists can have fun, too. Anyway, IR detectors would be best because the star’s gravity field redshifts UV and visible black‑body emissions to longer wavelengths. But your problem is, that’s not neutronium‑specific.”

“Right, any warm rock would emit IR. Is there something else?”

“Yes, there is, and we already have the right observatories in place and operating.”

“What do they detect?”

“Neutrinos, the lightest particles we know of, about a millionth the mass of an electron. Every time a proton absorbs an electron and converts to a neutron, neutrinos are emitted. That happens a lot in neutronium; a chunk of it ought to be a bright neutrino source. We’ve got a dozen neutrino telescopes in operation all over the world. If they spot something, you’ll hear about it.”

“Bye.”

“Don’t mention it.”

Abstract cosmic composition with colorful swirling ribbons, organic forms, and stars

~ Rich Olcott

Rugged asteroid surrounded by glowing debris in a colorful nebula

Neutral Under Pressure

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

The Acme Building’s elevator takes me to the 12th floor with no hiccups, for a change. I unlock my office door and there’s “Walt,” standing in the middle of the room brandishing his cane with what looks like a fat cell phone plugged into it somehow. “The place is clean, Mr Moire. No listeners in the elevator shaft, corridor or office space, and I put temporary foam over your windows to block laser‑bounce sound pickup.”

“That’s good to know, Walt. Should I give you credit for fixing the elevator?”

“Not publicly. Found a dark web relay routine freeloading elevator’s controller computer. Disabled it so the machine can do its real job.”

“Nice work. But why so surreptitious? You know I don’t do military consults. And why come up to my office instead of meeting at Eddie‘s or the park as usual?”

“Tradecraft, Mr Moire — never use the same location too often. Espionage is a thing, military or not, and it doesn’t recognize national boundaries. My people have their secrets, too.”

“Naturally. What are your people curious about this time?”

“Neutronium.”

“Neutronium?”

“Yes, what can you tell me about it?”

“It’s really dense. You’ve heard the line that atoms are mostly empty space. An atomic nucleus is maybe a few femtometers across, but it floats in a ball of space that’s a thousand to ten thousand times wider. The space isn’t empty, of course — it’s occupied by spread‑out electronic charge. Neutronium doesn’t have that not‑quite‑empty space. A neutronium ball with the Sun’s mass would be a dozen kilometers across.”

“Mashed‑together charge like a metal. Would neutronium be shiny?”

“Possibly. I’ve never seen any.”

“Are there neutronium ores you could mine for?”

“Not on Earth, guaranteed. Except for the noble metals like gold, ore atoms are isolated from each other, dispersed in minerals like oxides or sulfides. Neutronium by its nature would have to be in a massive isolated deposit.”

“By its nature?”

“An isolated neutron lives about 15 minutes before it spits out an electron and becomes a proton. A neutron near enough to another nuclear particle is stabilized by the weak nuclear force, but that’s ineffective beyond a few femtometers. Either a neutron’s in an atomic nucleus or it’s mashed up against other neutrons in neutronium or it’s dead.”

“How about a chunk of neutronium buried in one of these ultra‑dense asteroids I’ve read about, like 33 Polyhymnia, or 16 Psyche that we’ve sent a space mission to look at?”

“You have read up, haven’t you? Not even those two asteroids are dense enough to host more than a speck of neutronium. Asteroid mass and volume are separate measurements; you need both to figure mass‑per‑volume density. Each component is a challenging exercise in accurate observation. The first guesstimate for Polyhymnia was that it was more than 10 times denser than iron. That’s why you’ve heard of it. With better data now we think both Polyhymnia and Psyche are at about the density of iron. Higher than most but too low for neutronium by a factor of quintillions.”

“Where else could we go for neutronium?”

“This’ll take some background. The more massive the star, the bigger its diameter and the longer it lives, right?”

Walt gives me a suspicious eye. “You’re fudging, Mr Moire.”

“Nothing gets past you, Walt. More massive stars burn hotter. The heat bulges them out, as you’d expect. The fudge is they exhaust their fuel faster so they die sooner. When the fuel gives out and they go nova, big guys collapse harder than smaller ones can. Their collapse squeezes their residual core tighter. Collapsing a really big star crams its remains into a volume smaller than its Schwartzschild radius. That makes a black hole. Smaller stars can’t go that far. The crush might stop when the residue’s electrons are squeezed into its atomic nuclei. Protons there could capture them and become neutrons. If so, you’ve got neutronium and a neutron star.”

“A nova’s pretty violent, shoots material out randomly?”

“One of the sloppiest, most violent events in the Universe.”

“Could a nova have flung a neutronium fragment through our Solar System like something flung ‘Oumuamua? Could we detect that?”

“Not likely but probably.”

Rugged asteroid surrounded by glowing debris in a colorful nebula

~ Rich Olcott

Atmospheric Jiu-jitsu

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

A gorgeous early Spring day for a walk by the lake — blue sky, air just the right side of crisp, trees showing their young green leaves, geese goosily paddling around. As I pass the park bench I hear a familiar voice. “Hello, Mr Moire.”

“Morning, Walt. It’s been a while. What do your people want to know about now?”

“We’ve been reading your series of posts about the Coriolis Effect. You have masses of air pushing each other around, you have pendulums twisting about, and you have objects flying weird orbits around latitudes instead of the planet’s center. Which is the real Effect?”

“All three.”

“They’re so different. How can all three be right?”

“Knowing something of your interests, I can think of another Coriolis application will help clarify the connection. How do you steer an old‑fashioned artillery shell?”

“You don’t, you aim it.” <His eyes are looking inward.> “Those old howitzers, you traverse to the target’s coordinates, set the elevation for the distance and your munitions and whatever your barrel’s still good for, load ‘er up, let ‘er rip and wait for the forward observer to tell you how to adjust.”

“No correction for the Earth turning west‑to‑east beneath the shell’s trajectory?”

“No need. Inside a max 10‑mile range, the artillery, target and shell all share the same initial eastward vector. Windage and temperature inversions are more of a problem than Coriolis forces. That’s where judgement, feedback and reload speed come in.”

“Now stand that up against a cruise missile.”

“Very different situation. With cannons, all the propulsion happens at the start. That’s why they call it ballistic. Cruise missiles have an extended boost phase, maybe more than one, so they can do in‑flight steering. On the other hand, range is hundreds of miles or more so you do need to figure in relative easting.”

“And the easting correction takes power, right?”

“Of course.”

“From the missile’s point of view, that power goes to counteract the Coriolis force pushing it off‑course. You don’t see it from the ground but the missile does. Clearer now?”

“Give me a minute.” <sketches on his notepad> “Okay, counteracting attempt to deflect course — got it. Hmm, a pendulum’s even simpler, because it’s not trying to keep in sync with the Earth’s rotation. No forces in play crosswise to the swing plane so it can maintain orientation relative to the Universe. To museum visitors it looks like something’s twisting, but it’s us doing the moving. The air masses, though … forces are in play with that one.”

“It’s always important to keep track of who’s doing what to whom. That system has four distinct frames of reference: the Earth, a moving air mass, the air mass it collides with, and the Universe.”

“The Universe?”

“Sets the stage for Newton’s First Law, about conservation of linear momentum. Say there’s an air mass hovering over Dallas, latitude 30° north. Relative to the Earth it’s stationary, but relative to the Sun and the rest of the Universe it has an eastward vector clocking 1450 km/hour. Now suppose that mass moves north relative to the Earth.”

“But there’s already an airmass taking up space there, say in Manitoba. There’ll be a collision, northbound momentum against Manitoban inertia.”

“Here’s where Coriolis gets into the game. Manitoba may have zero motion relative to Earth, but Manitoba and its air mass are also moving eastward relative to the Universe. Manitoba’s speed is slower than Dallas’ but it’s not zero. Manitoba’s momentum deflects the Dallas mass into an even more easterly vector.”

“You’re saying that Coriolis plays jiu‑jitsu with the atmosphere.”

“I wouldn’t have come up with that interpretation, but it’s reasonable.”

“What about the weird orbits?”

“Not really orbits, more like equilibrium bands. The concept comes from the theoretical notion that every latitude along a meridian has a natural equilibrium speed where air pressure balances other forces. The bands would be parallel circles around the globe except for geography and transient disturbances. Dallas’ 1450‑km/h number was an example. If you exceed your local natural speed, centrifugal force moves you towards the Equator; if you’re a slowpoke, you’re shoved towards the nearest pole. Real weather’s more complicated.”

“Everything’s always more complicated.”

~ Rich Olcott

Sussing Out The Unseeable

On By rolcottIn Astronomy: Techniques, Cosmology, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“Hello, Mr Moire.”

“Afternoon, Walt. Pizza time again?”

“No, too public. Poor craft to be seen too often in the same place. There’s a park bench by the lake.”

“I know the spot.”

“Fifteen minutes.”

“Twenty.”

“Afternoon, Walt. What are your people curious about this time?”

“Word is that astronomers uncovered a huge amount of matter they’d been searching for. We’re interested in concealment techniques, so we want to know how it was hidden and how was it found.”

“Forty percent of all baryonic matter—”

“Baryonic?”

“Made out of atoms. Baryons are multi-quark particles like protons and—”

“Leave the weeds and get back to the topic. Where was that 40% hiding?”

“In plain sight, all over the sky, in strands forming a network that connects galaxies and galaxy clusters. They’re calling it the Cosmic Web.”

“Something that big … how was hidden?”

“Some techniques I’m sure you’ll recognize. First, the material in the strands is diffuse — just an atom or two per cubic meter. An Earth laboratory would be proud to pump down a vacuum ten million times more dense.”

<taking notes> “Spread your forces so there’s no prime target for counter‑attack, mm‑hm. But if the material’s that thin, surely it doesn’t mass much.”

“Remember how big space is. These filaments span the widths of multiple galaxies. Do the math. A thread could be on the order of 100 million lightyears long by 1000 lightyears in diameter. A lightyear is 1016 meters. The thread has a volume of about 1062 cubic meters. At 10-26 kilogram per cubic meter that’s 1036 kilograms which is comparable to the mass of a small galaxy. That’s just one thread. Add them up and you get roughly half the baryons in the Universe, all hiding in the Web.”

“Concealment by dispersal, got it. What’s another technique?”

“Camouflage. No, not tiny uniforms in a woodland pattern. These atoms fade into the background because oncoming light waves pass right by them unless the wave has exactly the right wavelength for an absorption.”

“So how did astronomers detect these scattered and camouflaged atoms?”

“A couple of different ways. X‑rays, for one.”

“But these atoms are camouflaged against passing light. X‑rays are light waves.”

“X‑rays the atoms emit. Everybody thinks that space is cold, but those lonely atoms bounce around with a kinetic energy equivalent to million‑degree temperatures. When two of them collide some of that kinetic energy escapes as high‑frequency light, X‑ray range. Not a whole lot, because the atoms are sparse, but enough that European and Japanese space telescopes were able to tweeze it out of the background.”

“Use sensitive mics to pick up whispered convo in the opposing line.”

<pause> “Right, more or less. What do you know about refraction?”

“Mmm… Newton and his prism, splitting white light into different colors. I’ve no idea how that works.”

“The short answer is that the speed of light depends on its wavelength and the medium it’s traversing. In a perfect vacuum, light always goes at top speed just like Einstein said, but charged particles in its path slow it down.”

“Even those atoms in space that you said can’t absorb light?”

“Yup. It’s called virtual coupling; quantum’s involved. One inaccurate way to describe the interaction is that atoms occasionally absorb wrong‑wavelength photons but spit them right back out again after a brief delay. Short wavelengths see more of that effect than long wavelengths do. With me?”

<pause> “Go on.”

“Does the phrase ‘Fast Radio Burst’ sound familiar?”

“Of course, but probably not the way you mean.”

“Ah. Right. For this context, Fast Radio Bursts are isolated pulses of radio‑frequency light from incredibly bright extra-galactic sources we don’t understand. They’re all over the sky. A pulse lasts only a millisecond or so. What’s important here is that refraction skews each pulse’s wavelength profile as it travels through the intergalactic medium. Researchers analyze the distortions to detect and characterize Web filaments in the direction each pulse came from.”

“Intercept the oppo’s communications to the front.”

“That’s about the size of it.”

“Bye.”

“Don’t mention it.”

The Cosmic Web
Visualization: Frank Summers (STScI); Simulation: Martin White and Lars Hernquist, Harvard University

~ 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.

A Loose-end Lagniappe

On By rolcottIn Astronomy: Planetary Science, Mathematics: Spherical Harmonics, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“We have some loose ends to tie up. Too early for pizza. Coffee at Cal’s?”

“Hello, ‘Walt‘. Fifteen minutes?”

“Confirmed.”

He’s at a back table, facing the door, of course. He points to the steaming mug and strawberry scone beside it on the table. I nod to acknowledge. ”So, Walt, what are these loose ends?”

“My people say that Juno‘s not on a 53‑day orbit any more. NASA’s jiggled it down to 33 days. What’s that do to the numbers you gave me?”

<sliding a folded paper scrap across the table> “I had a hunch you’d want more so I worked up estimates. Juno started with a 53‑day orbit but a Ganymede flyby dropped it to 43 days. A Europa flyby took Juno to a 38‑day orbit. Now it’s swerved by Io and we’re at 33 days. I threw in the 23‑day line for grins, no extra charge.”

“Half the orbit size but no significant change in the close‑in specs. That’s surprising.”

“Not really. It’s like a dog’s butt wagging its tail. At close approach, we call it perijove, Juno is only 76 500 kilometers out from Jupiter’s center. Its orbit thereabouts is pretty much nailed down by the big guy’s central field. But there’s no second attractor to constrain the orbit’s other extreme millions of kilometers out. Do an Oberth burn near perijove or arrange for a gravity tweak from a convenient moon, you get a big difference at the far end.”

“That wraps that.” <reaches for his cane, then settles back to do a Columbo> “Just one more thing, Moire. I came in with a question about the Sun’s effect on Juno. You took care of that pretty quick but spent a load of my time and consultancy budget on these spherical harmonics. How come?”

“As I recall, you and your people kept coming back for more detail. Also, the 225 000‑kilometer radius I got from R2‘s structure was essential in calculating these close‑in numbers. You’re getting your money’s worth. I’ll even throw in a lagniappe.”

“A free gift? I never trust them.”

“Such a mean world you live in, Walt.” <displaying an image on Old Reliable> “Here it is, take it or leave it.”

Top: F000 plus a time-varying contribution from F660
Bottom: C0 plus a time-varying contribution from C4

“What is it?”

“It’s a bridge between the physics of light and sound, and the physics of atoms and stars. When I say ‘coordinates,’ what words spring to your mind?”

“Traverse and elevation.”

“Interesting choice. Any other systems?”

“Mm, latitude, longitude and altitude. And x‑y‑z if you’re in a classroom.”

“Way beyond the classroom. You use spreadsheets, right?”

“Doesn’t everyone?”

“Rows‑columns‑sheets is x‑y‑z. On digital screens, pixels‑lines‑luminosity is x‑y‑z. Descarte’s rectilinear invention is so deeply embedded in our thinking we don’t even notice it. Perpendicular straight‑line coordinates fit things that are flat or nearly so, not so good for spheres and central‑force problems. Movement there is mostly about rotation, which is why your first two picks were angular instead of linear.”

“Okay, but our choice of coordinates is our choice. What have x‑y‑z or your Fnnm to do with natural things?”

“Overtones and resonance. Look at that black line in the movie. It could be a guitar string or a violin string, doesn’t matter. One end’s fixed to the instrument’s bridge, the other end’s under somebody’s finger. All other points on the string are free to move, subject to tension along the string. Then someone adds energy to the string by plucking or bowing it.”

“At one of those peaks or valleys, right?”

“Nope, anywhere, which goes to my point. The energy potentially could contort the string to any shape. Doesn’t happen. The only stable shapes are combinations of sine waves with an integer number of nodes, like C4‘s quartet. Adding even more energy gives you overtones, waves that add in‑between nodes to lower‑energy waves. C0‘s no‑nodes black line could run along x, y or z in any flat system.”

“So you’re going to tell me that your C‘s, J‘s and R‘s support wave structures for spheres.”

“Indeed. All four giant planets have stripes along their J arcs. Solar seismologists have uncovered C, R and maybe J wave structures inside the Sun.”

“Bye.”

“Don’t mention it.”

~ Rich Olcott

Completing The Triad

On By rolcottIn Astronomy: Planetary Science, Mathematics: Spherical Harmonics, UncategorizedLeave a comment

Walt’s mustache bristles as he gives me the eye. ”You claim three harmonics control how the Sun’s gravity could affect spacecraft orbits around a target planet like Jupiter. You said we don’t have to care about Jupiter’s gravitational zones and isolating the sectors probably isn’t doable. What’s the third?”

Time to twist the screws. ”Three harmonic systems, Walt, all working together and you’ve got their names wrong. They control nothing, they’re a framework for analysis. And Jupiter’s special. Solar gravity doesn’t affect its zonal harmonic arcs but that’s only because Jupiter’s polar axis is nearly perpendicular to its orbital plane. Zonal‑effect N‑S twisting at Jupiter is pennies on a C‑note. Any mission we send to Mars, Saturn or Uranus we’ll care a lot about their zonal harmonics because their axes have more tilt. An 82° tilt for Uranus, can’t get much more tilted than that. Sectorial harmonics may still help us navigate there because Uranus probably has a lot less magnetism than Jupiter.”

That rocks him but he comes back strong. ”The third kind of harmonic?!! C’mon, give!”

“Radial, the center‑out dimension. The gravitational force between bodies depends on center‑to‑center distances so yeah, your people would be interested.”

“I presume radial harmonics have numbers like Jn and Cm do?”

“They do. Sorry, this’ll get technical again but I’ll go as light as I can. Each radial harmonic is the product of two factors. You know about factors, right?”

“Sure, force multipliers.”

“You would know that kind. More generally, factors are things that get multiplied together. I’ll call the general radial harmonic Rn. It’s the product of two factors. The first is a sum of terms that begin with rn, where r is the distance. For instance, R3‘s first factor would look like a*r³+b*r²+c*r+d, where the a,b,c,d are just some numbers. Different radial harmonics have different exponents in their lead terms. You still with me?”

“Polynomials from high school algebra. Tell me something new.”

“The second factor decreases exponentially with n*r. No matter how large rn gets, when you multiply an rn polynomial by something that decreases exponentially, the (polynomial)×(exponential) product eventually gets really small.”

“Give me a second. … So what you’re saying is, at a big enough distance these radial harmonics just die away.”

“That’s where I was going.”

“How far is ‘enough’?”

“Depends on n. Higher values of n shut down faster.”

“So these Cms and Jns and Rns just add together?” <pauses, squints at me suspiciously> “Is there some reason you used n for both Jn and Rn?”

“No but yes, and yes. You combine a C, a J and an R using multiplication to get a full harmonic F, except there are rules. The J and R must belong to the same n. The m can’t be larger than n. From far away we’d model Jupiter’s gravity as F000=R0×J0×C0, which is an infinite sphere — R0 never dies away and J0×C0 says ‘no angular dependence.’ The Sun’s gravity acts along R0 and that’s what keeps Jupiter in orbit. If the problem demands combining full harmonics, you use addition.” <rousing a display on Old Reliable> “Here’s how a particular pair of harmonics combine to increase or decrease spherical gravity in specific directions.”

“But Juno doesn’t see those gravity lumps until it gets close‑in. How close?”

“R2‘s down to less than a part per thousand at three planetary radii, call it 225 000 kilometers away from the planet’s center.”

“How much time is it closer than that distance?”

“Complicated question. A precise answer requires some calculus — is your smart phone set up for elliptic integrals?”

“Of course not. A good estimate will do.”

“Okay, here’s the plan. What we’d like is total time spent while Juno travels along the ellipsoidal arc between points A and D where the orbit crosses the 225 000‑km circle. Unfortunately, Juno speeds up approaching point P, slows down going away — calculating the A‑D time is tricky. I’ll assume Juno travels straight lines AB and CD at the A-speed. I’ll also approximate the orbit’s close pass as a semicircle at P‑speed.” <tapping> “I get a 3.6-hour duration, less than 0.3% of the full 53-day orbit. Will that satisfy your people?”

“You’ll know if it doesn’t.”

~~ Rich Olcott