Through The Looking Glass, Darkly

On July 24, 2017November 30, 2025 By rolcottIn General: Fun Stuff, Mathematics: Dimensions, Physics: Entropy and Thermodynamics, Uncategorized1 Comment

The Acme Building is quiet on summer evenings. I was in my office, using the silence to catch up on paperwork. Suddenly I heard a fizzing sound. Naturally I looked around. She was leaning against the door frame.

White satin looked good on her, and she looked good in it. A voice like molten silver — “Hello, Mr Moire.”

“Hello yourself. What can I do for you?”

“I’m open to suggestions, but first you can help me find myself.”

“Excuse me, but you’re right here. And besides, who are you?”

“Not where I am but when I am. Anne.”

“You said it right the first time.”

“No, no, my name is Anne. At the moment. I think. Oh, it’s so confusing when your memory works in circles but not very well. Do you have the time?”

“Well, I was busy, but you’re here and much more interesting.”

“No, I mean, what time is it?”

I showed her my desk clock — date, time, even the phase of the moon.

“Half past gibbous already? Oh, bread-and-butter…”

“Wait — circles? Time’s one-dimensional. Clock readings increase or decrease, they don’t go sideways.”

“You don’t know Time as well as I do, Mr Moire. It’s a lot more complicated than that. Time can be triangular, haven’t you noticed?”

“Can’t say as I have.”

“That paperwork you’re working on, are you near a deadline?”

“Nah.”

“And given that expanse of time, you feel free to permit distractions. There are so many distractions.”

“You’re very distracting.”

“Thank you, I guess. But suppose you had an important deadline coming up tomorrow. That broad flow of possibilities at the beginning of the project has narrowed to just two — finish or don’t finish. Your Time has closed in on you.”

“So you’re saying we can think of Time as two-dimensional. The second dimension being…?”

“I don’t know. I just go there. That’s the problem.”

“Hmm… When you do, do you feel like you’re turning left or right?”

“No turning or moving forward or backward. Generally I have to … umm… ‘push’ like I’m going uphill, but that only works if there’s a ‘being pushed’ when I get past that. Otherwise I’m back where I started, whatever that means.”

“What do you see? What changes during the episode?”

“Little things. <brief fizzing sound. She … flickered.> Like ‘over there’ you’re wearing a bright green T-shirt instead of what you’re wearing here. And you’re using pen-and-paper instead of that laptop. Green doesn’t suit you.”

“I know, which is why there’s nothing green in my wardrobe, here. But that gives me an idea. Did you always have to ‘push’ to get ‘over there’?”

“Usually.”

“Fine. OK, I’m going to flip this coin. While it’s in the air, ‘push’ just lightly and come back to tell me which way the coin fell.”

<fizzing> “Heads.”

“It’s tails here. OK, we’re going to do that again but this time ‘push’ much harder.”

<louder fizzing> “That was weird. Your coin rolled off the desk and landed on edge in a crack in the floor so it’s not heads or tails.”

“AaaHAH!”

“?”

“Your ‘over theres’ have different levels of probability than ‘over here.’ They’re different realities. Actually, I’ll bet you travel across ranges of probability. Or tunnel through them, maybe. That’d why you have to ‘push’ to get past something that’s less probable in order to get to something that’s more probable. Like getting past a reality where the coin can just hang in the air or fly apart.”

“I’ve done that. Once I sneezed while ‘pushing’ and wound up sitting at a tea party where the cream and sugar just refused to stir into the tea. When I ‘pushed’ from there I practically fell into a coffee shop where the coffee was well-behaved.”

“Case closed. Now I can answer your question. Spacewise, you’re in my office on the twelfth floor. Timewise, I just showed you my clock. As for which reality, you’re in one with a very high probability because, well, you’re here.”

“So provincial. Oh, Mr Moire, how little you know.” <fizzing>

On the 12th floor of the Acme Building, high above the city, one man still tries to answer the Universe’s persistent questions — Sy Moire, Physics Eye.

~~ Rich Olcott

Twinkle, Twinkle, Tabby’s Star

On July 17, 2017November 30, 2025 By rolcottIn Astronomy: Planetary Science, Astronomy: Stellar Science, Astronomy: Techniques, Uncategorized2 Comments

Al was carrying his coffee pot past our table. “Refills? Hey, I heard you guys talking about Tabby’s Star. Have you seen the latest?”

“Ohmigawd, there’s more?”

“Yeah, Cathleen. They’ve finally found something that’s periodic.”

“Catch us up, Al. Cathleen said that the dimmings are irregular.”

“They’ve been, Sy. But remember Cathleen’s chart that showed big dips in 2011 and 2013, about 750 days apart? Well, guess what?”

“They’ve seen more dips at 750-day intervals, in 2015 and 2017.”

“Well, not quite. Nobody was looking in 2015. But Kickstarter funding let the team buy observing time in 2017. A dip came in right on schedule. Here’s the picture. [shows smartphone around]”

WTF 2017 peak after day 5 — Visible-light photometry of Tabby’s Star
14-28 May 2017
Image from Dr Boyajian’s blog

Cathleen snorted. “Damn shame we need crowd-funding to support Science these days.”

“True,” I agreed, “but the good news is that the support is there. Suddenly you’re scribbling on the back of that envelope. So what does this chart tell us?”

“I’m sure every astronomer out there will tell you, ‘It’s too soon to say anything for sure.‘ This is raw data, which means it’s hasn’t gone through the usual clean-up process to account for instrumental issues, long-term trending, things like that. The timing is great, though. The bottom of this dip is at 18May2017. The first dip bottomed out 2267 days earlier on 4March2011. Counting the 2015 case that no-one saw, there’d be three intervals from first to most recent. 2267÷3 makes the average 756 days. Add 756 to the first date and we’re at 28Mar2013, right in the midst of that year’s complex mess. It does fit together.”

“So whatever’s causing it has a 756-day orbit?”

“Could be. I know your next question. If the eclipsing material were in our Solar System, it’d be a bit outside the 687-day orbit of Mars. But we’ve already ruled out causes near our solar system. Tabby’s Star is about 1½ times our Sun’s mass. That 756-day orbit around Tabby, if it is one, is maybe 30% wider than the orbit of Mars. But.”

[both] “But?”

“But the dip profiles don’t match up from one cycle to the next. This dip’s only 2% or so, a tenth of the ones in 2011 and 2013. Of course, the 2013 event spanned multiple dips so Heaven knows which one we should match to. Even 2011 and 2017 don’t look the same. The usual quick-and-dirty way to compare dips is to pair up widths at half depth. That statistic for 2011 is about a day. This one is twice that or more. If the absorber is orbiting the star, it’s changing shape and can’t be a planet.”
“So what do we got, Sy?”

“Damifino, Al. Everything Cathleen just told us points to something like an enormous comet loaded with loose rocks that go flying along random paths away from the star.”

“Sorry, Sy, the infrared data rules out the comet dust that would have to be spewed out along with the rocks. Besides, someone calculated just how much rocky material would be required to reproduce the dimming we’ve seen already. You’d need a ‘comet’ somewhere between Earth-size and Jupiter-size, and maybe more than one, and with that much mass the rocks wouldn’t fly apart very well. Oh, and there’s that long-term fading, which the comet idea doesn’t account for.”

“So we’re down to…”

[sigh] “The explanation of last resort, which astronomers are very reluctant to talk about because journalists tend to go overboard. Maybe, just maybe, we’re witnessing an advanced civilization at work, constructing a Dyson sphere around a star 1500 light years away. People have talked about such things for decades. Think about it — the Sun sends out light in all directions. Earth intercepts only a billionth of that. If we could completely surround the Sun with solar panels we’d have access to a billion times more energy than if we covered our own planet with panels. Better yet, it’s all renewable and producing 24 hours a day. But even with advanced technology, panels around Tabby’s Star would still radiate in the infrared and we don’t see that.”

My smartphone chirped that same odd ringtone and it was that same odd number, 710-555-1701. “Hello, Ms Baird.”

“The Universe is not only stranger than you imagine, Mr Moire, it’s stranger than you can imagine.”

~~ Rich Olcott

Tabby’s Star — Weird Or Really Weird?

On July 10, 2017November 30, 2025 By rolcottIn Astronomy: Planetary Science, Astronomy: Stellar Science, Astronomy: Techniques, UncategorizedLeave a comment

I needed some time to mull over what Cathleen had told me about Tabby’s Star, so I went to the counter to replenish our coffee and scones. When I returned I said, “OK, let’s recap. Dr Boyajian’s Planet Hunters citizen scientists found a star that dims oddly. But I understand there’s lots of variable stars out there. What’s so special about this one that the SETI project got interested?”

“There’s variable stars and variable stars, but this one shouldn’t vary. Look, one of the triumphs of 20th-century science is that we pretty much understand how stars work. You tell me a handful of a star’s properties, things like radius, surface temperature, iron/hydrogen ratio, a couple more, and I can give you its whole life story from light-up to nova. We’ve catalogued about 70,000 variable stars. Virtually all of them do episodic brightening — pulsating or flaring up. There’s about a hundred that dim more or less regularly, but they’re supergiants with cool, sooty atmospheres. Tabby’s Star is a flat-out normal F-type main sequence star, about 1½ times the Sun’s mass and a little bit warmer. Like the clean-cut kid next door — no reason to expect trouble from it.”

“So if it’s not the star itself that’s dimming, then something must be getting between it and us.”

“Well, yeah. The question is what. There’s so many theories that one pair of authors wrote a 15-page paper just classifying and rating them.”

“Gimme a few.”

“Clouds of interstellar dust, for starters. Sodium’s sparse in stars and the interstellar medium, but it’s got two easily recognized strong absorption lines in the yellow part of the visible spectrum. Tabby’s sodium lines are broad and weak like you’d expect in a star’s atmosphere, but in the data they’re overlain by sharp, intense absorption peaks that can only come from sodium-bearing gas or dust in the nine-quadrillion-mile journey from there to here. So there’s dispersed matter in the line of sight, but it can account for at most 35% of the dimming. Furthermore, an interstellar cloud would have a hard time maintaining structures small enough to produce the sharp dim-and-recover pattern Boyajian found. Loosely-bound stuff like dust clouds and gas tends to smear out in space.”

“How about comets, or rings, or clumps of asteroids orbiting the star?”

“There’s evidence against all those, but I guess I haven’t mentioned it yet. You’ve seen the heat lamps over Eddie’s pizza bar?”

“Sure. Infrared radiation heats things up.”

“And warm things give off infrared radiation. ‘Warm’ meaning anything above absolute zero. Better yet, there’s a well-known relation between an object’s temperature and its infrared spectrum. Rocks or dust anywhere near the star would absorb energy from whatever kind of light and re-radiate it as heat infrared we could see. The spectrum would show more infrared than you’d expect from the star itself. And there isn’t any extra infrared.”

“None?”

“Not so’s our technology can detect. If there’s any there, it’s less than 0.2% of the total coming from the star, nowhere near enough to account for those 8%, 16% and 22% dips. So no, no comets or rings or asteroid clumps orbiting Tabby’s Star.”

“How about something orbiting our Sun, way far out where we’ve not found it yet?”

“Any light-blocking object near us, like maybe in the Oort Cloud that sends us long-term comets, should produce the same sort of weirdness from Tabby’s near neighbors. We don’t see that. One astronomer studied a star only 25 arc-seconds away — steady as a rock. So whatever’s causing the dimming is probably close to Tabby’s star. Oh, wait, here’s one more weirdness. I just saw a report…” [twiddles on tablet] “Yeah, here it is. Check out this chart.”“You’ll have to unravel that for me.”

“Sure. The Planet Hunter team was looking for transits, which generally take at most a few days, so the Kepler science team filtered out slow variations before passing the data along. After Boyajian’s report came out, two Keplerians looked back at the raw data. I told you about the 3-6% dimming (estimates vary) since 1890. The raw Kepler data show a 3% drop in four years!”

“I’m starting to think about Dyson Spheres and Larry Niven’s Ringworld.”

“Now you know why SETI got excited.”

~~ Rich Olcott

The Weirdest, And Naughtiest, Star in The Galaxy

On July 3, 2017November 30, 2025 By rolcottIn Astronomy: Planetary Science, Astronomy: Stellar Science, Astronomy: Techniques, UncategorizedLeave a comment

It was an interesting ringtone — aggressive but feminine, with a hint of desperation. And it was a ringtone I hadn’t programmed into my phone. The number was intriguing, too — 710-555-1701. It didn’t add up, so I answered the ring. “Moire here.”

“Hello, Mr Moire, this is Victoria Baird.”

“It’s been a long time, Ms Baird. What can I do for you?” Her voice and the memory of her pointed ears sent chills down my spine.

“This time it’s what I can do for you, Mr Moire. Here’s a tip — Tabby’s star.” I could hear the italics. I wanted to ask questions but the line went dead.

Considering the context, I called my Astronomy Department source. “Morning, Cathleen. It’s break time, can I buy you some of Al’s coffee and a scone?”

“You’re going to ask me questions, aren’t you? What am I going to have to bone up on? I know, it’s Tabby’s Star, right?”

“Got it in one, Cathleen. Meet you at Al’s?”

“Yeah, give me 15 minutes.”

A quarter-hour later we had a table, two mugs of coffee and a plate of scones in front of us. “So how’d you know I’d be asking about Tabby’s star? And what is it? And who is Tabby?”

“Tabby is Tabetha (she spells it with an ‘e’) Boyajian, PhD. She teaches Astronomy at Louisiana State, does research specializing in high-precision star measurement. In her spare time she manages a citizen-scientist project called Planet Hunters. The Hunters get their kicks combing through databases from the Kepler satellite telescope. They get all excited if the records indicate that a star’s been transited.”

“Oh, like that star-dimming that found the TRAPPIST-1 planets?”

“Exactly. I think they’ve got over a hundred candidate planetary systems and a couple-dozen confirmed ones to their credit by now. Anyhow, 2012 was a banner year for them, ’cause they raised an alert on what’s now being called the weirdest star in the galaxy.”

“Which would be Tabby’s Star. Got it. But what’s weird about it?”

“Poets like to write about ‘the constant stars.’ This star is world-champion not-constant. You know how stars seem to flicker when you look at them?”

“Yeah, that’s how I tell them apart from planets.”

“Then you know that the flickering comes from starlight getting messed up going through our turbulent atmosphere. Astronauts don’t see the flickering. Neither does Kepler up there, so it can reliably detect miniscule variations in a star’s output. Virtually all of the 150,000 stars it tracked for four years had rock-steady production. A few of them occasionally dimmed or flared by maybe a percent, but Tabby’s Star (formally known as KIC 8462852) got the Hunters’ attention when it dimmed by 16%.”

“Twenty times a normal dimming! Did it stay that way or did the light come back up again?”

“Oh, it came back all right, but the curve on the way up didn’t match the curve on the way down. That was even weirder. So the team scoured through the star’s 4-year record and found a dozen events on the 0.05-2% scale, plus one at 8% and another at 21%.”

“21%? That’s a big shadow.”

“Ya think? Especially since the between-event timing was seriously irregular and some of those events were complex with three or more separate components. But that’s not all the weirdness. Those dips lasted for hours or even days, longer than most planetary transits. After Boyajian and her 48 collaborators published their initial report, which has to have one of the naughtiest titles in the astronomical literature, some other —”

“Wait, a naughty title? C’mon, don’t tease.”

“OK <sigh>. The technical term for a star’s light output is flux. That paper was half about the observations and half about what might be causing the variation. Assuming the star’s real output is constant, the question becomes, ‘What happened to that missing light?‘ Or as the authors put it, ‘Where’s The Flux?‘ Since then both the paper and the star have been informally referred to as WTF. OK?”

“OK <sigh>. So you were saying there’s something else.”

“Yeah. Some other astronomers went digging in the archives. WTF has been dimming gradually for at least the past 100 years. Weird, eh?”

“Yeah. So what’s causing it?”

“We don’t even have good guesses.”

~~ Rich Olcott

Gozer, The Stay Puft Black Hole

On June 26, 2017November 30, 2025 By rolcottIn Astronomy: Stellar Science, Gravitational astronomy, Physics: Black Holes and Relativity, UncategorizedLeave a comment

We’re downstairs at Eddie’s Pizza. Vinnie orders his usual pepperoni. In memory of Sam Panapoulos, I order a Hawaiian. Then we’re back to talking black holes.

“I been thinking, Sy. These regular-size black holes, the ones close to the Sun’s mass, we got a lot of ’em?”

“I’ve seen an estimate of 50,000 in the Milky Way Galaxy so you could say they’re common. That’s one way to look at it. The other way is to compare 50,000 with the 250 billion stars in the galaxy. One out of 5,000,000 is a black hole, so they’re rare. Your choice, Vinnie.”

“But all three confirmed LIGO signals were the next bigger size range, maybe 10 to 30 solar masses; two of ’em hittin’ each other and they’ve all been more than a billion lightyears away. How come LIGO doesn’t see the little guys that are close to us?”

“Darn good question. Lessee… OK, I’ve got several possibilities. Maybe the close-in little guys do collide, but the signal’s too weak for us to detect. But we can put numbers to that. In each LIGO event we’ve seen, the collision released about 10% of their 40-to-60-Sun total mass-energy in the form of gravitational waves. LIGO’s just barely able to detect that, right?”

“They were excited they could, yeah.”

“So if a pair of little-guy black holes collided they’d release about 10% of two makes 0.2 solar masses worth of energy. That’d be way below our detection threshold if the collision is a billion light-years away. But we’re asking about collisions inside the Milky Way. Suppose the collision happened near the center, about 26,000 lightyears from us. Signal strength grows as the square of how close the source is, so multiply that ‘too weak to detect’ wave by (1 billion/26000)² =15×10¹², fifteen quadrillion. LIGO’d be deafened by a signal that strong.”

“But LIGO’s OK, so we can rule that out. Next guess.”

“Maybe the signal’s coming in at the wrong frequency. The equations say that just before a big-guy collision the two objects circle each other hundreds of times a second. That frequency is in the lower portion of the 20-20,000 cycles-per-second human audio range. LIGO’s instrumentation was tuned to pick up gravitational waves between 30 and 7,000. Sure enough, LIGO recorded chirps that were heard around the world.”

“So what frequency should LIGO be tuned to to pick up little-guy collisions?”

“We can put numbers to that, too. Physics says that at a given orbit radius, revolution frequency varies inversely with the square root of the mass. The big-guy collisions generated chirps between 100 and 400 cps. Little guy frequencies would be f₂/f₅₀=√(50/2)=5 times higher, between 500 and 2000 cps. Well within LIGO’s range.”

“We don’t hear those tweets so that idea’s out, too. What’s your third try?”

“Actually I like this one best. Maybe the little guys just don’t collide.”

“Why would you like that one?”

“Because maybe it’s telling us something. It could be that they don’t collide simply because they’re surrounded by so many other stars that they never meet up. But it also could be that binary black holes, the ones that are fated to collide with each other, are the only ones that can grow beyond 10 solar masses. And I’ve got a guess about how that could happen.”

“Alright, give.”

“Let’s start with how to grow a big guy. Upstairs we talked about making little guys. When a star’s core uses up one fuel, like hydrogen, there’s an explosive collapse that sets off a hotter fuel, like helium, until you get to iron which doesn’t play. At each step, unburnt fuel outside the core gets blown away. If the final core’s mass is greater than about three times the Sun’s you wind up with a black hole. But how about if you don’t run out of fuel?”

“How can that happen? The star’s got what it’s got.”

“Not if it’s got close neighbors that also expel unburnt fuel in their own burn-collapse cycles. Grab their cast-off fuel and your core can get heavier before you do your next collapse. Not impossible in a binary or cluster where all the stars are roughly the same age. Visualize kids tossing marshmallows into each other’s mouths.”

“Or paying for each other’s pizzas. And it’s your turn.”

~~ Rich Olcott

Prelude to A Waltz

On June 19, 2017November 30, 2025 By rolcottIn Astronomy: Stellar Science, Gravitational astronomy, Physics: Black Holes and Relativity, UncategorizedLeave a comment

An excited knock, but one I recognize. In comes Vinnie, waving his fresh copy of The New York Times.

“LIGO‘s done it again! They’ve seen another black hole collision!”

“Yeah, Vinnie, I’ve read the Abbott-and-a-thousand paper. Three catastrophic collisions detected in less than two years. The Universe is starting to look like a pretty busy place, isn’t it?”

“And they all involve really big black holes — 15, 20, even 30 times heavier than the Sun. Didn’t you once say black holes that size couldn’t exist?”

“Well, apparently they do. Of course the physicists are busily theorizing how that can happen. What do you know about how stars work, Vinnie?”

“They get energy from fusing hydrogen atoms to make helium atoms.”

“So far, so good, but then what happens when the hydrogen’s used up?”

“They go out, I guess.”

“Oh, it’s a lot more exciting than that. Does the fusion reaction happen everywhere in the star?”

“I woulda said, ‘Yes,’ but since you’re asking I’ll bet the answer is, ‘No.'”

“Properly suspicious, and you’re right. It takes a lot of heat and pressure to force a couple of positive nuclei close enough to fuse together despite charge repulsion. Pressures near the outer layers are way too low for that. For our Sun, for instance, you need to be 70% of the way to the center before fusion really kicks in. So you’ve got radiation pressure from the fusion pushing everything outward and gravity pulling everything toward the center. But what’s down there? Here’s a hint — hydrogen’s atomic weight is 1, helium’s is 4.”

“You’re telling me that the heavier atoms sink to the center?”

“I am.”

“So the center builds up a lot of helium. Oh, wait, helium atoms got two protons in there so it’s got to be harder to mash them together than mashing hydrogens, right?”
“And that’s why that region’s marked ash zone in this sketch. Wherever conditions are right for hydrogen fusion, helium’s basically inert. Like ash in a campfire it just sinks out of the way. Now the fire goes out. What would you expect next?”

“Radiation pressure’s gone but gravity’s still there … everything must slam inwards.”

“Slam is an excellent word choice, even though the star’s radius is measured in thousands of miles. What’s the slam going to do to the helium atoms?”

“Is it strong enough to start helium fusion?”

“That’s where I’m going. The star starts fusing helium at its core. That’s a much hotter reaction than hydrogen’s. When convective zone hydrogen that’s still falling inward meets fresh outbound radiation pressure, most of the hydrogen gets blasted away.”

“Fusing helium – that’s a new one on me. What’s that make?”

“Carbon and oxygen, mostly. They’re as inert during the helium-fusion phase as helium was when hydrogen was doing its thing.”

“So will the star do another nova cycle?”

“Maybe. Depends on the core’s mass. Its gravity may not be intense enough to fuse helium’s ashes. In that case you wind up with a white dwarf, which just sits there cooling off for billions of years. That’s what the Sun will do.”

“But suppose the star’s heavy enough to burn those ashes…”

“The core’s fresh light-up blows away infalling convective zone material. The core makes even heavier atoms. Given enough fuel, the sequence repeats, cycling faster and faster until it gets to iron. At each stage the star has less mass than before its explosion but the residual core is more dense and its gravity field is more intense. The process may stop at a neutron star, but if there was enough fuel to start with, you get a black hole.”

“That’s the theory that accounts for the Sun-size black holes?”

“Pretty much. I’ve left out lots of details, of course. But it doesn’t account for black holes the size of 30 Suns — really big stars go supernova and throw away so much of their mass they miss the black-hole sweet spot and terminate as a neutron star or white dwarf. That’s where the new LIGO observation comes in. It may have clued us in on how those big guys happen.”

“That sketch looks like a pizza slice.”

“You’re thinking dinner, right?”

“Yeah, and it’s your turn to buy.”

~~ Rich Olcott

Three Perils for a Quest(ion), Part 3

On June 12, 2017November 30, 2025 By rolcottIn Physics: Black Holes and Relativity, Physics: Quantum Mechanics, UncategorizedLeave a comment

“Things are finally slowing down. You folks got an interesting talk going, mind if I join you? I got biscotti.”

“Pull up a chair, Eddie. You know everybody?”

“You and Jeremy, yeah, but the young lady’s new here.”

“I’m Jennie, visiting from England.”

“Pleased to meetcha. So from what I overheard, we got Jeremy on some kinda Quest to a black hole’s crust. He’s passed two Perils. There’s a final one got something to do with a Firewall.”

“One minor correction, Eddie. He’s not going to a crust, because a black hole doesn’t have one. Nothing to stand on or crash into, anyway. He’s headed to its Event Horizon, which is the next best thing. If you’re headed inward, the Horizon marks the beginning of where it’s physically impossible to get out.”

“Hotel California, eh?”

“You could say that. The first two Perils had to do with the black hole’s intense gravitational field. The one ahead has to do with entangled virtual particles.”

“Entangled is the Lucy-and-Ethel thing you said where two particles coordinate instant-like no matter how far apart they are?”

“Good job of overhearing, there, Eddie. Jeremy, tell him abut virtual particles.”

“Umm, Mr Moire and I talked about a virtual particle snapping into and out of existence in empty space so quickly that the long-time zero average energy isn’t affected.”

“What we didn’t mention then is that when a virtual pair is created, they’re entangled. Furthermore, they’re anti-particles, which means that each is the opposite of the other — opposite charge, opposite spin, opposite several other things. Usually they don’t last long — they just meet each other again and annihilate, which is how the average energy stays at zero. Now think about creating a pair of virtual particles in the black hole’s intense gravitational field where the creation event sends them in opposite directions.”
“Umm… if they’re on opposite paths then one’s probably headed into the Horizon and the other is outbound. Is the outbound one Hawking radiation? Hey, if they’re entangled that means the inbound one still has a quantum connection with the one that escaped!”

“Wait on. If they’re entangled and something happening to one instantaneously affects its twin, but the gravity difference gives each a different rate of time dilation, how does that work then?”

“Paradox, Jennie! That’s part of what the Firewall is about. But it gets worse. You’d think that inbound particle would add mass to the black hole, right?”

“Surely.”

“But it doesn’t. In fact, it reduces the object’s mass by exactly each particle’s mass. That ‘long-time zero average energy‘ rule comes into play here. If the two are separated and can’t annihilate, then one must have positive energy and the other must have negative energy. Negative energy means negative mass, because of Einstein’s mass-energy equivalence. The positive-mass twin escapes as Hawking radiation while the negative-mass twin joins the black hole, shrinks it, and by the way, increases its temperature.”

“Surely not, Sy. Temperature is average kinetic energy. Adding negative energy to something has to decrease its temperature.”

“Unless the something is a black hole, Jennie. Hawking showed that a black hole’s temperature is inversely dependent on its mass. Reduce the mass, raise the temperature, which is why a very small black hole radiates more intensely than a big one. Chalk up another paradox.”

“Two paradoxes. Negative mass makes no sense. I can’t make a pizza with negative cheese. People would laugh.”

“Right. Here’s another. Suppose you drop some highly-structured object, say a diamond, into a black hole. Sooner or later, much later really, that diamond’s mass-energy will be radiated back out. But there’s no relationship between the structure that went in and the randomized particles that come out. Information loss, which is totally forbidden by thermodynamics. Another paradox.”

“The Firewall resolves all these paradoxes then?”

“Not really, Jennie. The notion is that there’s this thin layer of insanely intense energetic interactions, the Firewall, just outside of the Event Horizon. That energy is supposed to break everything apart — entanglements, pre-existing structures, quantum propagators (don’t ask), everything, so what gets through the horizon is mush. Many physicists think that’s bogus and a cop-out.”

“So no Firewall Peril?”

“Wanna take the chance?”

~~ Rich Olcott

Three Perils for a Quest(ion), Part 2

On June 5, 2017November 30, 2025 By rolcottIn Physics: Black Holes and Relativity, Physics: Quantum Mechanics, UncategorizedLeave a comment

Eddie came over to our table. “Either you folks order something else or I’ll have to charge you rent.” Typical Eddie.

“Banana splits sound good to you two?”

[Jeremy and Jennie] “Sure.”

“OK, Eddie, two banana splits, plus a coffee, black, for me. And an almond biscotti.”

“You want one, that’s a biscotto.”

“OK, a biscotto, Eddie. The desserts are on my tab.”

“Thanks, Mr Moire.”

“Thanks, Sy. I know you want to get on to the third Peril on Jeremy’s Quest for black hole evaporation, but how does he get past the Photon Sphere?”

“Yeah, how?”

“Frankly, Jeremy, the only way I can think of is to accept a little risk and go through it really fast. At 2/3 lightspeed, for instance, you and your two-meter-tall suit would transit that zero-thickness boundary in about 10 nanoseconds. In such a short time your atoms won’t get much out of position before the electromagnetic fields that hold your molecules together kick back in again.”

“OK, I’ve passed through. On to the Firewall … but what is it?”

“An object of contention, for one thing. A lot of physicists don’t believe it exists, but some claim there’s evidence for it in the 2015 LIGO observations. It was proposed a few years ago as a way out of some paradoxes.”

“Ooo, Paradoxes — loverly. What’re the paradoxes then?”

“Collisions between some of the fundamental principles of Physics-As-We-Know-It. One goes back to the Greeks — the idea that the same thing can’t be in two places at once.”

“Tell me about it. Here’s your desserts.”

“Thanks, Eddie. The place keeping you busy, eh?”

“Oh, yeah. Gotta be in the kitchen, gotta be runnin’ tables, all the time.”

“I could do wait-staff, Mr G. I’m thinking of dropping track anyway, Mr Moire, 5K’s don’t have much in common with base running which is what I care about. How about I show up for work on Monday, Mr G?”

“Kid calls me ‘Mr’ — already I like him. You’re on, Jeremy.”

“Woo-hoo! So what’s the link between the Firewall and the Greeks?”

“Link is the right word, though the technical term is entanglement. If you create two particles in a single event they seem to be linked together in a way that really bothered Einstein.”

“For example?”
“Polarizing sunglasses. They depend on a light wave’s crosswise electric field running either up-and-down or side-to-side. Light bouncing off water or road surface is predominately side-to-side polarized, so sunglasses are designed to block that kind. Imagine doing an experiment that creates a pair of photons named Lucy and Ethel. Because of how the experiment is set up, the two must have complementary polarizations. You confront Lucy with a side-to-side filter. That photon gets through, therefore Ethel should be blocked by a side-to-side filter but should go through an up-and-down filter. That’s what happens, no surprise. But suppose your test let Lucy pass an up-and-down filter. Ethel would pass a side-to-side filter.”

“But Sy, isn’t that because each photon has a specific polarization?”

“Yeah, Jennie, but here’s the weird part — they don’t. Suppose you confront Lucy with a filter set at some random angle. There’s only the one photon, no half-way passing, so either it passes or it doesn’t. Whenever Lucy chooses to pass, Ethel usually passes a filter perpendicular to that one. It’s like Ethel hears from Lucy what the deal was — and with zero delay, no matter how far away the second test is executed. It’s as though Lucy and Ethel are a single particle that occupies two different locations. In fact, that’s exactly how quantum mechanics models the situation. Quite contrary to the Greeks’ thinking.”

“You said that Einstein didn’t like entanglement, either. How come?”

“Einstein published the original entanglement mathematics in the 30s as a counterexample against Bohr’s quantum mechanics. The root of his relativity theories is that the speed of light is a universal speed limit. If nothing can go faster than light, instantaneous effects like this can’t happen. Unfortunately, recent experiments proved him wrong. Somehow, both Relativity and Quantum Mechanics are right, even though they seem to be incompatible.”

“And this collision is why there’s a problem with black hole evaporation?”

“It’s one of the collisions.”

“There’s more? Loverly.”

~~ Rich Olcott

Three Perils for a Quest(ion), Part 1

On May 29, 2017November 30, 2025 By rolcottIn Physics: Black Holes and Relativity, Physics: Quantum Mechanics, Uncategorized2 Comments

Eddie makes great pizzas but Jeremy thinks they stay in the oven just a little too long. As he crunched an extra-crispy wedge-edge he mused, “Gravity aside, I wonder what it’d be like to land on a black hole. I bet it’d be real slippery if it’s as smooth as Mr Moire says.”

Jennie cut in. “Don’t be daft, lad. Everyone’s read about the spaceman sliding through the event horizon unaware until it’s too late. Someone far away sees the bloke’s spacetime getting all distorted but in his local frame of reference everything’s right as rain. Right, Sy?”

“As rain, Jennie, if all you’re concerned about is relativity. But Spaceman Jeremy has lots of other things to be concerned about on his way to the event horizon. Which he couldn’t stand on anyway.”

“Why not, Mr Moire? I mean, I said ‘gravity aside’ so I ought to be able to stand up.”

“Nothing to stand on, Jeremy. It’d be like trying to stand on Earth’s orbit.”

“Pull the other one, Sy. How can they be alike?”

“Both of them are mathematical constructs rather than physical objects. An orbit is an imaginary line that depicts planet or satellite locations. An event horizon is an imaginary figure enclosing a region with such intense spacetime curvature that time points inward. They’re abstract objects, not concrete ones. But let’s get back to Jeremy’s black hole evaporation quest. He’ll have to pass three perils.”

“Ooo, a Quest with Perils — loverly. What are the Perils then?”

“The Roche Radius, the Photon Sphere and the Firewall. Got your armor on, Jeremy?”

“Ready, Mr Moire.”

“Stand up. The Roche effect is all about gravitational discrepancy between two points. The two meter distance between your head and feet isn’t enough for a perceptible difference in downward pull. However, when we deal with astronomical distances the differences can get significant. For instance, ocean water on the day side of Earth is closer to the Sun and experiences a stronger sunward pull than water on the night side.”

“Ah, so that’s why we get tides.”

“Right. Sit, sit, sit. So in 1849 Édouard Roche wondered how close two objects could get until tidal forces pulled one of them apart. He supposed the two objects were both just balls of rocks or fluid held together by gravity. Applying Newton’s Laws and some approximations he got a formula for threshold distance in terms of the big guy’s mass and the little guy’s density. Suppose you’re held together only by gravity and you’re nearing the Sun feet-first. Its mass is 2×10³⁰ kg/m³. Even including your space armor, your average density is about 1.5 kg/m³. According to Roche’s formula, if you got closer than 8.6×10⁶ kilometers your feet would break away and fall into the Sun before the rest of you would. Oh, that distance is about 1/7 the radius of Mercury’s orbit so it’s pretty close in.”

“But we’re talking black holes here. What if the Sun collapses to a black hole?”

“Surprisingly, it’s exactly the same distance. The primary’s operative property is its mass, not its diameter. Good thing Jeremy’s really held together by atomic and molecular electromagnetism, which is much stronger than gravity. Which brings us to his second Peril, the dreaded Photon Sphere.”

“Should I shudder, Sy?”

“Go ahead, Jennie. The Sphere is another mathematical object, not something physical you’d collide with, Jeremy. It’s a zero-thickness shell representing where electromagnetic waves can orbit a massive object like a black hole or a neutron star. Waves can penetrate the shell easily in either direction, but if one happens to fly in exactly along a tangent, it’s trapped on the Sphere.”

“That’s photons. Why is it a peril to me?”

“Remember that electromagnetism that holds you together? Photons carry that force. Granted, in a molecule they’re standing waves rather than the free waves we see with. The math is impossible, but here’s the Peril. Suppose one of your particularly important molecules happens to lie tangent to the Sphere while you’re traversing it. Suddenly, the forces holding that molecule together fly away from you at the speed of light. And that disruption inexorably travels along your body as you proceed on your Quest.”

[both shudder]

~~ Rich Olcott

The Thin Edge of Infinity

On May 22, 2017November 30, 2025 By rolcottIn Physics: Black Holes and Relativity, UncategorizedLeave a comment

Late in the day, project’s half done but it’s hungry time. I could head home for a meal and drive back, but instead I board the elevator down to Eddie’s Pizza on the second floor. The door opens on 8 and Jeremy gets on, with a girl.

“Oh, hi, Mr. Moire. Didja see I hit a triple in the last game? What if the Sun became a black hole? This is that English girl I told you about.”

“Hello, Jennie.”

“Wotcha, Sy.”

“You know each other?”

“Ra-ther. He wrote me into his blog a year ago. You were going on about particles then, right, Sy?”

“Right, Jennie, but that was particles confined in atoms. Jeremy’s interested in larger prey.”

“So I hear.”

The elevator lets us out at Eddie’s place. We luck into a table, order and resume talking. I open with, “What’s a particle?”

“Well, Sy, your post with Jeremy says it’s an abstract point with a minimal set of properties, like mass and charge, in a mathematical model of a real object with just that set of properties.”

“Ah, you’ve been reading my stuff. That simplifies things. So when can we treat a black hole like a particle? Did you see anything about that in my archives, Jennie?”

“The nearest I can recall was Professor ‘t Hooft’s statement. Ermm… if the Sun’s so far away that we can calculate planetary orbits accurately by treating it as a point, then we’re justified in doing so.”

“And if the Sun were to suddenly collapse to a black hole?”

“It’d be a lot smaller, even more like a point. No change in gravity then. But wouldn’t Earth be caught up in relativity effects like space compression?’

“Not unless you’re really close. Space compression around a non-rotating (Schwarzchild) black hole scales by a factor that looks like , where D is the object’s diameter and d is your distance from it. Suppose the Sun suddenly collapsed without losing any mass to become a Schwarzchild object. The object’s diameter would be a bit less than 4 miles. Earth is 93 million miles from the Sun so the compression factor here would be [poking numbers into my smartphone] 1.000_000_04. Nothing you’d notice. It’d be 1.000_000_10 at Mercury. You wouldn’t see even 1% compression until you got as close as 378 miles, 10% only inside of 43 miles. Fifty percent of the effect shows up in the last 13 miles. The edge of a black hole is sharper than this pizza knife.”

“How about if it’s spinning? Ms Plenum referred me to a reading about frame-dragging.”

“Ah, Jeremy, you’re thinking of Gargantua, the Interstellar movie’s strangely lopsided black hole. I just ran across this report by Robbie Gonzalez. He goes into detail on why the image is that way, and why it should have looked more like this picture. Check out the blueshift on the left and the shift into the infra-red on the right.”

better Gargantua — A more accurate depiction of Gargantua. Image from
James, et al., **Class. Quantum Grav. 32** (2015) 065001 (41pp),
licensed under **CC BY-NC-ND 3.0**

[both] “Awesome!”

“So it’s the spin making the weirdness then, Sy?”

“Yes, ma’am. If Gargantua weren’t rotating, then the space around it would be perfectly spherical. As Gonzalez explains, the movie’s plotline needed an even more extreme spacetime distortion than they could get from that. Dr Kip Thorne, their physics guru, added more by spinning his mathematical model nearly up to the physical limit.”

“I’ll bite, Mr Moire. What’s the limit?”

“Rotating so fast that points on the equator would be going at lightspeed. Can’t do that. Anyhow, extreme spin alters spacetime distortion, which goes from spherical to pumpkin-shaped with a twist. The radial scaling changes form, too, from to . A is proportional to spin. When A is small (not much spin) or the distance is large those A/d² terms essentially vanish relative to the others and the scaling looks just like the simple almost-a-point Schwarzchild case. When A is large or the distance is small the A/d² terms dominate top and bottom, the factor equals 1 and there’s dragging but no compression. In the middle, things get interesting and that’s where Dr Thorne played.”

“So no relativity jolt to Earth.”

“Yep.”

“Here’s your pizzas.”

“Thanks, Eddie.”

[sounds of disappearing pizza]

~~ Rich Olcott

Hard Science Ain't Hard

Author: rolcott

Through The Looking Glass, Darkly

Twinkle, Twinkle, Tabby’s Star

Tabby’s Star — Weird Or Really Weird?

The Weirdest, And Naughtiest, Star in The Galaxy

Gozer, The Stay Puft Black Hole

Prelude to A Waltz

Three Perils for a Quest(ion), Part 3

Three Perils for a Quest(ion), Part 2

Three Perils for a Quest(ion), Part 1

The Thin Edge of Infinity