Category: Physics

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.

The Beaming Beacon

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

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

M87* image – Credit EHT Collaboration

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

“As always, Vinnie, your memory impresses.”

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

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

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

“My article says it’s near 100%.”

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

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

“Blueshifting.”

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

“More blueshifting.”

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

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

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

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

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

“And the answer is…?”

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

~ Rich Olcott

Not Even A Sneeze in A Hurricane

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

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

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

“Second part first. Do you sneeze?”

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

“Ever been in a hurricane?”

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

“Did you sneeze during the storm?”

“Who remembers that sort of thing?”

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

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

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

“Exawha?”

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

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

“Safe, yes, but not practical.”

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

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

“I dunno. How much we got?”

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

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

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

“Why do you say that?”

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

“I’m always good for bad news. Give.”

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

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

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

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

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

~ Rich Olcott

Two’s Company, Three Is Perturbing

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

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

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

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

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

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

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

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

“He didn’t, not exactly anyway.”

“Not smart enough?”

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

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

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

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

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

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

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

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

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

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

“What’ve they got that’s better?”

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

“Good ol’ Newton.”

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

“I’ll stick with pinch‑and‑taste.”

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

~ Rich Olcott

Snap The Whip

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

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

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

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

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

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

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

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

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

“First trick, mmm? There’s more?”

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

“Yuck.”

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

“What if I squeeze real hard?”

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

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

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

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

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

~ Rich Olcott

Why Those Curtains Ripple

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

I’m in the scone line at Cal’s Coffee when suddenly there’s a too‑familiar poke at my back, a bit right of the spine and just below the shoulder blade. I don’t look around. “Morning, Cathleen.”

“Morning, Sy. Your niece Teena certainly likes auroras, doesn’t she?”

“She likes everything. She’s the embodiment of ‘unquenchable enthusiasm.’ At that age she’s allowed.”

“It’s a gift at any age. Some of the kids in my classes, they just can’t see the wonders no matter how I try. I show them aurora photos and they say, ‘Oh yes, red and green in the sky‘ and go back to their phone screens. Of course there’s no way to get them outside late at night at a location with minimal light pollution.”

“I feel your pain.”

“Thanks. By the way, your aurora write-ups have been all about Earth’s end of the magnetic show. When you you going to do the rest of the story?”

“How do you mean?”

“Magnetism on the Sun, how a CME works, that sort of thing.”

“As a physicist I know a lot about magnetism, but you’re going to have to educate me on the astronomy.”

Plane‑polarized Lorentz (electromagnetic) wave
 Electric (E) component is red
 Magnetic (B) component is blue
(Image by Loo Kang Wee and Fu-Kwun Hwang from Wikimedia Commons)
Licensed under CC ASA3.0 Unported

“Deal. You go first.”

<displaying an animation on Old Reliable> “We’ll have to flip between microscopic and macroscopic a couple times. Here’s the ultimate micro — a single charged particle bouncing up and down somewhere far away has generated this Lorentz‑force wave traveling all alone in the Universe. The force has two components, electric and magnetic, that travel together. Neither component does a thing until the wave encounters another charged particle.”

“An electron, right?”

“Could be but doesn’t have to be. All the electric component cares about is how much charge the particle’s carrying. The magnetic component cares about that and also about its speed and direction. Say the Lorentz wave is traveling east. The magnetic component reaches out perpendicular, to the north and south. If the particle’s headed in exactly the same direction, there’s no interaction. Any other direction, though, the particle’s forced to swerve perpendicular to both the field and the original travel. Its path twists up- or downward.”

A charged particle traversing a Lorentz wave

“But if the particle swerves, won’t it keep swerving?”

“Absolutely. The particle follows a helical path until the wave gives out or a stronger field comes along.”

“Wait. If a Lorentz wave redirects charge motion and moving charges generate Lorentz waves, then a swerved particle ought to mess up the original wave.”

“True. It’s complicated. You can simplify the problem by stepping back far enough that you don’t see individual particles any more and the whole assembly looks like a simple fluid. We’ve known for centuries how to do Physics with water and such. Newton invented hydrodynamics while battling the ghost of Descartes to prove that the Solar System’s motion was governed by gravity, not vortices in an interplanetary fluid. People had tried using Newton‑style hydrodynamics math to understand plasma phenomena but it didn’t work.”

<grinning> “I don’t imagine it would — all that twistiness would have thrown things for a loop.”

“Haha. Well, in the early 1940s Swedish physicist Hannes Alfven started developing ideas and techniques, extending hydrodynamics to cover systems containing charged particles. Their micro‑level electromagnetic interactions have macro‑level effects.”

“Like what?”

“Those aurora curtains up there. Alfven showed that in a magnetic field plasmas can self‑organize into what he called ‘double layers’, pairs of wide, thin sheets with positive particles on one side against negative particles in the other. Neither sheet is stable on its own but the paired‑up structure can persist. Better yet, plasma magnetic fields can support coherent waves like the ones making that curtain ripple.”

“Any plasma?”

“Sure.”

“Most of the astronomical objects I show my students are associated with plasmas — the stars themselves, of course, but also the planetary nebulae that survive nova explosions, the interstellar medium in galactic star‑forming regions, the Solar wind, CMEs…”

“Alfven said we can’t understand the Universe unless we understand magnetic fields and electric currents.”

~ Rich Olcott

Colors Made of Air

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

Teena’s whirling around in the night with her head thrown back. “I LUVV AURORAS!! They’re SO beautiful beautiful beautiful!”

“Yes, they are, Teena. They’re beautiful and magical, and for me it’s even better because they’re Physics at work right in front of us. Well, above us.”

“Oh, Sy, give it a rest.”

“No, really, Sis. I look at a rainbow and I’m dazzled by its glory against the rainclouds but I’m also aware that each particular glimpse of pure color comes to me by refraction through one individual droplet. Better yet, I appreciate the geometry that presents the entire spectrum in perfectly circular arcs. Marvels supported by underlying marvels. These curtains are another example of beauty emerging from hidden sources.”

“What do you mean?”

“Remember Teena’s teacher’s magnetic force lines that were organized and revealed by iron filings? Auroras are a bit like that, except one level deeper. Again we don’t see magnetic fields directly. What we do see is light coming to us from oxygen and nitrogen atoms that are bombarded by rampaging charged particles.”

“Wait, Uncle Sy, we learned that charges make magnetic fields when they move.”

“That, too. It works both ways, which is why they call it electromagnetism. A magnetic field steers protons and electrons which make their own field to push back on the first one. But my point is, the colors in each curtain and the curtains themselves tell us about the current state of the atmosphere and Earth’s magnetic field.”

“Okay, I can see how magnetic fields up there could steer charged particles to certain parts of the sky, but how does that tell us about the atmosphere? What do the colors have to do with it? Is this more rainbows and geometry?”

“Definitely not. Sis. Rainbows are sunlight refracted through water droplets. Aurora light’s emitted by atoms in our own atmosphere. Each color is like a fingerprint of a specific atom in specific circumstances. The uppermost reds, for instance come from oxygen atoms that rarely touch another atom of any kind. They’re at 150 or more kilometers altitude, way above the stratosphere. There aren’t many of them that far up which is why the curtain tops sort of fade away into infinity.”

Aurora, photo by AstroAnthony
licensed under CC BY-SA 4.0

“Oooo, now it’s going green and yellow!”

“Mm-hm, the bombardment’s reaching further now. Excited oxygen atoms emit green lower down in the atmosphere where collisions happen more often and don’t give the red‑emitters a chance to do their thing. The in‑between yellow isn’t really there — it’s what your eye tells you when it sees pure red and pure green overlapping.”

“Why do the curtains have that sharp lower edge, Sy? Surely we don’t run out of oxygen there.”

“Quite the reverse. That level’s about 100 kilometers up. It’s where the atmosphere gets so thick that collisions drain away an excited atom’s energy before it gets a chance to shine.”

“But why are there curtains at all? Why not simply fill the sky with a smooth color wash?”

IMAGE view of Aurora australis
Credit: NASA, public domain

“Mars gets auroras like that, or at least Perseverance just spotted one. We don’t, thanks to our well‑ordered magnetic field. Mars’ field is lumpy and too weak to funnel incoming charged particles to special spots like our poles. Actually, those curtains are just segments of rings that go all around Earth’s magnetic axis. The rings usually lurk about 2/3 of the way to our poles but a really strong solar event like this one can push them closer to the Equator.”

“Mars gets auroras? Uncle Sy, how about other planets?”

“Them, too, but theirs mostly don’t look like ours. You’d have to be able to see X‑rays on Mercury, for instance. Venus gets a general green glow for the same reason that Mars does. Jupiter is Texas for the Solar System — everything’s bigger there, including auroras in every color from X‑ray to infrared. Strong ordered field, so I’m sure there’s curtains up there.”

Sis yanks out her writer’s‑companion notebook and scribbles without looking down…
  ”Curtains made of colors
   Colors made of air.“

Aurora, photo by Bellezzasolo
licensed under CC BY-SA 4.0

~ Rich Olcott

Sky Lights

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

“Mom! Uncle Sy! Come outside NOW before it goes away!”

“Whah— oooh!”
 ”An aurora! Thanks for calling us.”

“Glowing curtains rippling across the sky! Spotlights shining down through them! Where do those come from?”

“From the Sun, Teena.”

“C’mon, Sy. The Sun’s 93 million miles away. Even if that bright streak up there is as much as 10 miles across, which I doubt, the beam from the Sun would be only a teeny‑tiny fraction of a degree wide. Not even magnetars send out anything that narrow.”

“Didn’t say it’s a beam, Sis. The whole display comes from the Sun as single package. Sort of. Sometimes.”

“Even for you, little brother, that’s a new level of weasel‑wording.”

“Well, it’s complicated.”

“So unravel it. Start from the beginning.”

“Okay. The Sun’s covered in plasma—”

“Eww!”

“Not that kind of plasma, Teena. This is mostly hydrogen atoms except they’re so hot that the electrons and protons break away from each other and travel separately. What have they told you in school about magnets?”

“Not much. Umm … electric currents push on magnets and that’s how motors work, and magnets push on electrons and that’s how a generator works. Oh, and Mr Cox laid a sheet of paper on top of a magnet and sprinkled iron filings on it so we could see the lines of force, but when I asked him what made the magnetism ’cause I didn’t see any wires he started talking about electrons in iron atoms and then the bell rang and I had to go to Spanish class.”

The shape of the bar magnet’s field, disclosed by iron filings chaining together.

<sigh> “The clock rules, doesn’t it? Anyway, he was on the right track, but I want to get back to those lines of force. Were they there before he sprinkled on those filings?”

“Mmm … Mom would say, ‘That’s a good question,’ but how could you know? I’m gonna say they were.”

“Your Mom would be right, but sorry, you’re wrong. With no iron filings in the picture, the magnetic field is nice and smooth, everywhere just the same or maybe only a little bit stronger or weaker than neighboring points. No lines. Conditions change when you put the first bit of iron anywhere in the field. As Mr Cox was probably saying when the bell interrupted, the electrons in the grain’s iron atoms align orbitals with the magnetic field. The alignment affects the surrounding field and that pulls in other iron bits that change the field even more.”

“But wouldn’t that make just a solid iron blob?”

“No, because a magnetic field has both strength and direction. Once the first particle points along the field, the iron bits it recruits rotate to point mostly in the same direction. You wind up with a chain of specks tracing out where they’ve acted together to alter the field. The chain’s surrounded by spaces where the field’s been stressed.”

“And then lotsa chains make lotsa lines, yeah!”

“I see where you’re headed, Sy. You’re going to claim that the vertical lines we see in the curtains trace out the Sun’s magnetic field.”

“Not quite, Sis. There’s only one magnetic field, a combination of Earth’s field, the Sun’s field, and the magnetic fields contained in whatever the Sun throws our way. Way out here Earth’s field is about ten thousand times stronger than the Sun’s is, but the fields inside a CME can range up to 10% or 20% of Earth’s. The moving curtains up there are the result of a magnetic tussle between us and a CME or maybe a flare’s outflow.”

CME blast (red‑orange) impacting Earth ‘s magnetic field (blue lines)
Credit: NASA/GSFC/SOHO/ESA

“But there aren’t any iron filings up there, Uncle Sy!”

“True, but there are free charged particles in the ionosphere thanks to UV radiation from the Sun. A free electron caught in a magnetic field whips into a tight spiral. Its field gets neighbor particles spiraling. Pretty soon you wind up with a chain of them spiraling together, lining up like the filings do.”

“The spotlights?”

“Probably ion blobs embedded in the CME, but that’s a guess.”

Aurora, photo by W.carter
licensed under CC BY-SA 4.0

~ Rich Olcott

A Play Beyond The Play

On By rolcottIn Cosmology, Gravitational astronomy, Uncategorized, Vera RubinLeave a comment

Vinnie takes a long thoughtful look at the image that had dashed his beautiful six‑universe idea. “Wait, Sy. I don’t like this picture”

“Because it messes up your invention?”

“No, because how can they know what that halo looks like? I mean, the whole thing with dark matter is that we can’t see it.”

“You’re right about that. Dark matter’s so transparent that even with five times more mass than normal matter, it doesn’t block CMB photons coming from 13.8 billion lightyears away. That still boggles my brain every once in a while. But dark matter’s gravitational effects — those we can see.”

“Yeah, I remember a long time ago we talked about Fritz Zwicky and Vera Rubin and how they told people about galaxies held together by too much gravity but nobody believed them.”

“Well, they did, after a while—”

“A long while, like a long while since those talks. Remind me what ‘too much gravity’ was about.”

“It was about conflicts between their observations and the prevailing theoretical models. Everyone thought that galaxies and galaxy clusters should operate pretty much like planetary orbits — your speed increases the closer you are to the center, up to Einstein’s speed limit. Newton’s Laws of Motion predict how fast you should move if you’re at a certain distance from a body with a certain mass. If you’re moving faster than that, you fly away.”

“Yeah, escape velocity. So the galaxies in Zwicky’s cluster didn’t follow Newton’s Laws?”

“They didn’t seem to. Galaxies that should have escaped were still in there. The only way he could explain the stability was to suppose the galaxies are only a small fraction of the cluster’s mass. Extra gravity from the extra mass must bind things together. Forty years later Rubin’s improved technology revealed that stars within galaxies had the same anomalous motion.”

“I’m guessing the ‘faster near the center’ rule didn’t hold, or else you wouldn’t be telling this story. Spun like a wheel, I bet.”

“When a wheel spins, every part of it rotates at the same angular speed, the same number of degrees per second, right?”

“Ahh, the bigger my circle the higher my airspeed so the rule would be ‘faster farther out’.”

“That’s the wheel rule, right, but Rubin’s data showed that stars within galaxies don’t obey that one either. She measured lots of stars in Andromeda and other galaxies. Their linear speeds, kilometers per second, are nearly identical from near the center all the way out. Even dust and gas clouds beyond the galactic starry edges also fit the ‘same linear speed everywhere’ rule. You’d lose the bet.”

“That just doesn’t feel right. How can just gravity make that happen?”

“It can if the right amount of dark matter’s distributed in the right‑shaped smeared‑out hollowed‑out spherical halo. The halo’s radial density profile looks about like this. Of course, profiles for different galaxies differ in spread‑outness and other details, but the models are pretty consistent.”

“Wait, if dark matter only does gravity like you said, why’s that hole in the middle? Why doesn’t everything just fall inward?”

“Dark matter has mass so it also has inertia, momentum and angular momentum, just as normal matter does. Suppose some of the dark matter has collected gravitationally into a blob and the blob is moving slower than escape velocity. If it’s flying straight at the center of gravity it’ll get there and stay there, more or less. But if the blob’s aimed in any other direction, it has angular momentum relative to the center. Momentum’s conserved for dark matter, too. The blob eventually goes into orbit and winds up as part of the shell.”

“Does Zwicky’s galaxy cluster have a halo, too?”

“Not in the same way. Each galaxy probably has its own halo but the galaxies are far apart relative to their size. The theoreticians have burned huge amounts of computer time simulating the chaos inside large ensembles of gravity‑driven blobs. I just read one paper about a 4‑billion‑particle calculation and mind you, a ‘particle’ in this study carried more than a million solar masses. Big halos host subhalos, with filaments of minihalos tying them together. What we can’t see is complicated, too.”

~ Rich Olcott