Category: Physics

A Tug at The Ol’ Gravity Strings

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

“Why, Jeremy, you’ve got such a stunned look on your face. What happened? Is there anything I can do to help?”

“Sorry, Mr Moire. I guess I’ve been thinking too much about this science fiction story I just read. Which gelato can I scoop for you?”

“Two dips of mint, in a cup. Eddie went heavy with the garlic on my pizza this evening. What got to you in the story?”

“The central plot device. Here’s your gelato. In the story, someone locates a rogue black hole hiding in the asteroid belt. Tiny, maybe a few thousandths of a millimeter across, but awful heavy. A military‑industrial combine uses a space tug to tow it to Earth orbit for some kind of energy source, but their magnetic grapple slips and the thing falls to Earth. Except it doesn’t just fall to Earth, it’s so small it falls into Earth and now it’s orbiting inside, eating away the core until everything crumbles in. I can’t stop thinking about that.”

“Sounds pretty bad, but it might help if we run the numbers.” <drawing Old Reliable from its holster> “First thing — Everything about a black hole depends on its mass, so just how massive is this one?” <tapping on Old Reliable’s screen with gelato spoon> “For round numbers let’s say its diameter is 0.002 millimeter. The Schwartzschild ‘radius’ r is half that. Solve Schwartschild’s r=2GM/c² equation for the mass … plug in that r‑value … mass is 6.7×1020 kilograms. That’s about 1% of the Moon’s mass. Heavy indeed. How did they find this object?”

“The story didn’t say. Probably some asteroid miner stumbled on it.”

“Darn lucky stumble, something only a few microns across. Not likely to transit the Sun or block light from any stars unless you’re right on top of it. Radiation from its accretion disk? Depends on the history — there’s a lot of open space in the asteroid belt but just maybe the beast encountered enough dust to form one. Probably not, though. Wait, how about Hawking radiation?”

“Oh, right, Stephen Hawking’s quantum magic trick that lets a black hole radiate light from just outside its Event Horizon. Does Old Reliable have the formulas for that?”

“Sure. From Hawking’s work we know the object’s temperature and that gives us its blackbody spectrum, then we’ve got the Bekenstein‑Hawking equation for the power it radiates. Mind you, the spectrum will be red‑shifted to some extent because those photons have to crawl out of a gravity well, but this’ll give us a first cut.” <more tapping> “Chilly. 170 kelvins, that’s 100⁰C below room temperature. Most of its sub‑nanowatt emission will be at far infrared wavelengths. A terrible beacon. But suppose someone did find this thing. I wonder what’ll it take to move it here.”

“Can you calculate that?”

“Roughly. Suppose your space tug follows the cheapest possible flight path from somewhere near Ceres. Assuming the tug itself has negligible mass … ” <more tapping> “Whoa! That is literally an astronomical amount of delta-V. Not anything a rocket could do. Never mind. But where were they planning to put the object? What level orbit?”

“Well, it’s intended to beam power down to Earth. Ions in the Van Allen Belts would soak up a lot of the energy unless they station it below the Belts. Say 250 miles up along with the ISS.”

“Hoo boy! A thousand times closer than the Moon. Force is inverse to distance squared, remember. Wait, that’s distance to the center and Earth’s radius is about 4000 miles so the 250 miles is on top of that. 250,000 divided by 4250 … quotient squared … is a distance factor of almost 3500. Put 1% of the Moon that close to the Earth and you’ve got ocean tides 36 times stronger than lunar tides. Land does tides, too, so there’d be earthquakes. Um. The ISS is on a 90‑minute orbit so you’d have those quakes and ocean tides sixteen times a day. I wouldn’t worry about the black hole hollowing out the Earth, the tidal effect alone would do a great job of messing us up.”

“The whole project is such a bad idea that no-one would or could do it. I feel better now.”

~~ Rich Olcott

Reflection, Rotation And Spacetime

On By rolcottIn Cosmology, Mathematics, Physics: Einstein, UncategorizedLeave a comment

“Afternoon, Al.”

“Hiya, Sy. Hey, which of these two scones d’ya like better?”

“”Mm … this oniony one, sorta. The other is too vegetable for me ‑ grass, I think, and maybe asparagus? What’s going on?”

“Experimenting, Sy, experimenting. I’m going for ‘Taste of Spring.’ The first one was spring onion, the second was fiddlehead ferns. I picked ’em myself.”

“Very seasonal, but I’m afraid neither goes well with coffee. I’ll take a caramel scone, please, plus a mug of my usual mud.”

“Aw, Sy, caramel’s a winter flavor. Here you go. Say, while you’re here, maybe you could clear up something for me?”

“I can try. What’s the something?”

“After your multiverse series I got out my astronomy magazines to read up on the Big Bang. Several of the articles said that we’ve gone through several … um, I think they said ‘epochs‘ … separated by episodes of symmetry breaking. What’s that all about?”

“It’s about a central notion in modern Physics. Name me some kinds of symmetry.”

“Mmm, there’s left‑right, of course, and the turning kind like a snowflake has. Come to think — I like listening to Bach and Vivaldi when I’m planet‑watching. I don’t know why but their stuff reminds me of geometry and feels like symmetry.”

“Would it help to know that the word comes from the Greek for ‘same measure‘? Symmetry is about transformations, like your mirror and rotation operations, that affect a system but don’t significantly change to its measurable properties. Rotate that snowflake 60° and it looks exactly the same. Both the geometric symmetries you named are two‑dimensional but the principle applies all over the place. Bach and the whole Baroque era were just saturated with symmetry. His music was so regular it even looked good on the page. Even buildings and artworks back then were planned to look balanced, as much mass and structure on the left as on the right.”

“I don’t read music, just listen to it. Why does Bach sound symmetric?”

“There’s another kind of symmetry, called a ‘translation‘ don’t ask why, where the transformation moves something along a line within some larger structure. That paper napkin dispenser, for instance. It’s got a stack of napkins that all look alike. I pull one off, napkins move up one unit but the stack doesn’t look any different.”

“Except I gotta refill it when it runs low, but I get your drift. You’re saying Bach takes a phrase and repeats it over and over and that sounds like translational symmetry along the music’s timeline.”

“Yup, maybe up or down a few tones, maybe a different register or instrument. The repeats are the thing. Play his Third Brandenberg Concerto next time you’re at your telescope, you’ll see what I mean.”

“Symmetry’s not just math then.”

“Like I said, it’s everywhere. You’ve seen diagrams of DNA’s spiral staircase. It combines translation with rotation symmetry, does about 10 translation steps per turn, over and over. The Universe has a symmetry you don’t see at all. No‑one did until Lorentz and Poincaré revised Heaviside’s version of Maxwell’s electromagnetism equations for Minkowski space. Einstein, Hilbert and Grossman used that work to give us and the Universe a new symmetry.”

“Einstein didn’t do the math?”

“The crew I just named were world‑class in math, he wasn’t. Einstein’s strengths were his physical intuition and his ability to pick problems his math buddies would find interesting. Look, Newton’s Universe depends on absolute space and time. The distance between two objects at a given time is always the same, no matter who’s measuring it or how fast anyone is moving. All observers measure the same duration between two incidents regardless. Follow me?”

“Makes sense. That’s how things work hereabouts, anyway.”

“That’s how they work everywhere until you get to high speeds or high gravity. Lorentz proved that the distances and durations you measure depend on your velocity relative to what you’re measuring. Extreme cases lead to inconsistent numbers. Newton’s absolute space and time are pliable. To Einstein such instability was an abomination. Physics needs a firm foundation, a symmetry between all observers to support consistent measurements throughout the Universe. Einstein’s Relativity Theory rescued Physics with symmetrical mathematical transformations that enforce consistency.”

~~ Rich Olcott

Noodles or A Sandwich?

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

“Wait, Sy, your anti-Universe idea says there are exactly two um, sub‑Universes. Even the word ‘multiverse‘ suggests more than that.”

“You’re right, Susan, most of the multiverse proposals go to the other extreme. Maybe the most extreme version grew in reaction to one popular interpretation of quantum theory. Do you know about the ‘Many Worlds‘ notion?”

“Many Worlds? Is that the one about when I decide between noodles for lunch or a sandwich, the Universe splits and there’s one of me enjoying each one?”

“That’s the popular idea. The physics idea is way smaller, far bigger and even harder to swallow. Physicists have been arguing about it for a half‑century.”

“Come again? Smaller AND bigger?”

“Smaller because it’s a quantum‑based idea about microscopic phenomena. Doesn’t say anything about things big enough to touch. Remember how quantum calculations predict statistics, not exact values? They can’t give you anything but averages and spreads. Einstein and Bohr had a couple of marquee debates about that back in the 1930s. Bohr maintained that our only path to understanding observations at the micro‑scale was to accept that events there are random and there’s no point discussing anything deeper than statistics. Einstein’s position was that the very fact that we’re successfully using an average‑based strategy says that there must be finer‑grained phenomena to average over. He called it ‘the underlying reality.’ The string theory folks have chased that possibility all the way down to the Planck‑length scale. They’ve found lots of lovely math but not much else. Hugh Everett had a different concept.”

“With that build‑up, it’d better have something to do with Many Worlds.”

“Oh, it does. Pieces of the idea have been lying around for centuries, but Everett pulled them all together and dressed them up in a quantum suit. Put simply, in his PhD thesis he showed how QM’s statistics can result from averaging over Universes. Well, one Universe per observation, but you experience a sequence of Universes and that’s what you average over.”

“How can you show something like that?”

“By going down the rabbit hole step by step and staying strictly within the formal QM framework. First step was to abstractify the operation of observing. He said it’s a matter of two separate systems, an observer A and a subject B. The A could be a person or electronics or whatever. What’s important is that A has the ability to assess and record B‘s states and how they change. Given all that, the next step is to say that both A and B are quantized, in the sense that each has a quantum state.”

“Wait, EACH has a quantum state? Even if A is a human or a massive NMR machine?”

“That’s one of the hard‑to‑swallows, but formally speaking he’s okay. If a micro‑system can have a quantum state then so can a macro‑system made up of micro‑systems. You just multiply the micro‑states together to get the macro‑state. Which gets us to the next step — when A interrogates B, the two become entangled. We then can only talk about the combined quantum state of the A+B system. Everett referred to an Einstein quote when he wrote that a mouse doesn’t change the Moon by looking at it, but the Moon changes the mouse. The next step’s a doozy so take a deep breath.”

“Ready, I suppose.”

“B could have been in any of its quantum states, suppose it’s #10. After the observation, A+B must be an entangled mixture of whatever A was, combined with each of B‘s possible final states. Suppose B might switch to #42. Now we can have A+B(#42), separate from a persisting A+B(#10), plus many other possibles. As time goes by, A+B(#42) moves along its worldline independent of whatever happens to A+B(#10).”

“If they’re independent than each is in its own Universe. That’s the Many Worlds thing.”

“Now consider just how many worlds. We’re talking every potential observing macro‑system of any size, entangled with all possible quantum states of every existing micro‑system anywhere in our Observable Universe. We’re a long way from your noodles or sandwich decision.”

“An infinity of infinities.”

“Each in its own massive world.”

“Hard to swallow.”

~~ Rich Olcott

A Nightcap And Secrets

On By rolcottIn Computer science, Physics: Quantum Mechanics, UncategorizedLeave a comment

“A coffee nightcap, Sy? It’s decaf so Teena can have some.”

“Sounds good, Sis.”

“Why didn’t Mr Einstein like entanglement, Uncle Sy? Thanks, Mom. A little more cream in it, please.”

“I’ll bet it has to do with the instant-effect aspect, right, Sy?”

“Thanks, Sis, and you’re right as usual. All of Relativity theory rests on the claim that nothing, not light or gravity or causality itself, can travel faster than light in a vacuum. There’s good strong arguments and evidence to support that, but Einstein himself proved that entanglement effects aren’t constrained to lightspeed. Annoyed him no end.”

“Well, your coin story‘s very nice, but it’s just a story. Is there evidence for entanglement?”

“Oh, yes, though it was fifty years after Einstein’s entanglement paper before our technology got good enough to do the experiments. Since then a whole industry of academics and entrepreneurs has grown up to build and apply devices that generate entangled systems.”

“Systems?”

“Mm-hm. Most of the work has been done with pairs of photons, but people have entangled pairs of everything from swarms of ultra‑cold atoms to electrons trapped in small imperfect diamonds. It’s always a matter of linking the pair members through some shared binary property.”

“Binary! I know what that is. Brian has a computer toy he lets me play with. You tell it where to drive this little car and it asks for decisions like left‑right or go‑stop and they’re all yes or no and the screen shows your answer as ‘0’or ‘1’ and that’s binary, right?”

“Absolutely, Teena. The entangled thingies are always created in pairs, remember? Everything about each twin is identical except for that one property, like the two coin metals, so it’s yes, no, or some mixture. Cars can’t do mixtures because they’re too big for quantum.”

“What kinds of properties are we talking about? It’s not really gold and silver, is it?”

“No, you’re right about that, Sis. Transmutation takes way too much power. Entangled quantum states have little or no energy separation which is one reason the experiments are so hard. Photons are the easiest to work with so that’s where most of the entanglement work has been done. Typically the process splits a laser beam into two rays that have contrasting polarizations, say vertical and horizontal. Or the researchers might work with particles like electrons that you can split into right‑ and left‑handed spin. Whatever, call ’em ones and zeroes, you’ve got a bridge between quantum and computing.”

“Brian says binary can do secret codes.”

“He’s right about that. Codes are about hiding information. Entanglement is real good at hiding quantum information behind some strict rules. Rule one is, if you inspect an entangled particle, you break the entanglement.”

“Sounds reasonable. When you measure it you make it part of a big system and it’s not quantum any more.”

“Right, Sis. Rule two, an entanglement only links pairs. No triples or broadcasts. Rule three is for photons — you can have two independent ways to inspect a property, but you need to use the same way for both photons or you’ve got a 50% chance of getting a mismatch.”

“Oho! I see where the hiding comes in. Hmm… From what I’ve read, encryption’s big problem is guarding the key. I think those three rules make a good way to do that. Suppose Rocky and Bullwinkle want to protect their coded messages from Boris Badinoff. They share a series of entangled photon pairs. and they agree to a measurement protocol based on the published daily prices for a series of stocks — for each photon in a series, measure it with Method 1 if the corresponding price is an odd number, Method 2 if it’s even. Rocky measures his photon. If he measures a ‘1’ then Bullwinkle sees a ‘0’ for that photon and he knows Rocky saw a ‘1.’ Rocky encrypts his message using his measured bit string. Bullwinkle flips his bit string and decrypts.”

“Brilliant. Even if Boris knows the proper sequence of measurements, if he peeks at an entangled photon that breaks the entanglement. When Bullwinkle decodes gibberish Rocky has to build another key. Your Mom’s a very smart person, Teena.”

~ Rich Olcott

Tiramisu And Gemstones

On By rolcottIn Physics: Quantum Mechanics, UncategorizedLeave a comment

“Sis, you say there’s dessert?”

“Of course there is, Sy. Teena, please bring in the tray from the fridge.”

“Tiramisu! You did indeed go above and beyond. Thank you, Teena. Your Mom’s question must be a doozey.”

“I’ll let you enjoy a few spoonfulls before I hit you with it.” <minutes with spoon noises and yumming> “Okay. tell me about entanglement.”

“Whoa! What brought that on?”

“I’ve seen the word bandied about in the popular science press—”

“And pseudoscience—”

“Well, yes. I’m writing something where the notion might come in handy if it makes sense.”

“How can you tell what’s pseudoscience?”

“Good question, Teena. I look for gee-whiz sentences, especially ones that include weasely words like ‘might‘ and ‘could.’ Most important, does the article make or quote big claims that can’t be disproven? I’d want to see pointers to evidence strong enough to match the claims. A respectable piece would include comments from other people working in the same field. Things like that.”

“What your Mom said, and also has the author used a technical term like ‘energy‘ or ‘quantum‘ but stretched it far away from its home base? Usually when they do that and you have even an elementary idea what the term really means, it’s pretty clear that the author doesn’t understand what they’re writing about. That goes double for a lot of what you’ll see on YouTube and social media in general. It’s just so easy to put gibberish up there because there’s no‑one to contradict a claim, or if there is, it’s too late because the junk has already spread. ‘Entanglement‘ is just the latest buzzword to join the junk‑science game.”

“So what can you tell us about entanglement that’s non‑junky?”

“First thing is, it’s strictly a microscopic phenomenon, molecule‑tiny and smaller. Anything you read about people or gemstones being entangled, you can stop reading right there unless it’s for fun.”

“Weren’t Rapunzel and the prince entangled?

“They and all the movie’s other characters were tangled up in the story, yes, but that’s not the kind of entanglement your Mom’s asking about. This kind seems to involve something that Einstein called ‘spooky action at a distance‘. He didn’t like it.”

“‘Seems to‘?”

“Caught me, Sis, but it’s an important point. You make a system do something by acting on it, right? We’re used to actions where force is transmitted by direct contact, like hitting a ball with a bat. We’ve known how direct contact works with solids and fluids since Newton. We’ve extended the theory to indirect contact via electric and other fields thanks to Maxwell and Einstein and a host of other physicists. ‘Action at a distance‘ is about making something happen without either direct or indirect contact and that’s weird.”

“Can you give us an example?”

“How about an entanglement story? Suppose there’s a machine that makes coins, nicely packaged up in gift boxes. They’re for sweethearts so it always makes the coins in pairs, one gold and one silver. These are microscopic coins so quantum rules apply — every coin is half gold and half silver until its box is opened, at which point it becomes all one pure metal.”

“Like Schrödinger’s asleep‑awake kitty‑cat!”

“Exactly, Teena. So Bob buys a pair of boxes, keeps one and gives the other to Alice before he flies off in his rocket to the Moon. Quantum says both coins are both metals. When he lands, he opens his box and finds a silver coin. What kind of coin does Alice have?”

“Gold, of course.”

“For sure. Bob’s coin‑checking instantly affected Alice’s coin a quarter‑million miles away. Spooky, huh?”

“But wait a minute. Alice’s coin doesn’t move. It’s not like Bob pushed on it or anything. The only thing that changed was its composition.”

“Sis, you’ve nailed it. That’s why I said ‘seems to‘. Entanglement’s not really action at a distance. No energy or force is exerted, it’s simply an information thing about quantum properties. Which, come to think of it, is why there’s no entanglement of people or gemstones. Even a bacterium has billions and billions of quantum‑level properties. Entanglement‑tweaking one or two or even a thousand atoms won’t affect the object as a whole.”

~~ Rich Olcott

The Frame Game

On By rolcottIn Physics: Einstein, Physics: Fundamentals, Space Travel, UncategorizedLeave a comment

A familiar footstep outside my office, “C’mon in, Vinnie, the door’s open.”

“Hi, Sy, how ya doin’?”

“Can’t complain. Yourself?”

“Fine, fine. Hey, I been thinking about something you said while Al and us were talking about rockets and orbits and such. You remember that?”

“We’ve done that in quantity. What statement in particular?”

“It was about when you’re in the ISS, you still see like 88% of Earth’s gravity. But I seen video of those astronauts just floating around in the station. Seems to me those two don’t add up.”

“Hah! We’re talking physics of motion here. What’s the magic word?”

“You’re saying it’s frames? I thought black holes did that.”

“Black holes are an extreme example, but frame‑thinking is an essential tool in analyzing any kind of relative motion. Einstein’s famous ‘happy thought‘ about a man in a free‑falling elevator—”

“Whoa, why is that a happy thought? I been nervous about elevators ever since that time we got stuck in one.”

“At least it wasn’t falling, right? Point is, the elevator and whoever’s in it agree that Newton’s First Law of Motion is valid for everything they see in there.”

“Wait, which Law is that?”

“‘Things either don’t move or else they move at a steady pace along a straight line.’ Suppose you’re that guy—”

“I’d rather not.”

“… and the elevator is in a zero‑gravity field. You take something out of your pocket, put it the air in front of you and it stays there. You give it a tap and it floats away in a straight line. Any different behavior means that your entire frame — you, the elevator and anything else in there — is being accelerated by some force. Let’s take two possibilities. Case one, you and the elevator are resting on terra firma, tightly held by the force of gravity.”

“I like that one.”

“Case two, you and the elevator are way out in space, zero‑gravity again, but you’re in a rocket under 1-g acceleration. Einstein got happy because he realized that you’d feel the same either way. You’d have no mechanical way to distinguish between the two cases.”

“What’s that mean, mechanical?”

“It excludes sneaky ways of outside influence by magnetic fields and such. Anyhow, Einstein’s insight was key to extending Newton’s First Law to figuring acceleration for an entire frame. Like, for instance, an orbiting ISS.”

“Ah, you’re saying that floating astronauts in an 88% Earth-gravity field is fine because the ISS and the guys share the frame feeling that 88% but the guys are floating relative to that frame. But down here if we could look in there we’d see how both kinds of motion literally add up.”

“Exactly. It’s just much easier to think about only one kind at a time.”

“Wait. You said the ISS is being accelerated. I thought it’s going a steady 17500 miles an hour which it’s got to do to stay 250 miles up.”

“Is it going in a straight line?”

“Well, no, it’s going in a circle, mostly, except when it has to dodge some space junk.”

“So the First Law doesn’t apply. Acceleration is change in momentum, and the ISS momentum is constantly changing.”

“But it’s moving steady.”

“But not in a straight line. Momentum is a vector that points in a specific direction. Change the direction, you change the momentum. Newton’s Second Law links momentum change with force and acceleration. Any orbiting object undergoes angular acceleration.”

“Angular acceleration, that’s a new one. It’s degrees per second per second?”

“Yup, or radians. There’s two kinds, though — orbiting and spinning. The ISS doesn’t spin because it has to keep its solar panels facing the Sun.”

“But I’ve seen sci-fi movies set in something that spins to create artificial gravity. Like that 2001 Space Odyssey where the guy does his running exercise inside the ship.”

“Sure, and people have designed space stations that spin for the same reason. You’d have a cascade of frames — the station orbiting some planet, the station spinning, maybe even a ballerina inside doing pirouettes.”

“How do you calculate all that?”

“You don’t. You work with whichever frame is useful for what you’re trying to accomplish.”

“Makes my head spin.”

~~ Rich Olcott

Science or Not-science?

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

Vinnie trundles up to Jeremy’s gelato stand. “I’ll take a Neapolitan, one each chocolate, vanilla and strawberry.”

“Umm… Eddie forgot to order more three-dip cones and I’m all out. I can give you three separate cones or a dish.”

“The dish’ll be fine, way less messy. Hey, Sy, I got a new theory.”

“Mm… Unless you’ve got a lot of firm evidence it can’t be a theory. Could be a conjecture or if it’s really good maybe a hypothesis. What’s your idea?”

“Thing is, Sy, there can’t be any evidence. Ever. That’s the fun of it.”

“Conjecture, then. C’mon, out with it.”

“Well, you remember all that stuff about how time bends toward a black hole’s mass and that’s how gravity works?”

“Sure, except it’s not just black holes. Time bends the same way toward every mass, it’s just more intense with black holes.”

“Understood. Anyway, we talked once about how stars collapse to form black holes but that’s only up to a certain size, I forget what—”

“Ten to fifteen solar masses. Beyond that the collapse goes supernova and doesn’t leave much behind but dust.”

“Right. So you said we don’t know how to make size‑30 black holes like the first pair that LIGO found.”

“We’ve got a slew of hypotheses but the jury’s still out.”

“That’s what I hear. Well, if we don’t even know that much then we for‑sure don’t know how to make the supermassive black hole the science magazines say we’ve got in the middle of the Milky Way.”

“We’ve found that nearly every galaxy has one, some a lot bigger than ours. Why that’s true is one of the biggest mysteries in astrophysics.”

“And I know the answer! What if those supermassive guys started out as just big lumps of dark matter and then they wrapped themselves in more dark matter and everything else?”

“Cute idea, but the astronomy data says we can account for galaxy shapes and behavior if they’re embedded at the center of a spherical halo of dark matter.”

“Not a problem, Sy. Look at the numbers. Our superguy is a size‑4‑million, right? The whole Milky Way’s a billion times heavier than that. Tuck an extra billionth into the middle of the swirl and the stars wouldn’t see the difference.”

“Okay, but there’s more data that says dark matter spreads itself pretty evenly, doesn’t seem to clump up like you need it to.”

“Yeah, but maybe there’s two kinds, one kind clumpy and the other kind not. Only way to find out is to look inside a superguy but time blocks information flow out of there. So no‑one can say I’m wrong!”

“But sir, that’s not science!”

“Why not, kid?”

“The unit my philosophy class did on Popper.”

“The stuff you sniff or the penguins guy?”

“Neither, Karl Popper the philosopher. Dr Crom really likes Popper’s work so we spent a lot of time reading him. Popper was one of the Austrian intellectuals the Nazis chased out when they took power in the 1930s. Popper traveled around, wound up in New Zealand where he wrote his Open Society book that shredded Hegel and Marx. Those sections were fun reading even if they were wordy. Anyway, one of Popper’s big things was the demarcation problem, how to tell the difference between what’s a scientific assertion and what’s not. He decided the best criterion was if there’s a way to prove the assertion false. Not whether it was false but whether it could at least be tested. I was surprised by how many goofy things the Greeks said that would qualify as Popper‑scientific even though they were just made up and have been proven wrong.”

“Well there you go, Vinnie. Physics and the Universe don’t let us see into a supermassive black hole, therefore your idea isn’t testable even in principle. Jeremy’s right, it’s not scientific even though it’s all dressed up in a Science suit.”

“I can still call it a conjecture, though, right, Sy?”

“Conjecture it is. Might even be true, but we’ll never know unless we somehow find out something about dark matter that surprises us. We’ve been surprised a lot, though, so don’t give up hope.”

~~ Rich Olcott

Wait For It

On By rolcottIn General: Serious Stuff, Physics, UncategorizedLeave a comment

“So, Jeremy, have I convinced you that there’s poetry in Physics?”

“Not quite, Mr Moire. Symbols can carry implications and equation syntax is like a rhyme scheme, okay, but what about the larger elements we’ve studied like forms and metaphors?”

“Forms? Hoo boy, do we have forms! Books, theses, peer-reviewed papers, conference presentations, poster sessions, seminars, the list goes on and that’s just to show results. Research has forms — theoretical, experimental, and computer simulation which is sort of halfway between. Even within the theory division we have separate forms for solving equations to get mathematically exact solutions, versus perturbation techniques that get there by successive approximations. On the experimental side—”

“I get the picture, Mr Moire. Metaphorically there’s lots of poetry in Physics.”

“Sorry, you’re only partway there. My real point is that Physics is metaphor, a whole cascade of metaphors.”

“Ha, that’s a metaphor!”

“Caught me. But seriously, Science in general and Physics in particular underwent a paradigm shift in Galileo’s era. Before his century, a thousand years of European thought was rooted in Aristotle’s paradigm that centered on analysis and deduction. Thinkers didn’t much care about experiment or observing the physical world. No‑one messed with quantitative observations except for the engineers who had to build things that wouldn’t fall down. Things changed when Tycho Brahe and Galileo launched the use of numbers as metaphors for phenomena.”

“Oh, yeah, Galileo and the Leaning Tower experiment.”

“Which may or may not have happened. Reports differ. Either way, his ‘all things fall at the same speed‘ conclusion was based on many experimental trials where he rolled balls of different material, sizes and weights down a smooth trough and timed each roll.”

“That’d have to be a long trough. I read how he used to count his pulse beats to measure time. One or two seconds would be only one or two beats, not much precision.”

“True, except that he used water as a metaphor for time. His experiments started with a full jug of water piped to flow into an empty basin which he’d weighed beforehand. His laboratory arrangement opened a valve in the water pipe when he released the ball. It shut the valve when the ball crossed a finish line. After calibration, the weight of released water represented the elapsed time, down to a small fraction of a second. Distance divided by time gave him speed and he had his experimental data.”

“Pretty smart.”

“His genius was in devising quantitative challenges to metaphor‑based suppositions. His paradigm of observation, calculation and experimental testing far outlasted the traditionalist factions who tried to suppress his works. Of course that was after a century when Renaissance navigators and cartographers produced maps as metaphors for oceans and continents.”

“Wait, Mr Moire. In English class we learned that a metaphor says something is something else but an analogy is when you treat something like something else. Water standing for time, measurements on a map standing for distances — aren’t those analogies rather than metaphors?”

“Good point. But the distinction gets hazy when things get abstract. Take energy, for example. It’s not an object or even a specific kind of motion like a missile trajectory or an ocean wave. Energy’s a quantity that we measure somewhere somehow and then claim that the same quantity is conserved when it’s converted or transferred somewhere else. That’s not an analogy, it’s a metaphor for a whole parade of ways that energy can be stored or manifested. Thermodynamics and quantum mechanics depend on that metaphor. You can’t do much anywhere in Physics without paying some attention to it. People worry about that, though.”

“Why’s that?”

“We don’t really understand why energy and our other fundamental metaphors work as well as they do. No metaphor is perfect, there are always discrepancies, but Physics turns out to be amazingly exact. Chemistry equations balance to within the accuracy of their measuring equipment. Biology’s too complex to mathematize but they’re making progress. Nobel Prize winner Eugene Wigner once wrote a paper entitled, ‘The Unreasonable Effectiveness of Mathematics in The Natural Sciences.’ It’s a concern.”

“Well, after all that, there’s only one thing to say. If you’re in Physics, metaphors be with you.”

~~ Rich Olcott

Imagine A Skyrocket Inside A Black Hole

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

Vinnie’s never been a patient man. “We’re still waiting, Sy. What’s the time-cause-effect thing got to do with black holes and information?”

“You’ve got most of the pieces, Vinnie. Put ’em together yourself.”

“Geez, I gotta think? Lessee, what do I know about black holes? Way down inside there’s a huge mass in a teeny singularity space. Gravity’s so intense that relativity theory and quantum mechanics both give up. That can’t be it. Maybe the disk and jets? No, ’cause some holes don’t have them, I think. Gotta be the Event Horizon which is where stuff can’t get out from. How’m I doing, Sy?”

“You’re on the right track. Keep going.”

“Okay, so we just talked about how mass scrambles spacetime, tilts the time axis down to point towards where mass is so axes stop being perpendicular and if you’re near a mass then time moves you even closer to it unless you push away and that’s how gravity works. That’s part of it, right?”

“As rain. So mass and gravity affect time, then what?”

“Ah, Einstein said that cause‑and‑effect runs parallel with time ’cause you can’t have an effect before what caused it. You’re saying that if gravity tilts time, it’ll tilt cause‑and‑effect?”

“So far as we know.”

“That’s a little weasel-ish.”

“Can’t help it. The time‑directed flow of causality is a basic assumption looking for counter‑examples. No‑one’s come up with a good one, though there’s a huge literature of dubious testimonials. Something called a ‘closed timelike curve‘ shows up in some solutions to Einstein’s equations for extreme conditions like near or inside a black hole. Not a practical concern at our present stage of technology — black holes are out of reach and the solutions depend on weird things like matter with negative mass. So anyhow, what happens to causality where gravity tilts time?”

“I see where you’re going. If time’s tilted toward the singularity inside a black hole, than so is cause‑and‑effect. Nothing in there can cause something to happen outside. Hey, bring up that OVR graphics app on Old Reliable, I’ll draw you a picture.”

“Sure.”

“See, way out in space here this circle’s a frame where time, that’s the red line, is perpendicular to the space dimensions, that’s the black line, but it’s way out in space so there’s no gravity and the black line ain’t pointing anywhere in particular. Red line goes from cause in the middle to effect out beyond somewhere. Then inside the black hole here’s a second frame. Its black line is pointing to where the mass is and time is tilted that way too and nothing’s getting away from there.”

“Great. Now add one more frame right on the border of your black hole. Make the black line still point toward the singularity but make the red line tangent to the circle.”

“Like this?”

“Perfect. Now why’d we put it there?”

“You’re saying that somewhere between cause-effect going wherever and cause-effect only going deeper into the black hole there’s a sweet spot where it doesn’t do either?”

“Exactly, and that somewhere is the Event Horizon. Suppose we’re in a mothership and you’re in our shuttlecraft in normal space. You fire off a skyrocket. Both spacecraft see sparks going in every direction. If you dive below an Event Horizon and fire another skyrocket, in your frame you’d see a normal starburst display. If we could check that from the mothership frame, we’d see all the sparks headed inward but we can’t because they’re all headed inward. All the sparkly effects take place closer in.”

“How about lighting a firework on the Horizon?”

“Good luck with that. Mathematically at least, the boundary is infinitely thin.”

“So bottom line, light’s trapped inside the black hole because time doesn’t let the photons have an effect further outward than they started. Do I have that right?”

“For sure. In fact, you can even think of the hole as an infinite number of concentric shells, each carrying a causality sign reading ‘Abandon hope, all ye who enter here‘. So what’s that say about information?”

“Hah, we’re finally there. Got it. Information can generate effects. If time can trap cause‑effect, then it can trap information, too.”

~~ Rich Olcott

Tilting at Black Holes

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

“What’s the cause-effect-time thing got to do with black holes and information?”

“We’re getting there, Al. What happens to spacetime near a black hole?”

“Everybody knows that, Sy, spacetime gets stretched and squeezed until there’s infinite time dilation at the Event Horizon.”

“As usual, Vinnie, what everybody knows isn’t quite what is. Yes, Schwarzschild’s famous solution includes that Event Horizon infinity but it’s an artifact of his coordinate system. Al, you know about coordinate systems?”

“I’m a star-watcher, Sy. Sure, I know about latitude and longitude, declination and right ascension, all that stuff no problem.”

“Good. Well, Einstein wrote his General Relativity equations using generalized coordinates, like x,y,z but with no requirement that they be straight lines or at right angles. Schwarzschild solved the equations for a non‑rotating sphere so naturally he used spherical coordinates — radius, latitude and longitude. Since then other people have solved the equations for more complicated cases using more complicated coordinate systems. Their solutions don’t have that infinity.”

“No infinity?”

“Not that one, anyhow. The singularity at the hole’s geometric center is a real thing, not an artifact. So’s a general Event Horizon, but it’s not quite where Schwarzschild said it should be and it doesn’t have quite the properties that everybody thinks they know it has. It’s still weird, though.”

“How so?”

“First thing you have to understand is that when you get close to a black hole, you don’t feel any different. Except for the spaghettification, of course.”

“It’s frames again, ain’t it?”

“With black holes it’s always frames, Vinnie. If you’re living in a distorted space you won’t notice it. Whirl a meter‑long sword around, you’d always see it as a meter long. A distant observer would see you and everything around you as being distorted right along with your space. They’ll see that sword shrink and grow as it passes through different parts of the distortion.”

“Weird.”

“We’re just getting started, Al. Time’s involved, too. <grabbing a paper napkin and sketching> Here’s three axes, just like x,y,z except one’s time, the G one points along a gravity field, and the third one is perpendicular to the other two. By the way, Al, great idea, getting paper napkins printed like graph paper.”

“My location’s between the Physics and Astronomy buildings, Sy. Gotta consider my clientele. Besides, I got a deal on the shipment. What’s the twirly around that third axis?”

“It’s a reminder that there’s a couple of space dimensions that aren’t in the picture. Now suppose the red ball is a shuttlecraft on an exploration mission. The blue lines are its frame. The thick vertical red line shows it’s not moving because there’s no spatial extent along G. <another paper napkin, more sketching> This second drawing is the mothership’s view from a comfortable distance of the shuttlecraft near a black hole.”

“You’ve got the time axis tilted. What’s that about?”

“Spacetime being distorted by the black hole. You’ve heard Vinnie and me talk about time dilation and space compression like they’re two different phenomena. Thing is, they’re two sides of the same coin. On this graph that shows up as time tilted to mix in with the BH direction.”

“How about those twirly directions?”

“Vinnie, you had to ask. In the simple case where everything’s holding still and you’re not too close to the black hole, those two aren’t much affected. If the big guy’s spinning or if the Event Horizon spans a significant amount of your sky, all four dimensions get stressed. Let’s keep things simple, okay?”

“Fine. So the time axis is tilted, so what?”

“We in the distant mothership see the shuttlecraft moving along pure tilted time. The shuttlecraft doesn’t. The dotted red lines mark its measurements in its blue‑line personal frame. Shuttlecraft clocks run slower than the mothership’s. Worse, it’s falling toward the black hole.”

“Can’t it get away?”

“Al, it’s a shuttlecraft. It can just accelerate to the left.”

“If it’s not too close, Vinnie. The accelerative force it needs is the product of both masses, divided by the distance squared. Sound familiar?”

“That’s Newton’s Law of Gravity. This is how gravity works?”

“General Relativity cut its teeth on describing that tilt.”

~~ Rich Olcott