biology, physical experiment, science, short, Weird Food

Real Mad Science 2: Mead

Mad Science Mead.png

I used to be pretty fond of booze. My favorite libations were Johnnie Walker Black Label, cheap supermarket Moscato, this horrible fluorescent-blue fruity cognac stuff called Hpnotiq (yes, really), and White Russians. But, towards the end of my college career, I made a nasty error: I got careless with Jägermeister. Jäger, exactly like plutonium or nitroglycerin, is very unforgiving of carelessness. The next day was among the ugliest in my life, and I’ve hardly touched hard liquor since then.

That’s actually a good thing, since it nudged me towards drinking less stomach-scorching things like proper decent wine and beer (and alcoholic ginger beer). And, since I’ve been in a mad science mood lately, I decided I’d take advantage of Amazon’s “Black Friday is happening some time during this month money money money” sale and pick up a little proper brewing equipment.

Several words of warning. 1) Home brewing comes with risks. You could get nasty unwanted yeasts or bacteria or mold that turn your brew toxic. To that end, I sterilized my equipment with a cheap and easy (and slightly nostril-stinging) potassium metabisulfite-citric acid wash. 2) Booze can get you into trouble if you don’t treat it with respect, and it’ll get you into a lot of trouble if you’re under drinking age. 3) Home brewing is illegal some places.

Now that I’ve made it painfully obvious that I’m trying not to get sued, it’s time to make mead! Mead is a fermented honey beverage favorited by Norsemen, English Majors, Beowulf, and pretty much everybody in Skyrim. Here’s how I made it:

I added two cups of honey (about 475 mL) to a saucepan. Because it was a really cold day, I added some water to make the honey less viscous. (Filtered well water, mind you.) To make sure the yeast had vitamins and minerals that pure honey might not provide, I added a generous handful (roughly 1 cup, or 100 – 150 grams) of cranberries, along with a modest handful of raisins. They were just what I had lying around. For flavor, I added about a teaspoon of cinnamon. I brought the whole mixture to a boil. I checked the temperature with an instant-read meat thermometer (never use the proper tool for the job, I always say). Once it reached 212° Fahrenheit (100° Celsiusigrade), I started a ten-minute timer. There are probably nasty unwanted things like weird bacteria, wild yeasts, mold, and microscopic politicians in the fruit and maybe the water and honey, so I figured ten minutes at a boil would heat everything enough to kill them.

Before I started boiling the mixture, I had prepared my brewing gear according to reasonable sanitary standards. Into a 1 gallon (3,750 mL) glass carboy (moonshine jug, as I’m sure many people call them), I added half a gallon (roughly 2,000 mL) of clean filtered well water. To that, I added two teaspoons of powdered potassium metabisulfite and one tablespoon of granulated food-grade citric acid. The reaction produces sulfur dioxide, which kills germs. (Don’t smell the jug while the chemicals are sitting in there: sulfur dioxide really burns the nose…) Just before it was time to pour the fruit-honey-water mixture into the carboy, I gave the carboy and the airlock (which keeps dust and other potential germ-carrying stuff falling into the carboy during fermenting) a rinse with clean water. I let the boiled mixture cool and then added it slowly to the carboy, which I’d warmed in the oven. I didn’t want to risk temperature differentials shattering the glass. Luckily, there were no problems. I bloomed 2 grams of distiller’s active dry yeast in a cup of warm water with two tablespoons of sugar dissolved in it, then added the yeast to the mixture. I topped it up almost to the top with clean water, then added the airlock, filled it with water, and gave it a gentle shake to mix the yeast in.

That was yesterday. Today, when I took the picture, the mead’s bubbling merrily away. It’s eating sugar and making things like carbon dioxide and ethanol. The airlock produces a bubble once every five or ten seconds, which tells me the fermentation’s going well. I’m not sure how long you’re supposed to leave mead, but I guess I’ll wait until the bubbling stops, which will tell me I’ve got a bunch of dead yeast drowned in ethanol. I suppose I’ll make the tasting of the mead part of my weird food series…

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electronics, physical experiment, real mad science, science, silly

Real Mad Science #1

I like the idea of those little USB power banks. If your phone dies, you can plug it into one, and boom! It’s like you’ve got a whole other battery to run your device off of. Because that is, literally, what you’ve got.

I didn’t have a power bank. I usually don’t need one, since I rarely travel too far from home, on account of the world scares me. But I decided I did want to have a powerbank for emergencies. And since I’ve been doing a bit of soldering lately anyway, I decided why not make my own.

A sensible person would have, say, bought the cheapest possible cordless drill battery and used the cells from that. I am not a sensible person. Here’s my improvised power bank (which I must add, actually works, although I forgot to turn the phone’s screen on for proof):

Ghetto Power Bank.png

That’s what normal DIY techie people do, right? They wire two lantern batteries in parallel, solder the leads to a car cigarette lighter USB charger and plug their phone into that. Right?

These are ridiculously cheap lantern batteries. Probably zinc chloride “heavy duty” cells, which means they’ll probably leak horrible corrosive stuff as they age. But, wonder of wonders, the bastards work. A few dollars, some solder, and some throwing away of common sense, and I have a perfectly functional powerbank. It’s not rechargeable, of course, but I don’t need it to be. This is for, for instance, those times when the power goes out and I can’t charge my phone, but I really wanna keep watching Big Clive videos on YouTube, and I need a charge.

There you have it: the first (and definitely not the last) act of Sublime Curiosity Real Mad Science. I should probably punch up the name.

EDIT: Here’s the powerbank after I neatened it up with a little extra solder, too much hot glue, and a switch, so that the car adapter wouldn’t run all the time and slowly drain the batteries.

Better Ghetto Powerbank.png

EDIT 2: I did a little poking around on the Internet, and found that, in all likelihood, each of these lantern batteries holds 11,000 millamp-hours. Since they’re in series, I’ve just gone and made myself a 11 amp-hour powerbank! From watching too much Big Clive, I know that an iPhone like mine will take 500 millamps if it can, but with these batteries, that’s something like 22 hours of continuous charging. Not bad, for $8 worth of batteries!

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silly, thought experiment

Short: Zeno from Coast to Coast

There’s an old joke. A mathematician and an engineer die in a car crash and go up to Heaven. They meet Saint Peter up there, and he leads them to a mile-long hallway with a big pearly door with a gold handle at the other end. Saint Peter says “Both of you have done good things and evil things in your lives. To test if you’re inherently good-natured and worthy of getting into Heaven, I’m going to put you through a challenge. Whenever I sound my trumpet, you’re allowed to walk half the remaining distance to the door. If you get to the door, you can open it and go to Heaven. But if you move more than I tell you to, or try to cheat, you’ll go to Hell.”

The two guys confer for a second. The mathematician says “It’s a trick. We’re going to Hell anyway: no matter how many times you divide the distance in half, it’ll never be zero. We’ll never actually reach the door.”

They don’t get a chance to say anything else: Saint Peter sounds his trumpet. Both guys walk half a mile, to the middle of the hallway. The mathematician is getting antsy. Saint Peter sounds his trumpet again, and they walk a quarter-mile. He sounds it again: they walk an eighth of a mile. Again: 330 feet. Again: 165 feet. By now, the mathematician’s shaking and sweating and turning beet-red. The engineer starts to say something to him, but the mathematician screams and starts running back the way he came. He doesn’t get ten paces before a hole opens beneath him and he falls into a pit of fire and brimstone.

After Saint Peter’s sounded his trumpet ten times, the engineer’s only a foot or so from the door. He turns back and looks at Peter and says “Is it all right if I reach out and turn the handle?” Saint Peter says “Of course.” The engineer opens the door. On the other side is Heaven, full of angels on clouds and such. Saint Peter says “Well, you opened the door. Go ahead and walk through.” The engineer walks through Saint Peter goes with him and says “One warning, though: all our rulers are warped, our T-squares are crooked, and our compasses are made out of rubber.” The engineer thinks for a second and says “I see. Look, is it still possible for me to go to Hell? Have they got an opening?”

That joke is one of the many warped forms of Zeno’s Paradox. It should be impossible to reach any destination, since first you have to cover half the distance, and then you have to cover a quarter of the distance, and then an eighth, and so on, and you never actually arrive. Well, I’m going to take that literally. I’m going to imagine traveling from the west coast of the United States (specifically, from The Riptide bar and honky-tonk on Taraval and 47th, in San Francisco, California) to the east coast (specifically, to the parking lot of the Holiday Inn in Wrightsville Beach, North Carolina). That’s a distance of 4,014 kilometers. I’m going to imagine covering that distance in the same fashion as in that joke: covering half the remaining distance each time. I’m going to move once every ten seconds.

1/2

I travel 2,007 kilometers in 10 seconds. I’m traveling at about 201 kilometers per second, meaning I carve a ram-heated plasma trail through the air, setting a swath of the United States on fire as I travel. If I were human (which I’m clearly not, if I’m doing this kinda shit), I’d be pulped by the acceleration required to follow the curvature of the Earth at these speeds. I stop not too far from Dodge City, Kansas. Good thing I already have to move again, because I’m pretty sure there’s an angry mob gathering.

1/2 + 1/4 = 3/4

I travel 1,003.5 kilometers in 10 seconds. I’m still setting fire to every object I pass, blinding bystanders, and knocking down trees and buildings with my shockwave. I’ve broken every window in Wichita, Kansas and Springfield, Missouri. I pause, momentarily, in the westernmost tip of Kentucky. If I were human, I’d still have been pulped by the acceleration.

1/2 + 1/4 + 1/8 = 7/8

I travel just under 502 kilometers in 10 seconds. I’m moving as fast as some of the fastest shooting stars, but at ground level. I’m wrecking everything I pass in a way the Chelyabinsk meteorite could only aspire to. My shockwave and fireball cause burns, injuries, and structural damage in Knoxville and Nashville. I scream over the Blue Ridge Mountains and stop just short of Asheville, North Carolina, which I’ve been to, and which is a nice town.

1/2 + 1/4 + 1/8 + 1/16 = 5/16

I travel 251 kilometers this jump. The centripetal acceleration required to follow the curve of the Earth is an almost-survivable 10 gees. I’m still meteoric, though, blasting through Asheville, narrowly missing Gastonia, and ruining the lives of everyone in south Charlotte. I stop not far past Charlotte. I didn’t plan it this way, but I’ve visited my hometown on my accidental rampage.

31/32

I travel 125 kilometers. Still fast enough to cause a hell of a shockwave and probably a bit of a plasma trail, but now I’m only going as fast as a high-velocity railgun projectile. To stick to the Earth, I have to accelerate downwards at 2.5 gees, which is very much survivable, especially for only ten seconds. I stop not far north of Lumberton, North Carolina, which I’ve never visited, but I’ve heard is another nice little town. We’ve got a lot of those in North Carolina, actually. It’s kinda cool.

63/64

I travel roughly 63 kilometers in 10 seconds. I’m moving at the speed of a very ambitious bullet. My centripetal acceleration is just over half a gee. I stop in a track of farmland with not much around me.

127/128

This jump covers 31 kilometers at the speed of a sniper-rifle bullet. My acceleration is 0.15 gees, which is the kind of acceleration people experience in cars on a regular basis. I’m not far outside the city limits of Wilmington, NC, in the woods between a church and a water treatment plant (according to Google Earth.)

255/256

I’m still moving like a bullet, covering 15.7 kilometers in 10 seconds. I stop over a river in Wilmington’s northern outskirts, near a drawbridge and what looks like an oil-tank complex.

511/512

I travel 7,839 meters in 10 seconds, which brings me down to the muzzle velocity of an ordinary handgun. I come to a stop on the roof of a Home Depot in Wilmington.

1023/1024

This jump is 3,920 meters at around Mach 1. I’m still probably bursting eardrums wherever I pass, but those newly-deaf people should count themselves lucky: there’s a lot of people burned to ash on the West Coast.

2047/2048

1,960 meters at the speed of an ordinary airplane. I stop in a marsh on the bank of the estuary that separates Wrightsville Beach from Wilmington. People are no longer being injured by my passage, but they’re probably pretty horrified to see a human being moving this fast. Plus, it’s been over a minute and 45 seconds since my accidental rampage began. That’s probably fast enough for people to post pictures of my path of destruction on Twitter.

4095/4096

I only travel 979.911 meters this time at an almost-sensible 219 mph (352 km/h). I manage to cross the estuary, although I’m still in the damn marsh, not yet to Wrightsville Beach. I stop near what, on Google Maps (on November 27th, 2016, anyway) looks like a horrifying half-mile long translucent river-worm:

Weird Thing in Wrightsville.png

Some may say it’s just a boat wake. I say they’re just blinding themselves to the truth that Big Google Data Brother Government Conspiracy (LLC) is trying to hide from the people. That’s what you’re supposed to say when you find weird shit in Google Earth, right?

8191/8192

I’m still going way over the posted speed limit as I cover the next 489.956 meters. Still stuck in this damned marsh, too.

16383/16384

A 244.978-meter jump at a sensible 54 mph (88 km/h). I’m starting to feel a little like the mathematician in the joke: all of a sudden, things are moving painfully slow.At least I’m out of the stupid marsh, and passing through a fairly pleasant-looking seaside housing development.

32767/32768

122.489 meters covered at a very pleasant 27 mph (44 kph). I’m almost within the ordinary residential speed limit! I’m only a block from the Holiday Inn, so tantalizingly close. I must persevere! I wanna be the engineer in the joke, not the mathematician! Hell sounds terrible!

65535/65536

A nice neat number. 2^16. 10000000000000000, in binary. I travel 61.244 meters. Less than the length of any sort of football field. I’m moving at 6.1 meters per second. A decent sprinter could manage that. Usain Bolt could most certainly manage that.

131071/131072

30.522 meters this time. I’m jogging across the parking lot, almost a literal stone’s throw from the Atlantic.

262143/262144

15.311 meters covered this jump, and 15.311 left to go. I can look into the windows of the Holiday Inn, and see all the employees on their phones reading about the carnage in California.

524287/524288

7.656 meters. A man passing me in the Holiday Inn parking lot wonders why I’m walking so damn slow.

1048575/1048576

3.828 meters. I’m walking at less than 1 mile per hour, which feels really weird when I do it in real life. I’m starting to regret many decisions. Plus, people are starting to get suspicious of me.

2097151/2097152

1.914 meters left to go. If I fell flat on my face (which is starting to seem like a good idea…), my head would push the front door open.

1 – 2^(-22)

Less than a meter to go. As I stand almost within arm’s reach of the hotel’s front door, people are giving me looks usually reserved for those who start talking about lizard people at bus stops.

1 – 2^(-23)

Half a meter. Finally–finally–I can reach out and push the door open. And thus, my bizarre trip comes to an end. I’ve covered 4,013,716.5 meters in about 3 minutes and 45 seconds. I’ve killed many, many people and injured countless others. There will be an investigation. Even though this isn’t exactly the sort of thing the FBI is used to, they’ll probably do their damndest to figure out just who or what set the west coast on fire, smashed millions of windows, and made a sonic boom over North Carolina. There’s probably enough security camera evidence to find me. Until then, I’ll just catch some sun on Wrightsville Beach.

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physics, Space, thought experiment

Hypothetical Nightmares | Black Holes, Part 3

Imagine taking all the mass in the Milky Way (estimated to be around a trillion solar masses) and collapsing it into a black hole. The result wouldn’t be an ordinary black hole. Not even to astrophysicists, for whom all sorts of weird shit is ordinary.

The largest black hole candidate is the black hole at the center of the quasar S5 0014+813, estimated at 40 billion solar masses. In other words, almost a hundred times smaller than our hypothetical hole. As I said last time, as far as astronomical objects go, black holes are a fairly comfortable size. Even the largest don’t get much bigger than a really large star. Here, though, is how big our trillion-sun black hole would be, if we replaced the sun with it:

Galaxy Mass Black Hole.png

(Rendered in Universe Sandbox 2.)

The thing circled in orange is the black hole. When I started tinkering with the simulation, I was kinda hoping there’d be one or two dwarf planets outside the event horizon, so their orbits could at least offer a sense of scale. No such luck: the hole has a Schwarzschild radius of 0.312 light-years, which reaches well into the Oort cloud. That is, the galaxy-mass black hole’s event horizon alone would extend beyond the heliopause, and would therefore reach right into interstellar space. Proxima Centauri, around 4.2 light-years from Earth, is circled in white.

The immediate neighborhood around a black hole like this would be rough. We’re talking “feral children eating the corpse of a murder victim while two garbagemen fight to the death with hatchets over who gets to empty the cans on this street” kind of rough. That kinda neighborhood. No object closer than half a light-year would actually be able to orbit the hole: it would either have to fall into the hole or fly off to infinity.

That is, of course, if the hole isn’t spinning. As I said last time, you can orbit closer to a spinning hole. But I’m going to make a leap here and say that our galaxy-mass black hole isn’t likely to be spinning very fast. Some rough calculations suggest that, if it were rotating at half the maximum speed,the rotational kinetic energy alone would have several billion times the mass of the sun. I’m going to assume there’s not enough angular momentum in the galaxy to spin a hole up that much. I could be wrong. Let me know in the comments.

Spin or no spin, it’s gonna be a rough ride anywhere near the hole. Atoms orbiting at the innermost stable orbit (the photon sphere) are moving very close to the speed of light, and therefore, to them, the ambient starlight and cosmic microwave background ahead of them is blue-shifted and aberrated into a horrifying violet death-laser, while the universe behind is red-shifted into an icy-cold nothingness.

But, as we saw last time, once you get outside a large hole’s accretion disk, things settle down a lot. When it comes to gravity and tides, ultra-massive black holes like these are gentle giants. You could hover just outside the event horizon by accelerating upwards at 1.5 gees, which a healthy human could probably tolerate indefinitely, and which is very much achievable with ordinary rocket engines. The tides are no problem, even right up against the horizon. They’re measured in quadrillionths of a meter per second per meter.

Of course, if you’re hovering that close to a trillion-solar-mass black hole, you’re still going to die horribly. Let’s say your fuel depot is orbiting a light-year from the hole’s center, and they’re dropping you rocket fuel in the form of frozen blocks of hydrogen and oxygen. By the time they reach you, those blocks are traveling at a large fraction of the speed of light, and will therefore turn into horrifying thermonuclear bombs if you try to catch them.

But, assuming its accretion disk isn’t too big and angry, a hole this size could support a pretty pleasant galaxy. The supermassive black hole suspected to lie at the center of the Milky Way makes up at about 4.3 parts per million of the Milky Way’s mass. If the ratio were the same for our ultra-massive hole, then it could host around 200 quadrillion solar masses’ worth of stars, or, in more fun units, 80,000 Milky Ways. Actually, it might not be a galaxy at all: it might be a very tightly-packed supercluster of galaxies, all orbiting a gigantic black hole. A pretty little microcosm of the universe at large. Kinda. All enclosed within something like one or two million light-years. A weird region of space where intergalactic travel might be feasible with fairly ordinary antimatter rockets.

You’ll notice that I’ve skipped an important question: Are there any trillion-solar-mass black holes in the universe? Well, none that we know of. But unlike some of the other experiments to come in this article, black holes this size aren’t outside the realm of possibility.

I frequently reference a morbid little cosmology paper titled A Dying Universe. If you’re as warped as I am, you’ll probably enjoy it. It’s a good read, extrapolating, based on current physics, what the universe will be like up to 10^100 years in the future (which they call cosmological decade 100). If you couldn’t guess by the title, the news isn’t good. A hundred trillion years from now (Cosmological Decade 14), so much of the star-forming stuff in galaxies will either be trapped as stellar corpses or will have evaporated into intergalactic space that new stars will stop forming. The galaxies will go dark, and the only stars that shine will be those formed by collisions between high-mass brown dwarfs. By CD 30 (a million trillion trillion years from now), gravitational encounters between stars in the galaxy will have given all the stars either enough of a forward kick to escape altogether, or enough of a backward kick that they fall into a tight orbit around the central black hole. Eventually, gravitational radiation will draw them inexorably into the black hole. By CD 30, the local supercluster of galaxies will consist of a few hundred thousand black holes of around ten billion solar masses, along with a bunch of escaping rogue stars. By this time, the only source of light will be very occasional supernovae resulting from the collisions of things like neutron stars and white dwarfs. Eventually, the local supercluster will probably do what the galaxy did: the lower-mass black holes will get kicked out by the slingshot effect, and the higher-mass ones will coalesce into a super-hole that might grow as large as a few trillion solar masses. Shame that everything in the universe is pretty much dead, so no cool super-galaxies can form. But the long and the short of it is that such a hole isn’t outside the realm of possibility, although you and I will never see one.

The Opposite Extreme

But what about really tiny black holes? In the first post in this series, I talked about falling into a black hole with the mass of the Moon. But what about even smaller holes?

Hobo Sullivan is a Little Black Pinhole

Yeah, I feel like that sometimes. I mass about 131 kilograms (unfortunately; I’m working on that). If, by some bizarre accident (I’m guessing the intervention of one of those smart-ass genies who twist your wishes around and ruin your shit), I was turned into a black hole, I’d be a pinprick in space far, far smaller than a proton. And then, within a tenth of a nanosecond, I would evaporate by Hawking radiation (if it exists; we’re still not 100% sure). When a black hole is this small, Hawking radiation is nasty shit. It would have a temperature of a hundred million trillion degrees, and I’d go off like four Tsar Bombas, releasing over 200 megatons of high-energy radiation. Not enough to destroy the Earth, but enough to ruin the year for the inhabitants of a medium-sized country.

There’s no point in trying to work out things like surface tides or surface gravity: I’d be gone so fast that, in the time between my becoming a black hole and my evaporation, a beam of light would have traveled a foot or two. Everything around me is as good as stationary for my brief lifetime.

A Burial Fit for a Pharaoh. Well, for a weird pharaoh.

Things change dramatically once black holes get a little bigger. A hole with the mass of the Great Pyramid of Giza (around 6 billion kilograms) would take half a million years to evaporate. It would still be screaming-hot: we’re talking trillions of Kelvin, which is hot enough that nearby matter will vaporize, turn to plasma, the protons and neutrons will evaporate out of nuclei, and then the protons and neutrons themselves will melt into a quark-gluon soup. But, assuming the black hole is held in place exactly where the pyramid once stood, we won’t see that. We’ll only see a ball of plasma and incandescent air the size of a university campus or a big football stadium, throbbing and booming and setting fire to everything for a hundred kilometers in every direction. The Hawking radiation wouldn’t inject quite enough energy to boil the planet, but it would probably be enough (combined with things like the fact that it’s setting most of Egypt on fire) to spoil the climate in the long run.

This isn’t an issue if the black hole is where black holes belong: the vacuum of space. Out there, the hole won’t gobble up Earth matter and keep growing until it destroys us. Instead, it’ll keep radiating brighter and brighter until it dies in a fantastic explosion, much like the me-mass black hole did.

Can’t you just buy a space heater like a normal person?

It’s starting to get cold here in North Carolina. Much as I love the cold, I’ve been forced to turn my heater on. But, you know, electric heating is kinda inefficient, and this house isn’t all that well insulated. I wonder if I could heat the house using Hawking radiation instead…

Technically, yes. Technically in the sense of “Yeah, technically the equations say yes.” Technically in the same way that you could technically eat 98,000 bacon double cheeseburgers at birth and then go on a 75-year fast, because technically, that averages out to 2,000 Calories per day. What I mean is that while the numbers say you can, isolated equations never take into account all the other factors that make this a really terrible idea.

A black hole with the mass of a very large asteroiod (like Ceres, Vesta, or Pallas) would produce Hawking radiation at a temperature of 500 Kelvin, which is probably too hot to cook with, but cool enough not to glow red-hot. That seems like a sensible heat source. Except for the fact that, as soon as you let it go, it’s going to fall through the floor, gobble up everything within a building-sized channel, and convert that everything into superheated plasma by frictional effects as it falls into the hole. And except for the fact that if you’re in the same neighborhood as the hole, you’ll simultaneously be pulled into it at great speed by its gravity, and pulled apart into a bloody mass of fettuccine by tidal forces. And except for the fact that, as the black hole orbits inside the Earth, it’s going to open up a kilometer-wide tunnel around it and superheat the rock, which will cause all sorts of cataclysmic seismic activity, and ultimately, the Earth will either collapse into the hole, or be blasted apart by the luminosity of the forming accretion disk, or some combination thereof.

Back to the Original Extreme

But there’s one more frontier we haven’t explored. (I was watching Star Trek yesterday.) That is: the biggest black hole we can reasonably (well, semi-reasonably) imagine existing. That’s a black hole with a mass of around 1 x 10^52 kilograms: a black hole with the mass of the observable universe. Minus the mass of the Earth and the Sun, which make less of a dent in that number than stealing a penny makes a dent in Warren Buffett’s bank account.

The hole has a Schwarzschild radius of about 1.6 billion light-years, which is a good fraction of the radius of the observable universe. Not that the observable universe matters much anymore: all the stuff that was out there is stuck in a black hole now.

For the Earth and Sun, though, things don’t change very much (assuming you set them at a modest distance from the hole). After all, even light needs over 10 billion years to circumnavigate a hole this size. Sure, the Earth and Sun will be orbiting the hole, rather than the former orbiting the latter, but since we’re dealing with gravitational accelerations less than 3 nanometers per second per second, and tides you probably couldn’t physically measure (4e-34 m/s/m at the horizon, and less further out, which falls into the realm of the Planck scale), life on Earth would probably proceed more or less as normal. The hole can’t inflict any accretion-disk horror on the Sun and Earth: there’s nothing left to accrete. Here on Earth, we’d just be floating for all eternity, living our lives, but with a very black night sky. If we ever bothered to invent radio astronomy, we’d probably realize there was a gigantic something in the sky, since plasma from the Sun would escape and fall into a stream orbiting around the hole, but we’d never see it. What a weird world that would be…

Then again, if the world’s not weird by the end of one of my articles, then I’m really not doing my job…

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physics, thought experiment

Spin to Win | Black Holes, Part 2

In the previous part of this series, I tried to analyze what it would be like to fly an Apollo Command Module into black holes of various sizes. This time, though, I’m going to restrict myself to a single 1-million-solar-mass black hole. The difference is that, this time, I’m going to let the black hole spin (at 98% of the maximum possible spin, which is pretty average for a fast-spinning hole). But I’m getting ahead of myself. Before I go on, here’s my vehicle:

Apollo 11.jpg

(From the website of the Smithsonian Air and Space Museum)

That’s the actual command module Michael Collins, Buzz Aldrin, and Neil Armstrong took to the Moon (minus the Plexiglas shroud, of course). It would fit in even a medium-sized living room. This time, the crew will consist of me, Jürgen Prochnow (Das Boot Jürgen, naturally. Captain’s hat and all), and Charlize Theron. I was gonna take David Bowie and Abe Lincoln along again, but frankly, I’ve put Bowie through enough, and Lincoln was just so damn grim all the time.

Anyway, back to the subject at hand: the scary monster that is a rapidly-spinning black hole. All the black holes I discussed in the last part were Schwarzschild black holes, meaning they had no spin or electric charge. This black hole, though, is a Kerr black hole: it spins. The spin means this trip is a whole new ballgame. We’re still going to die horribly, of course, but hey, at least it’ll be interesting.

The first difference is that you can get closer to the event horizon of a spinning black hole. For a non-spinning black hole, there are no stable circular orbits closer than one and a half times the radius of the event horizon (the Schwarzschild radius), because in order to be in a circular orbit any closer, you’d have to travel faster than light. For spinning ones, there’s a lozenge-shaped region outside the event horizon called the ergosphere (My first-born daughter will be Ergosphere Sullivan). Objects near a rotating hole (or any rotating mass, to a lesser extent) are dragged along with the hole’s rotation. But inside the ergosphere, though, they’re being dragged along so fast that, no matter what, they can’t stand still. Inside the ergosphere, you have to rotate with the hole, because traveling anti-spinward would require going faster than the speed of light.

Here’s roughly what a free-fall trajectory into our Kerr black hole would look like (looking down at the hole’s north pole):

098-kerr-black-hole-infall

The ergosphere is the gray part. The event horizon is the black part.

Jürgen and Charlize are suspicious of me, but I gave them my word that we’re just orbiting the black hole. To make some observations. For science, and all that. When they’re not looking, I’m gonna hit the retro-rocket and plunge us to our deaths. I feel like there’s a flaw in my reasoning, but I don’t have time for such things.

Even orbits don’t work the way they normally do, near a spinning hole. Orbits around ordinary objects are very close to simple ellipses or circles. But, sitting in our command module, here’s what our orbit looks like (starting from parameters that should have given us a nice elliptical orbit):

Kerr BH Stable Orbit.png

This is because, when we orbit closer to the hole, we get a kick from the spin that twists our orbit around.

From nearby, a non-rotating black hole looks like its name: a black circle of nothingness, surrounded by a distorted background of stars and galaxies. From our orbit around the spinning million-solar-mass hole, though, the picture is much different:

Orbiting a Kerr Black Hole.jpg

(Picture and simulation by Alain Riazuelo.)

In that picture, the hole’s equator rotates from left to right. The reason the horizon is D-shaped is that photons coming from that direction were able to get a lot closer to the horizon, since they were moving in the direction of the rotation. On the opposite side, the horizon is bigger because those photons were going upstream, so to speak, and many of them were pulled to a halt by the spin and then either pulled into the hole, flung away, or pulled into a spinward orbit. Black holes are bullies. Spinning ones say “If you get too close, I’m going to eat you. And if you’re standing within a few arm’s lengths, you have to spin around me, or else I’ll eat you.”

(Incidentally, if you read about the movie’s background, the black hole in Interstellar was spinning at something like 99.999999% of the maximum rate. Its horizon would have been D-shaped like the picture above, from up close. From a distance, it would have looked…well, it would have looked like it did in the movie. They got it right, because they hired Kip motherfucking Thorne, Mr. Black Hole himself, to help write their ray-tracing code.

Speaking of Interstellar, the fact that you can get so much closer to a spinning black hole than a non-spinning one (providing you’re orbiting spinward) means you can get much deeper into its time-dilating gravity well. That means, as long as the tides aren’t strong enough to kill you, you can experience much bigger timewarps. The only way to get the same timewarp from a non-rotating black hole is to apply horrendously large forces to hover just outside the horizon. It’s much more practical to do in the vicinity of a spinning hole. Well, I mean, it’s no less practical than putting a Command Module in orbit around a black hole.

According to the equations from this Physics Stack Exchange discussion, as Jürgen, Charlize, and I zip around the hole close to the innermost stable orbit, time is flowing upwards of four times slower than it is for observers far away. I’m gonna keep us in orbit for a week, to lull my crewmates into complacency, so I’ll have the element of surprise when I try to kill us all. Well, we think it’s a week. Everyone outside thinks we’re orbit for a month and change

Then, without warning, I flip us around, turn on the engines, and take us into the hole. Jürgen fixes me with those steely blue eyes and that pants-shittingly intimidating face he was doing all through Das Boot. Charlize spends fifteen seconds trying to reason with me, then realizes I’m beyond all help and starts beating the shit out of me. Did you see Fury Road? She can punch. Neither of them can do anything to stop me, though: we’re already seconds from death.

But because this is a big black hole, the tides are gentle, at least outside the horizon. They’re stronger than the tides the Moon exerts on the Earth (which are measured in hundreds of nanometers per second per second), but they’re not what’s going to tear us to pieces.

What’s going to tear us to pieces is frame-dragging. Let’s go back to the metaphor of the whirlpool. The water moves much faster close to the center than it does far away. Because your boat is a physical object with a non-zero size, when you get really close, the water on one side of your boat is moving significantly faster than the water on the other side, because the near side is significantly closer than the far side. This blog hasn’t had any horrible pictures recently. Here’s one to explain the frame-dragging we experience:

Horrible Frame Dragging.png

In this picture, the capsule orbits bottom-to-top, and the hole rotates clockwise (this is the opposite of the view in the orbit plots; in this picture, we’re looking at the hole from the bottom, looking at its south pole; the reason has nothing to do with the fact that I screwed up and drew my horrible picture backwards).

Space closer to the hole is moving faster than space farther from the hole. The gradient transfers some of the hole’s angular momentum to the capsule, which is bad news, because that means the capsule starts spinning. It spins in the opposite direction of the hole (counter-clockwise, in the Horrible Picture (TM)).

I say the spin is bad news because, from the research for “Death by Centrifuge“, I know that things get really messy and horrible if you’re in a vehicle that rotates too fast.

Here’s a fun fact: Neil Armstrong came perilously close to death on his first spaceflight. During Gemini 8, while Armstrong and crewmate Dave Scott were practicing station-keeping and docking maneuvers with an uncrewed Agena target vehicle, the linked spacecraft started spinning. Unbeknownst to them, one of the Gemini capsule’s thrusters was stuck wide-open. Thinking it was the Agena causing the problem, they undocked. That’s when the shit really hit the fan, though I think Armstrong probably described it more gracefully. A video is worth a thousand words: here’s what it looked like when they undocked. Before long, the capsule was tumbling at 60 revolutions per minute (1 per second), wobbling around all three axes.

Did you ever spin in a circle when you were a kid? I did. Did you ever try it again as an adult, just to see what it was like? I did. I spent the next fifteen minutes lying in the grass (because I couldn’t tell which way was down) wondering if I should just go ahead and puke. Human beings don’t handle rotation well. According to this literature survey (thanks to Nyrath of Project Rho for helping direct me to it; it was hell to try and find a proper paper otherwise), average people do okay spinning at 1.7 RPM. At 2.2 RPM, susceptible people will probably start puking everywhere. At 5.44 RPM, ordinary tasks become stressful, because, thanks to the Coriolis effect (that troublemaking bastard), things like limbs, bodies, and inner-ear fluid don’t move normally, which plays hell with coordination. Also, it makes you puke. At 10 RPM, even the tough subjects in the study were seriously distressed.

Armstrong and Scott were spinning six times faster. When you spin, your brain loses the ability to compensate for movements of the eyes: you lose the ability to stabilize the image on your retinas, and the world wobbles and jumps. That’s bad news, especially if, for instance, you’re stuck inside a metal can which is spinning way too fast, and the only way you can stop it spinning way too fast (so that you don’t die) is by focusing your eyes on buttons and moving your Coriolis-afflicted hands to press them. Armstrong was an especially tough, calm dude, and he managed it, even though both men were starting to have serious vision problems. He did what any good troubleshooter would do: he switched the thrusters off and then on again (more or less). That saved the mission.

Now, I don’t know how fast the black hole will spin us, because the math is very complicated. But considering it’s a black hole we’re dealing with, probably pretty fast. Like I said, nothing about black holes is subtle. At 10 RPM, I throw up. My vomit describes a curved Coriolis-arc through the cabin and splatters on the wall. Jürgen doesn’t throw up until 20 RPM (after all, he’s a seafaring submarine captain). Charlize doesn’t throw up until 25,because she’s a badass.

At 60 RPM, I’m already screaming my head off, hyperventilating, and desperately regretting my decision to plunge us into a black hole. I try to hit buttons (pretty much at random), but I can’t get my fingers to go where I want them, and I press all the wrong ones. Jürgen is trying to calm me down and telling me he wants proper damage reports, but in my panic, I’ve forgotten all my German. Charlize has written both of us off and is trying to re-orient us and thrust away from the horizon, but it’s already too late.

At 60 RPM, the centrifugal acceleration on the periphery of the CM is already over 7 gees. There’s probably a bit of metal creaking, but nothing too serious. Because the crew couches are only a foot or so from the center of mass, we only experience an acceleration of 1.2 gees. For the moment, our main problem is that we’re punching and/or throwing up on each other.

At 120 RPM, the command module is starting to complain. Its extremities experience 28 gees. Panels slam shut. A cable pops loose and causes a short that trips the circuit breakers and kills our power. Even in our couches, we’re feeling almost 5 gees. I’m making a face like this:

gloc-face-735x413.jpg

(Source.)

At 200 RPM, the heat shield, experiencing 77 gees of centrifugal acceleration, cracks and flies off. It’s possible that the kick it gets from leaving our sorry asses behind, combined with the kick from being in the hole’s ergosphere (sounds dirty) is enough to slingshot the fragments to safety. Kind of a moot point, though, since I only care about the human parts, and all of those have blacked out at 13 gees.

Somewhere between 200 RPM and 500 RPM, the hull finally tears open. The bottom dome is flung off, letting important things like our air, our barf bags, and possibly our crew couches, fly out. Not that it matters: at 83 gees, we’ve all got ruptured aortas, brain hemorrhages, and we’re all in cardiac arrest.

At 1000 RPM (16.7 revolutions per second), the command module is flung decisively apart. Thanks to conservation of angular momentum, all the pieces are spinning pretty fast, too. Jürgen, Charlize, and I, are very dead, and in the goriest of possible ways: pulped by centrifugal force, and then shredded as we were spun apart.

The fragments closer to the horizon appear to accelerate ahead of us. The parts farther away fall behind. Most of the fragments fall into the hole. Spaghettification takes a while: once again, a more massive hole has weaker tides near the horizon.

As for what happens as we fall into the really nasty part of the hole (because it was sunshine and jellybeans before…), physics isn’t sure. The simplest models predict a ring-shaped singularity, rather than a point-shaped one. Some models predict that the ring singularity might act as an actual usable wormhole to another universe. But it’s also possible that effects I don’t pretend to understand (which have to do with weird inner horizons only rotating holes have) blue-shift the infalling light, creating a radiation bath that burns our atoms into subatomic ash. Either way, we’re not going to be visiting any worlds untold.

Once again, I’ve killed myself and two much cooler people. At least I only did it once this time. In the next and final part, I’m going to spend a little more time playing around with far less realistic black holes. (WARNING! Don’t actually play with black holes. If you have to ask why, then you skipped to the end of both articles.)

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math, short, thought experiment

Short: Probabilities

For this thought experiment, let’s equate a probability of 1 (100% chance, a certainty) with the diameter of the observable universe. The diameter of the observable universe is about 93 billion light-years (because, during the 13.8 billion years since it started, the universe has been steadily expanding). With this analogy, let’s consider some probabilities!

According to the National Weather Service, your odds of being struck by lightning this year (if you live in the US, that is) are 1 in 1,042,000. Less than one in a million. One part in a million of the diameter of the universe is 93,000 light-years, which is far enough to take you outside the Milky Way, but on a cosmic scale, absolutely tiny.

The odds of winning the jackpot with a single ticket in the U.S. Powerball lottery are around 1 in 292 million. That’s like 318 light-years set against the diameter of the universe. 318 light-years is a long way. Even so, it’s an almost-reasonable distance. Most of the brighter stars you see in the night sky are closer than that. That’s almost the Sun’s neighborhood. Compared to the entire universe. Maybe that’s why they say the lottery is for suckers…

The odds of being struck by lightning three times in your lifetime are, mathematically, 1 in 1,000,000,000,000,000,000. The actual odds are even lower, since there’s a non-zero chance that you’ll be killed by a lightning strike, making getting another impossible. If your odds of dying in a lightning strike are 10%, then your odds of surviving are 9/10, and your odds of surviving the first two so you can get the third are (1 in a million) * (9/10) * (1 in a million) * (9 in 10) * (1 in a million), or about 81 in one hundred million trillion.That’s 81 in 100,000,000,000,000,000,000. That’s roughly the diameter of the Earth-moon system compared to the diameter of the universe.

The odds of putting 100 pennies in a cup, shaking them up, and scattering them so they all land flat, and then having every single coin come up heads, are 1 in 1, 267, 650, 600, 228, 229, 401, 496, 703, 205, 376. That’s the diameter of a grain of sand compared to the entire universe. Literally.

Get a standard deck of cards. Take out the jokers and the instructions. Shuffle the deck and pick a card at random. Do this 25 times. The odds of picking the jack of clubs every single time are like a proton compared to the visible universe.

If you pick 43 letters at random, the odds of forming the string

actisceneielsinoreaplatformbeforethecastlef

(that is, the first 43 letters of Hamlet) are as small as one Planck length (which is the smallest unit of distance that ever gets used in actual physics) compared to the visible universe. For reference, a Planck length is ten million trillion times smaller than a proton, which is itself a trillion times smaller than a grain of salt.

Incidentally, if you assembled random 43-letter strings, you would have to do it

32, 143, 980, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000

times to have a 99% chance of producing the first 43 letters of Hamlet in one of them. But a human bard did it in, at most, a couple hundred tries. Isn’t that weird? More probability stuff (and black hole stuff) to come!

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physics, Space, thought experiment

Houston, We Have Several Problems: Black Holes, Part 1

There aren’t many movies that I loved as a kid and can still stand to watch as a grownup. I remember loving Beauty and the Beast, but I don’t know if I could watch it now, because I’ve developed an irrational hatred of musical numbers. I certainly couldn’t watch that amazingly cheesy monster truck movie where the guy who drove Snakebite drugged the guy who drove Bigfoot. Apollo 13, though, aged well. It’s high on the list of my favorite space movies. Thanks to that movie (and the much weirder, but still pretty damn good Marooned), this vehicle is comfortably familiar to me:

Apollo_CSM_lunar_orbit.jpg

(From Wikipedia.)

That there is the Apollo 15 command-service module. The command module (astronaut container) is the shiny cone at the front. Because I had cool parents, I got to go to the Johnson Space Center as a kid and see an actual command module, in person. As far as spacecraft go, it’s pretty small. If you stole one, you could hide it in your average garage. Now there‘s a good scene for a movie: some mad scientist with a stolen command module in his garage, tinkering with it while 80’s electronic montage music plays. Turning it into a time machine or something.

Once again, I imagine many of you are wondering what the hell I’m talking about. Don’t fret, there’s always (well, almost always) a method to my madness. Earlier today, I got thinking about the classic thought experiment: What would it be like to fall into a black hole. That thought experiment normally involves just dropping some hapless human (usually without even a spacesuit) right into one. You guys know me, though: if I’m going to do a weird thought experiment, I’m going to go into far more detail than necessary. That’s the fun part!

The point is, I’m going to start off my series on black holes by imagining what would happen if you dropped a pristine command module into black holes of various masses. The command module needs a three-person crew, and my crew will consist of myself, a young David Bowie, and Abraham Lincoln. Despite what you may think, no, I’m not on drugs. This is all natural, which, if you think about it, is much scarier.

A Mini Black Hole

As XKCD pointed out, a black hole with the mass of the Moon would not be a terribly dramatic-looking object. Even accounting for gravitational lensing, it would be next to impossible to see unless you were close to it, or you were looking really hard, or you had an X-ray/gamma-ray telescope. Nobody knows for sure whether black holes with masses this small actually exist. They might possibly have formed from the compression of the high-density plasma that filled the early universe, but so far, nobody’s spotted their telltale radiation.

But me, Bowie, and Lincoln are about to see one, and far too close.

At 1,700 kilometers, we’ve already gone from flying to falling. There’s nothing exciting happening, though, because as physicists always say, from a reasonable distance, a black hole’s gravitational field is no different from the gravitational field of a regular old object of the same mass. The tidal acceleration (which is the real killer when it comes to black holes) amounts to less than a millionth of a gee. Detectable, but only just.

At 100 kilometers, the tides are noticeable. Lincoln’s top-hat (which he foolishly left untethered. There wasn’t time to explain space flight and free-fall to a 19th-century politician) is slowly migrating to the end of the cabin. The tidal acceleration (the difference in pull between the center of the CM and either of its ends) is similar to the gravity of Pluto. The command module is stretching, but no more than, say, a 747 flexes in flight. Only detectable with fancy things like strain gauges.

At 10 km, we’re really motoring. Traveling at 31 kilometers per second, we’ve broken the record set by Apollo 10 for the fastest-moving humans. Bowie’s crazy Ziggy Stardust hair is getting misshapen by differential acceleration, which by now amounts to almost a full gee. Anything untethered (Lincoln’s hat, Bowie’s guitar, my cup of coffee, et cetera) is stuck at either end of the cabin.

At 5 km, we’re all shrieking in pain. The stray objects at the ends of the cabin are starting to get smashed. We’re all being stretched front-to-back (since that’s how you sit in a command module). The tides are pulling the command module like a rubber band, but a command module’s a compact and sturdy thing, so apart from some alarming creaking of metal, and maybe some cracking in the heat shield, it’s still in one piece.

All three of us die very quickly not long after the 2.5 km mark. Since the university still won’t let me use their finite-element physics package (well, more accurately, they won’t let me in the physics department…), I can only conjecture what will kill us, but it’ll either be the fact that the blood in our backs is being pulled toward the black hole much harder than the blood at our fronts (probably turning us very nasty colors and causing lots of horrible hemorrhages), or the fact that the command module has been stressed beyond its limits and sprung a leak. I’d wager the viewports would shatter before anything else happened, as their frames start to bend out of shape.

Time dilation hasn’t really kicked in, even by 500 meters, so an observer at a safe distance would see the CM crumple in real-time. The cone collapses like an umbrella being closed. Fragments of broken glass, shards of metal, control panels, shattered heat shield, and pieces of a legendary rocker, a melancholic President, and an idiot are spilling out of the wreckage.

By 10 meters, the command module is no longer falling straight down. It’s started falling inward, compressing side-to-side even as it stretches top-to-bottom. The individual components and fragments cast off from the wreck stretch and pull apart. Metal panels tear in two. Glass shards crack. Bits of flesh tear messily in half. The fragments divide and divide and divide. As they approach the event horizon, they explode into purple-white incandescent plasma: because the atoms are falling inward towards a point, they slam sideways into each other at high speeds. All 13,000 pounds of command module and crew either help bulk up the black hole, or form a radiant accretion disk denser than lead and smaller than a grape.

A 5-Solar-Mass Black Hole

In black hole thought experiments, the starting-point is usually a 1-solar-mass black hole. That makes sense: as far as astronomical objects go, the Sun is nicely familiar. But like I said before, scientists aren’t sure if there are any 1-solar-mass black holes anywhere in the Universe. As far as we know, all black holes in this mass range form from stars, and supernova leftovers smaller than something like 3 solar masses can still be supported by things like radiation pressure, degeneracy pressure, and the fact that atoms don’t like other atoms too close to them. In practice, there aren’t any known black hole candidates smaller than about 3 solar masses. There are a couple around 5 solar masses, and 5 is a nice round number, so that’s what I’m going with. We’re resetting this weird-ass experiment and dropping me, Bowie, and Lincoln into a stellar black hole.

At 380,000 kilometers (the distance from the Earth to the Moon), the tidal acceleration is detectable, but not noticeable. Good thing we’re free-falling (I should’ve made Tom Petty the third crewmember…), because if we were held stationary (say, by a magic platform hovering at a fixed altitude above the hole), we’d be flattened by a lethal 469-gee acceleration. Good thing, too, that we’re in an enclosed spacecraft: if the black hole has an accretion disk orbiting around it, we’re probably close enough that an unshielded human would be scalded to death by its heat, light, and X-rays. For our purposes, though, we’ll assume this black hole’s been floating through interstellar space for a long time, and has already cannibalized its own accretion disk, rendering it almost dark.

As we reach 10,000 km from the black hole, the same thing happens that happened with the mini black hole. David Bowie, who has gotten out of his seat to have a second tube of strawberry-banana pudding, finds it difficult to climb back to his couch against the gravity gradient. He’s being gently pelted by loose objects. Lincoln is just sitting in his couch looking very grave. I’m screaming my head off, so I miss all of this.

At 5,000 kilometers, the command module starts to creak. David Bowie is now stuck upside-down at the top of the cabin. I, having lost my shit and tried to open the hatch to end it quickly, have fallen to the bottom and broken my coccyx. Lincoln is still sitting in his couch looking very grave. We’re experiencing a total acceleration of over a million gees. If we tried to maintain a constant altitude, that million gees would turn us and the command module into a sheet of very thin and very gory foil. We’re moving almost as fast as the electrons shot from the electron gun of an old CRT TV.

Between 5,000 and 1,000 kilometers, the command module starts popping apart. It’s not as fast as the last time. First, the phenolic plastic of the heat shield cracks and pulls free of the insulation beneath. Then, the circular perimeter of the cone starts to crumple and wrinkle. (True story: the command module was built with crumple zones, just like a car, so that it didn’t pulp the astronauts too much when it hit the ocean at splashdown.) Not long after, the pressure hull finally ruptures, spewing white jets of gas and condensation in all directions like a leaky balloon. Then, the bottom of the pressure hull bursts. Think of a sledgehammer hitting a sheet of aluminum foil. All the guts of the command module spill out: wires, seats, guitars, apples (I was hungry), tophats, shoes, hoses, spare spacesuits, screaming idiots (I fell out). We’re moving 10% of the speed of light.

By 100 kilometers, the command module has spaghettified into a long stream of debris. The individual metal parts, although badly warped by being torn from their mountings, are mostly holding together, though they’re really starting to stretch. Anything softer is shattering/pulping/shredding. The black hole’s event horizon is the largest object in the sky: a fist-sized black disk of nothingness surrounded by a very pretty mandala of distorted stars and galaxies. It looks something like this:

scr00004

(Screenshot from the unbelievably awesome (and free) program Space Engine.)

We can’t see it, though: we’re all dead.

By 25 kilometers, we’re just a stream of fine dust hurtling towards the event horizon at close to the speed of light. For an observer at a great distance, our disintegration proceeds in slow motion, both from the massive speed at which we’re traveling, and from the time-dilating effects of extreme gravity.

As we scream through 14.8 kilometers, we’ve almost reached the event horizon. The individual atoms the command module used to be made of are accelerating apart, spraying the whole CM into a narrow stream of plasma. Outside observers, though, just see the incandescent dust slow to a halt, change color from electric-arc purple to brilliant blue-white to the color of the sun to the color of hot steel to red-hot to black. What happens when we hit the singularity not long after is anybody’s guess. By definition, at a singularity, the equations you’re working with just quit making sense.

Sagittarius A*

There’s a very massive and very dense thing at the center of the Milky Way. It has about 3.6 million times the mass of the Sun, and because there’s a star (poetically called S0-102) that orbits pretty close to it (relatively speaking, anyway: its closest-approach distance is still larger than the distance from the Sun to Pluto), we know it has to be quite small, and therefore quite dense. According to our current understanding of physics, any mass like that would inevitably collapse into a black hole no matter what. The short version: it’s probably a black hole. (Note 1: as of this writing in November 2016, radio astronomers have finally committed to using a gigantic virtual telescope to take a picture of the actual event horizon in 2017, which is awesome) (Note 2: Though the actual mechanism for their formation isn’t known, some astrophysicists have done simulations suggesting that they formed from super-massive stars in the early universe. These days, the largest stars are a few hundred solar masses, with the largest stars for which we have firm evidence weighing around 120 solar masses. That’s massive, but not super-massive. These super-massive primordial stars contained thousands of solar masses. The one in that article massed 55,500. Some may have exceeded a million.)

Because a black hole (or, at least, its event horizon) is as compact as you can make anything, black holes tend to be really small compared to normal objects of similar mass. A Moon-mass black hole would look like a black dust-grain. An Earth-mass one would look like a pea. A Sun-mass one (and remember, there’s a lot of stuff in the Sun) would be the size of a small town. The 5-solar-mass hole we considered a second ago would be the size of a city. Sagittarius A*, though, containing so much mass, is actually a proper astronomical-sized object: 15 times larger than the Sun. If some deity with a really sick sense of humor replaced the Sun with Sgr A*, it would hang in the sky, a little smaller than a fist at arm’s length. We would also all be dead. For many reasons: no sunlight, radiation from the accretion disk, and the fact that we’d be orbiting so fast that grains of dust would heat the upper atmosphere lethally hot.

At 1 AU (the average distance from the Earth to the Sun), Sgr A*’s event horizon is much larger in the sky than the Moon. We’re accelerating at 1800 gees, but we don’t feel it, because we’re in free-fall. The tidal acceleration is minuscule: less than a micron per second per second. Once again, we’re pretending the black hole has no accretion disk, because if it did, its radiation would probably have incinerated us by now.

By the time we pass through Mercury’s orbit (0.387 AU) (assuming we actually are in this nightmarish black-hole solar system), we’re going one-third the speed of light, accelerating at over 15,000 gees. The tides are still detectable only by specialized instruments.

By 0.1 AU, we’re moving three-quarters the speed of light. David Bowie is singing “Space Oddity”, because I’ve smuggled a durian fruit onboard and threatened to cut it open if he doesn’t. Lincoln is starting to get sick of this shit, but this just gives him that same grave expression he has in all his photographs. The tides are detectable by instruments, but probably not by our human senses. Hitting a stationary dust particle the size of a bacterium unleashes a burst of light as bright as a studio flash.

At 0.071 AU, we pass through the event horizon without even realizing it. Falling into a black hole intact is a little like having a gigantic black bag closed around you: the event horizon already covers more than half of the sky, thanks to the fact that the black hole bends light toward the horizon. The sky shrinks into an ever-diminishing circle in a black void. The circle grows brighter and bluer with every passing second.

By 0.05 AU, stray objects are drifting to the ends of the cabin again: the tides are finally picking up. David Bowie is holding me down and punching me repeatedly, because he’s sick of me resurrecting him and killing him over and over. Lincoln is letting him do it, because frankly, I’ve cracked his statesman’s patience with my bullshit. We’re only 30 seconds from the singularity.

Even at 0.01 AU, the tides aren’t stretching the capsule. The effects might be palpable, but they’re nothing compared to what we’ve already been through in the previous experiments. We’re riding down a shaft of blue-shifted light, concentrated into a point straight overhead: everything that’s fallen into the hole recently can’t help but curve inward, until it’s falling almost ruler-straight towards the singularity.

At one Sun radius from the singularity, the differential acceleration is approaching one gee. Things are starting to get uncomfortable. David Bowie has stopped punching me, because he’s fallen to the top of the capsule again. Lincoln, though, still has the strength to pick up a pen and stab me in the sternum. He’s cursing at me, and as I start to bleed to death, I observe that Lincoln is much more creative with his swears than I would have given him credit for.

At 150,000 km, we start to get woozy on account of the blood in our bodies pooling in all the wrong places. We narrowly avoid a collision with Matthew McConaughey in a spacesuit, who has gone from muttering about quantum data to describing the peculiar aging patterns of high-school girls.

At 50,000 km, moving very, very nearly the speed of light, the command module finally starts to disintegrate. Seconds later, we spaghettify, just as before, and strike the singularity. And, once again, we run afoul of the fact that physicists have very little idea what happens that deep in a gravity well. For reference, at 100 meters from the singularity (and ignoring relativistic effects and pretending we can use the Newtonian equation for tides down here), the differential acceleration is measured with twenty-digit numbers. If the capsule were infinitely rigid and didn’t spaghettify, by the time its bottom touched the singularity, the tides would be measured in 25-digit numbers. If, somehow, we’d survived our trip to the singularity, we’d be accelerating so fast that, thanks to the Unruh effectempty space would be so hot we’d instantly vaporize.

And here’s where physics breaks down. If I’m reading this paper right, the distance between any point and the singularity is infinity, because space-time is so strongly curved near it.

Imagine that space is two-dimensional. It contains two-dimensional stars with two-dimensional mass. That curves two-dimensional space into a three-dimensional manifold. The gravity well (technically, the metric) around a very dense (but non-black-hole) looks roughly like this:

GravityPotential.jpg

(From Wikipedia.)

If you measure the circumference of the object, you can calculate its diameter: divide by two times pi. But when you measure its actual diameter, you’ll find it’s larger than that, because of the way strong gravitation stretches spacetime. In the case of a black hole, spacetime looks more like this:

Fig1.png

(From the paper cited above.)

The cylindrical part of the trumpet is (if I’m understanding this correctly) infinitely long. The “straight-line” distance through the black hole, on a line that just barely misses the singularity, is much larger than you’d expect. But the distance through the black hole, measured on a line that hits the singularity is infinite. All lines that hit the singularity just stop there.

But, to be honest, I really don’t know what it’d be like down there. Nobody does. The first person to figure out what gravity and particle physics do under conditions like that will probably be getting a shiny medal from some Swedes.

Standard