Properties of Space

On By rolcottIn Cosmology, Physics: Electromagnetism, Physics: Waves, UncategorizedLeave a comment

Vinnie gives me the side‑eye. “Wait, Sy. Back there you said Maxwell got the speed of light from the properties of space. What does any of that even mean?”

“Do you remember Newton’s equation for the force of gravity between two objects?”

“Of course not. Lessee… the force’d be bigger when either one gets bigger, and it’d get smaller when the distance between ’em gets bigger and there’s some constant number to make the units right, right?”

“Close enough, it’s the distance squared. The equation’s F=Gm1m2/r². The G is the constant you mentioned. It does more than turn mass‑units times mass‑units divided by length‑units‑squared into force‑units. It says how many force‑units. For one pair of objects at a certain distance, turn the G‑dial up and you get more force. Make sense?”

“Yeah, that looks right.”

“The value of G sets the force‑distance scale for how two objects attract each other everywhere in the Universe. That value is a property of space. So is the fact that the value is the same in all directions.”

“Huh! Never thought of it like a scale factor. Space has other properties like that?”

“Certainly. Coulomb’s Law for the electrostatic force between two charged objects has the same basic structure, FE=–(q1q2/r²)/CE. In any units you like you replace the q‘s with object charge amounts and r with the distance between them. For each set of change‑ and distance‑units there’s a well‑researched value of CE to convert your charge and distance numbers into force‑units. Under the covers, though, CE is a scale factor that controls the range of the electrostatic force. It’s the same everywhere in the Universe and it’s completely independent of Newton’s gravity scale factor.”

“Hey, what about ‘like charges repel, opposites attract’?”

“That’s what the minus sign’s in there for. If the q‘s have the same charge, the force is negative, that’s repulsion; opposite charges make for positive, attractive force.”

“If there’s a CE for electric there’s gotta be a CM for magnetic.”

“Sort of. The electrostatic force doesn’t care about direction. Magnetism does care so the equation’s more complicated. You’re right, though, there is a similar universal scale factor we might as well call CM.”

<chuckle> “Electric, magnetic, I don’t suppose we could mix those two somehow for an electromagnetic scale factor?”

<grin> “Did you read ahead in the book? Yes we can, and Maxwell’s equations showed us how. If you multiply the two C‘s together, you get one over the square of the speed of light. Re‑arranging a little, c=√(1/CECM), so c, the electromagnetic scale factor for velocity, is based on those space properties. Einstein showed that no material object can have a velocity greater than c.”

“I’ll take your word for the arithmetic, but how does that combination make for a speed limit?”

“There’s an easy answer you’re not going to like — it’s a speed because the units come out meters per second.”

“That’s a cheat. I don’t like it at all and it doesn’t account for the limit part. Explain it with Physics, no fancy equations.”

“Tough assignment. Okay, typical waves have a displacement force, like wind or something pushing up on an ocean wave, that works against a restoring force, such as gravity pulling down. Electromagnetic waves are different. The electric component supplies the up force, but the magnetic component twists sideways instead of restoring down. The wave travels as a helix. The CE and CM properties determine how tightly it spirals through space. That’s lightspeed.”

“And the limit part?”

“Einstein maintained that anything that happens must follow the same rules for all observers no matter how each is moving. The only way that can be true is if space is subject to the Lorentz contraction √[1-(v/vmax)²] for some universal maximum speed vmax. Maxwell’s electromagnetism equations showed that vmax is c. Okay?”

“I suppose.”

~ Rich Olcott

  • * Vinnie hates equations even with regular letters, Greek letters make it worse. Hence my using CE and CM instead of the conventional ε0 and μ0 notation. Sue me.

Squaring The Circle

On 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 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 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?”

From Terry Pratchett’s book
Carpe Jugulum

“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.”

Adapted from images by
IAU and Sky & Telescope magazine
(Roger Sinnott & Rick Fienberg)
CC BY 3.0

“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 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.”

Adapted from images by
IAU and Sky & Telescope magazine
(Roger Sinnott & Rick Fienberg)
CC BY 3.0

~ 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

Black, White And Wormy

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

“Whaddaya mean, Sy, if white holes exist? You just told me how they’re in the equations just like black holes.”

“Math gives us only models of reality, Vinnie. Remarkably good models, some of them, but they’re only abstractions. Necessarily they leave out things that might skew math results away from physical results or the other way around. Einstein believed his math properly reflected how the Universe works, but even so, he doubted that black holes could exist. He didn’t think it’d be possible to collect that much mass into such a small space. Two decades after he said that, Oppenheimer figured out how that could happen.”

“Oppenheimer like the A‑bomb movie guy?”

“Same Oppenheimer. He was a major physicist even before they put him in charge of the Manhattan Project. He did a paper in 1939 showing how a star‑collapse could create the most common type of black hole we know of. Twenty‑five years after that the astronomers found proof that black holes exist.”

“Well, if Einstein was wrong about black holes, why wasn’t he wrong about white holes?”

“We need another Oppenheimer to solve that. So far, no‑one has come up with a mechanism that would create a stand‑alone white hole. That level of stress on spacetime requires an enormous amount of mass‑energy in a tiny volume. Whatever does that must somehow do it with a time‑twist opposite to how a black hole is formed. Worse yet, by definition the white hole’s Event Horizon leaks matter and energy. The thing ought to evaporate almost as soon as it’s formed.”

“I heard weaseling. You said, ‘a stand‑alone white hole,’ like there’s maybe another kind. How about that?”

“Could be, maybe not, depending on who’s talking and whether or not they’re accounting for magnetic fields, neutrinos or quantum effects. The discussion generally involves wormholes.”

“Wormholes.”

“Mm-hm. Some cosmologists think that wormholes might bridge between highly stressed points in spacetime. Black hole or white, the stress is what matters. The idea’s been around nearly as long as our modern idea of black holes. No surprise, ‘wormhole’ was coined by John Archibald Wheeler, the same guy who came up with the phrases ‘black hole’ and ‘quantum foam’.”

“Quantum—. Nope, not gonna bite. Get back to white holes.”

“I’m getting there. Anyway, the relativity theory community embraced black holes, white holes and wormholes as primary tools for studying how spacetime works.”

“How’re they gonna do that? That squib Cal showed me said we’ve never seen a white hole.”

“Fair question. Last I heard, the string theory community confidently predicted 10500 different Universes with little hope of narrowing the field. In contrast, relativity theory is firmly constrained by well‑founded math, a century of confirmation from experimental tests and a growing amount of good black hole data. Perfectly good math says that wormholes and white holes could form but only under certain unlikely conditions. Those conditions constrain white holes like Oppenheimer’s conditions constrained forming a stellar‑size black hole.”

“So how do we make one?”

“We don’t. If the Universe can make the right conditions happen somewhere in spacetime, it could contain white holes and maybe a network of wormholes; otherwise, not. Maybe we don’t see them because they’ve all evaporated.”

“I remember reading one time that with quantum, anything not forbidden must happen.”

“Pretty much true, but we’re not talking quantum here. Macro‑scale, some things don’t happen even though they’re not forbidden.”

“Name one.”

“Anti‑matter. The laws of physics work equally well for atoms with positive or negative nuclear charge. We’ve yet to come up with an explanation for why all the nuclear matter we see in the Universe has the positive‑nucleus structure. The mystery’s got me considering a guess for Cathleen’s next Crazy Theories seminar.”

“Oh, yeah? Let’s have it.”

“Strictly confidential, okay?”

“Sure, sure.”

“Suppose the Big Bang’s chaos set up just the right conditions to make a pair of CPT‑twin black holes, expanding in opposite directions along spacetime’s time dimension. Suppose we’re inside one twin. Our time flows normally. If we could see into the other twin, we’d see inside‑out atoms and clocks running backwards. From our perspective the twin would be a white hole.”

“Stay outta that wormhole bridge.”

~ Rich Olcott

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