Squaring The Circle

On September 29, 2025November 28, 2025 By rolcottIn Cosmology, UncategorizedLeave a comment

Vinnie gives me the eye. “That crazy theory of yours is SO bogus, Sy, and there’s a coupla things you said we ain’t heard before.”

“What’s wrong with my Mach’s Principle of Time?”

“If the rest of the Universe is squirting one thing forward along Time, then everything’s squirting everything forward. No push‑back in the other direction. You might as well say that everything’s running away from the Big Bang.”

“That’s probably a better explanation. What are the couple of things?”

“One of them was, ‘geodesic,‘ as in ‘motion along a geodesic.‘ What’s a geodesic?”

“The shortest path between two points.”

“That’s a straight line, Mr Moire. First day in Geometry class.”

“True in Euclid’s era, Jeremy, but things have moved on since then. These days the phrase ‘shortest path’ defines ‘straight line’ rather than the other way around. Furthermore, the choice depends on how you define ‘shortest’. In Minkowski’s spacetime, for instance, do you mean ‘least distance’ or ‘least interval’?”

“How are those different?”

“The word ‘distance’ is a space‑only measurement. Minkowski plotted space in x,y,z terms just like Newton would have if he could’ve brought himself to use René Descartes’ cartesian coordinates. You know Euclid’s a²+b²=c² so you should have no problem calculating 3D distance as d=√(x²+y²+z²).”

“That makes sense. So what’s ‘interval’ about then?”

“Time has entered the picture. In Minkowski’s framework you handle two ‘events’ that may be at different locations and different times by using what he called the ‘interval,’ s. It measures the path between events as
s=√[(x²+y²+z²)–(ct)²]. Usually we avoid the square root sign and work with s².”

“That minus sign looks weird. Where’d it come from?”

“When Minkowski was designing his spacetime, he needed a time scale that could be combined with the x,y,z lengths but was perpendicular to each of them. Multiplying time by lightspeed c gave a length, but it wasn’t perpendicular. He could get that if he multiplied by i=√(–1) to get cti as a partner for x,y,z. Fortunately, that forced the minus sign into the sum‑of‑squares
(x²+y²+z²)–(ct)² formula.”

Vinnie’s getting impatient. “What is an actual geodesic, who cares about them, and what do these equations have to do with anything?”

“A geodesic is a path in spacetime. Light always travels along a geodesic. The modern version of Newton’s First Law says that any object not subject to an outside force travels along a geodesic. By definition the geodesic is the shortest path, but you can’t select which path from A to B is the shortest unless you can measure or calculate them. There’s math to tell us how to do that. Time’s a given in a Newtonian Universe, not a coordinate, so geodesics are distance‑only. We calculate d along paths that Euclid would recognize as straight lines. That’s why the First Law is usually stated in terms of straight lines.”

“So the lines can go all curvy?”

“Depends, Vinnie. When you’re piloting an over‑water flight, you fly a steady bearing, right?”

“Whenever ATC and the weather lets me. It’s the shortest route.”

“So according to your instruments you’re flying a straight line. But if someone were tracking you from the ISS they’d say you’re flying along a Great Circle, the intersection of Earth’s surface with some planar surface. You prefer Great Circles because they’re shortest‑distance routes. That makes them geodesics for travel on a planetary surface. Each Circle’s a curve when viewed from off the surface.”

“Back to that minus sign, Mr Moire. Why was it fortunate?”

“It’s at the heart of Relativity Theory. The expression links space and time in opposite senses. It’s why space compression always comes along with time dilation.”

“Oh, like at an Event Horizon. Wait, can’t that s²=(x²+y²+z²)–(ct)² arithmetic come out zero or even negative? What would those even mean?”

“The theory covers all three possibilities. If the sum is zero, then the distance between the two events exactly matches the time it would take light to travel between them. If the sum is positive the way I’ve written it then we say the geodesic is ‘spacelike’ because the distance exceeds light’s travel time. If it’s negative we’ve got a ‘timelike’ geodesic; A could signal B with time to spare.”

~ Rich Olcott

The Time Is Out of Joint

On September 22, 2025November 28, 2025 By rolcottIn Cosmology, Crazy Theories, UncategorizedLeave a comment

Vinnie galumphs over to our table. “Hi, guys. Hey, Sy, I just read your Confluence post. I thought that we gave up on things happening simultaneous because of Einstein and relativity but I guess that wasn’t the reason.”

“Oh, things do happen simultaneously, no‑one claims they don’t, it’s just that it’s impossible for two widely‑separated observers to have evidence that two widely‑separated events happened simultaneously. That’s a very different proposition.”

“Ah, that makes me feel better. The ‘nothing is simultaneous‘ idea was making me itchy ’cause I know for sure that a good juggler lets go with one hand just as they’re catching with the other. How’s Einstein involved then?”

“Lightspeed’s a known constant. Knowing distance and lightspeed lets you calculate between‑event time, right? The key to simultaneity was understanding why lightspeed is a constant. We’d known lightspeed wasn’t infinite within the Solar System since Rømer’s time, but people doubted his number applied everywhere. Maxwell’s theory of electromagnetism derived lightspeed from the properties of space itself so it’s universal. Only in Newton’s Universe was it possible for two distant observers to agree that two also‑distant events were simultaneous.”

“Why was Newton’s Universe special?

“Space held still and didn’t bend. Astronomers A and B had a stable baseline between them. After measuring the baseline with light they could measure the angles each observed between the events. Some trigonometry let them send each other congratulatory messages on seeing a simultaneous pair of incidents. After Einstein’s work, they knew better.”

“It’s frames again, ain’t it?”

“Of course, Vinnie. A‘s frame is almost certainly moving relative to B‘s frame. Motion puts the Lorentz relativity factor into the game, making each astronomer’s clock run faster than the other’s. Worse, each astronomer sees that the other’s yardsticks are too short.”

Jeremy gives me a confused look.

“Space compression goes along with time dilation, Jeremy. Professor Hanneken will explain it all when your class gets to that unit. Bottom line, things can happen simultaneously in Einstein’s Universe, but no‑one can agree on which things.”

“Wait, if every frame has its own time‑rate, how can two spaceships rendezvous for an operation?”

“Good question, Jeremy. Einstein had an answer but complications hide under the covers. He suggested that A start a timer when sending a light pulse to a mirror at B. A waits for the reflection. B starts a timer when they see A‘s pulse. A measures the pulse’s round‑trip time. Each creates a clock that advances one tick for half of the round-trip time. B sets their clock back by one tick. That done, they agree to meet some number of ticks later.”

“Hmm… That should work, but you said there are complications.”

“There are always complications. For instance, suppose B is slingshotting around a black hole so that pulse and reflection travel different pathlengths. Or suppose one frame is rotating edge‑on to the other. In practice the ships would re‑sync repeatedly while approaching the rendezvous point.”

Vinnie erupts. “HAW! Successive approximation again!”

“Indeed. If we could extend the method to more than two participants we’d have a true Universal Coordinated Time.”

“Don’t we have that, Mr Moire? The Big Bang happened 14 billion years ago. Couldn’t we measure time from that?”

“Sort of. Last I looked the number was 13.787 plus‑or‑minus 20 million years. Too much slop for an instantaneous fleet‑level rendezvous like the final battle scene in StarTrek:Picard. But you’ve brought up an interesting question for a Crazy Theories seminar. One of Cosmology’s deepest unsolved questions is, ‘How does inertia work?’ Do you remember Newton’s First Law?”

<closes eyes> “In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a net force.“

“Right. In other words, every object resists change to its current steady motion along a geodesic. Why is that? There’s no coherent, well‑founded, well‑tested theory. Einstein liked Mach’s Principle, which says inertia exists because every object is attracted through space to all the mass in the Universe. Suppose there’s a Mach’s Principle for Time, saying that objects squirt up the Time axis because they’re repelled by all the mass in the Universe.”

Vinnie hoots, “Bo-o-o-ohh-GUS!”

~ Rich Olcott

Hillerman, Pratchett And Narrativium

On September 15, 2025November 30, 2025 By rolcottIn Astronomy, General: Fun Stuff, UncategorizedLeave a comment

No-one else in the place so Jeremy’s been eavesdropping on my conversation with Cal. “Lieutenant Leaphorn says there are no coincidences.”

“Oh, you’ve read Tony Hillerman’s mystery stories then?”

“Of course, Mr Moire. It’s fun getting a sympathetic outsider’s view of what my family and Elders have taught me. He writes Leaphorn as a very wise man.”

“With some interesting quirks for a professional crime solver. He doesn’t trust clues, yet he does trust apparent coincidences enough to follow up on them.”

“It does the job for him, though.”

“Mm‑hm, but that’s in stories. Have you read any of Terry Pratchett’s Discworld books?”

“What are they about?”

“Pretty much everything, but through a lens of laughter and anger. Rather like Jonathan Swift. Pratchett was one of England’s most popular authors, wrote more than 40 novels in his too‑brief life. He identified narrativium as the most powerful force in the human universe. Just as the nuclear strong force holds the atomic nucleus together using gluons and mesons, narrativium holds stories together using coincidences and tropes.”

“Doesn’t sound powerful.”

“Good stories, ones that we’d say have legs, absolutely must have internal logic that gets us from one element to the next. Without that narrative flow they just fall apart; no‑one cares enough to remember them. As a writer myself, I’ve often wrestled with a story structure that refused to click together — sparse narrativium — or went in the wrong direction — wayward narrativium.”

“You said ‘the human universe’ like that’s different from the Universe around us.”

“The story universe is a multiverse made of words, pictures and numbers, crafted by humans to explain why one event follows another. The events could be in the objective world made of atoms or within the story world itself. Legal systems, history, science, they’re all pure narrativium. So is money, mostly. We don’t know of anything else in the Universe that builds stories like we do.”

“How about apes?”

“An open question, especially for orangutans. One of Pratchett’s important characters is The Librarian, a university staff member who had accidentally been changed from human to orangutan. He refuses to be restored because he prefers his new form. Which gives you a taste of Pratchett’s humor and his high regard for orangutans. But let’s get back to Leaphorn and coincidences.”

“Regaining control over your narrativium, huh?”

“Guilty as charged. Leaphorn’s standpoint is that there are no coincidences because the world runs on patterns, that events necessarily connect one to the next. When he finds the pattern, he solves the mystery.”

“Very Diné. Our Way is to look for and restore harmony and balance.”

“Mm‑hm. But remember, Leaphorn is only a character in Hillerman’s narrativium‑driven stories. The atom‑world may not fit that model. A coincidence for you may not be a coincidence for someone else, depending. Those two concurrent June novas, for example. For most of the Universe they’re not concurrent.”

“I hope this doesn’t involve relativistic clocks. Professor Hanneken hasn’t gotten us to Einstein’s theories yet.”

“No relativity; this is straight geometry. Rømer could have handled it 350 years ago.” <brief tapping on Old Reliable’s screen> “Here’s a quick sketch and the numbers are random. The two novas are connected by the blue arc as we’d see them in the sky if we were in Earth’s southern hemisphere. We live in the yellow solar system, 400 lightyears from each of them so we see both events simultaneously, 400 years after they happened. We call that a coincidence and Cal’s skywatcher buddies go nuts. Suppose there are astronomers on the white and black systems.”

<grins> “Those four colors aren’t random, Mr Moire.”

<grins back> “Caught me, Jeremy. Anyway, the white system’s astronomers see Vela’s nova 200 years after they see the one in Lupus. The astronomers in the black system record just the reverse sequence. Neither community even thinks of the two as a pair. No coincidence for them, no role for narrativium.”

~ Rich Olcott

This is the 531st post in an unbroken decade‑long weekly series that I originally thought might keep going for 6 months. <whew!>

Confluence

On September 8, 2025November 30, 2025 By rolcottIn Astronomy, Astronomy: Multi-messenger, General: Fun Stuff, UncategorizedLeave a comment

“My usual cup of — Whoa! Jeremy, surprised to see you behind the counter here. Where’s Cal?”

“Hi, Mr Moire. Cal just got three new astronomy magazines in the same delivery so he’s over there bingeing. He said if I can handle the pizza place gelato stand he can trust me with his coffee and scones. I’m just happy to get another job ’cause things are extra tough back on the rez these days. Here’s your coffee, which flavor scone can I get for you?”

“Thanks, Jeremy. Smooth upsell. I’ll take a strawberry one. … Morning, Cal. Having fun?”

“Morning, Sy. Yeah, lotsa pretty pictures to look at. Funny coincidence, all three magazines have lists of coincidences. This one says February 23, 1987 we got a neutrino spike from supernova SN 1987A right after we saw its light. The coincidence told us that neutrinos fly almost fast as light so the neutrino’s mass gotta be pretty small. 1987’s also the year the Star Tours Disney park attractions opened for the Star Wars fans. The very same year Gene Roddenberry and the Paramount studio released the first episodes of Star Trek: The Next Generation. How about that?”

“Pretty good year.”

“Mm‑hm. Didja know here in 2025 we’ve got that Mercury‑Venus‑Jupiter-Saturn‑Uranus‑Neptune straight‑line arrangement up in the sky and sometimes the Moon lines up with it?”

“I’ve read about it.”

“Not only that, but right at the September equinox, Neptune’s gonna be in opposition. That means our rotation axis will be broadside to the Sun just as Neptune will be exactly behind us. It’ll be as close to us as it can get and it’s face‑on to the Sun so it’s gonna be at its brightest. Cool, huh?”

“Good time for Hubble Space Telescope to take another look at it.”

“Those oughta be awesome images. Here’s another coincidence — Virgo’s the September sign, mostly, and its brightest star is Spica. All the zodiac constellations are in the ecliptic plane where all the planet orbits are. Planets can get in the way between us and Spica. The last planet to do that was Venus in 1783. The next planet to do that will be Venus again, in 2197.”

“That’ll be a long wait. You’ve read off things we see from Earth. How about interesting coincidences out in the Universe?”

“Covered in this other magazine’s list. Hah, they mention 1987, too, no surprise. Ummm, in 2017 the Fermi satellite’s GRB instrument registered a gamma‑ray burst at the same time that LIGO caught a gravitational wave from the same direction. With both light and gravity in the picture they say it was two neutron stars colliding.”

“Another exercise in multi-messenger astronomy. Very cool.”

“Ummm … Galaxy NGC 3690 shot off two supernovas just a few months apart last year. Wait, that name’s familiar … Got it, it’s half of Arp 299. 299’s a pair of colliding galaxies so there’s a lot of gas and dust and stuff floating around to set off stars that are in the brink. If I remember right, we’ve seen about eight supers there since 2018.”

“Hmm, many events with a common cause. Makes sense.”

“Oh, it’s a nice idea, alright, but explain V462 Lupi and V572 Velorum. Just a couple months ago, two novas less than 2 weeks apart in two different constellations 20 degrees apart in the sky. Bright enough you could see ’em both with good eyes if you were below the Equator and knew where to look and looked in the first week of June. My skywatcher internet buddies down there went nuts.”

“How far are those events from us?”

“The magazine doesn’t say. Probably the astronomers are still working on it. Could be ten thousand lightyears, but I’d bet they’re a lot closer than that.”

“On average, visible stars are about 900 lightyears away. Twenty degrees would put them about 300 lightyears apart. They’re separated by a slew of stars that haven’t blown up. One or both could be farther away than that, naturally. Whatever, it’s hard to figure a coordinating cause for such a distant co‑occurrence. Sometimes a coincidence is just a coincidence.”

~ Rich Olcott

Sussing Out The Unseeable

On September 1, 2025December 1, 2025 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.”

~ Rich Olcott

Hard Science Ain't Hard

Month: September 2025

Squaring The Circle

The Time Is Out of Joint

Hillerman, Pratchett And Narrativium

Confluence

Sussing Out The Unseeable