astronomy, physics, science, Space, thought experiment

If the Sun went Supernova

I have to preface this article by saying that yes, I know I’m hardly the first person to consider this question.

I also have to add that, according to current physics (as of this writing in December 2017), the Sun won’t ever go supernova. It’s not massive enough to produce supernova conditions. But hey, I’ll gladly take any excuse to talk about supernovae, because supernovae are the kind of brain-bending, scary-as-hell, can’t-wrap-your-feeble-meat-computer-around-it events that make astronomy so creepy and amazing.

So, for the purposes of this thought experiment, let’s say that, at time T + 0.000 seconds, all the ingredients of a core-collapse supernova magically appear at the center of the Sun. What would that look like, from our point of view here on Earth? Well, that’s what I’m here to find out!

From T + 0.000 seconds to 499.000 seconds

This is the boring period where nothing happens. Well, actually, this is the nice period where life on Earth can continue to exist, but astrophysically, that’s pretty boring. Here’s what the Sun looks like during this period:

Normal Sun.png

Pretty much normal. Then, around 8 minutes and 19 seconds (499 seconds) after the supernova, the Earth is hit by a blast of radiation unlike anything ever witnessed by humans.

Neutrinos are very weird, troublesome particles. As of this writing, their precise mass isn’t known, but it’s believed that they do have mass. And that mass is tiny. To get an idea of just how tiny: a bacterium is about 45 million times less massive than a grain of salt. A bacterium is 783 billion times as massive as a proton. Protons are pretty tiny, ghostly particles. Electrons are even ghostlier: 1836 times less massive than a proton. (In a five-gallon / 19 liter bucket of water, the total mass of all the electrons is about the mass of a smallish sugar cube; smaller than an average low-value coin.)

As of this writing (December 2017, once again), the upper bound on the mass of a neutrino is 4.26 million times smaller than the mass of an electron. On top of that, they have no electric charge, so the only way they can interact with ordinary matter is by the mysterious weak nuclear force. They interact so weakly that (very approximately), out of all the neutrinos that pass through the widest part of the Earth, only one in 6.393 billion will collide with an atom.

But, as XKCD eloquently pointed out, supernovae are so enormous and produce so many neutrinos that their ghostliness is canceled out. According to XKCD’s math, 8 minutes after the Sun went supernova, every living creature on Earth would absorb something like 21 Sieverts of neutrino radiation. Radiation doses that high have an almost 100% mortality rate. You know in Hollywood how they talk about the “walking ghost” phase of radiation poisoning? Where you get sick for a day or two, and then you’re apparently fine until the effects of the radiation catch up with you and you die horribly? At 21 Sieverts, that doesn’t happen. You get very sick within seconds, and you get increasingly sick for the next one to ten days or so, and then you die horribly. You suffer from severe vomiting, diarrhea, fatigue, confusion, fluid loss, fever, cardiac complications, neurological complications, and worsening infections as your immune system dies. (If you’re brave and have a strong stomach, you can read about what 15-20 Sieverts/Gray did to a poor fellow who was involved in a radiation accident in Japan. It’s NSFW. It’s pretty grisly.)

But the point is that we’d all die when the neutrinos hit. I’m no religious scholar, but I think it’d be appropriate to call the scene Biblical. It’d be no less scary than the scary-ass shit that happens in in Revelation 16. (In the King James Bible, angels pour out vials of death that poison the water, the earth, and the Sun, and people either drop dead or start swearing and screaming.) In our supernova Armageddon, the air flares an eerie electric blue from Cherenkov radiation, like this…

685px-Advanced_Test_Reactor

(Source.)

…and a few seconds later, every creature with a central nervous system starts convulsing. Every human being on the planet starts explosively evacuating out both ends. If you had a Jupiter-sized bunker made of lead, you’d die just as fast as someone on the surface. In the realm of materials humans can actually make, there’s no such thing as neutrino shielding.

But let’s pretend we can ignore the neutrinos. We can’t. They contain 99% of a supernova’s energy output (which is why they can kill planets despite barely interacting with matter). But let’s pretend we can, because otherwise, the only spectators will be red, swollen, feverish, and vomiting, and frankly, I don’t need any new nightmares.

T + 499.000 seconds to 568.570 seconds (8m13s to 9m28.570s)

If we could ignore the neutrino radiation (we really, really can’t), this would be another quiet period. That’s kinda weird, considering how much energy was just released. A typical supernova releases somewhere in the neighborhood of 1 × 10^44 Joules, give or take an order of magnitude. The task of conveying just how much energy that is might be beyond my skills, so I’m just going to throw a bunch of metaphors at you in a panic.

According to the infamous equation E = m c^2, 10^44 Joules would mass 190 times as much as Earth. The energy alone would have half the mass of Jupiter. 10^44 Joules is (roughly) ten times as much energy as the Sun will radiate in its remaining 5 billion years. If you represented the yield of the Tsar Bomba, the largest nuclear device ever set off, by the diameter of a human hair, then the dinosaur-killing (probably) Chicxulub impact would stretch halfway across a football field, Earth’s gravitational binding energy (which is more or less the energy needed to blow up the planet) would reach a third of the way to the Sun, and the energy of a supernova would reach well past the Andromeda galaxy. 1 Joule is about as much energy as it takes to pick up an egg, a golf ball, a small apple, or a tennis ball (assuming “pick up” means “raise to 150 cm against Earth gravity.”) A supernova releases 10^44 of those Joules. If you gathered together 10^44 water molecules, they’d form a cube 90 kilometers on an edge. It would reach almost to the edge of space. (And it would very rapidly stop being a cube and start being an apocalyptic flood.)

Screw it. I think XKCD put it best: however big you think a supernova is, it’s bigger than that. Probably by a factor of at least a million.

And yet, ignoring neutrino radiation (we really can’t do that), we wouldn’t know anything about the supernova until nine and a half minutes after it happened. Most of that is because it takes light almost eight and a quarter minutes to travel from Sun to Earth. But ionized gas is also remarkably opaque to radiation, so when a star goes supernova, the shockwave that carries the non-neutrino part of its energy to the surface only travels at about 10,000 kilometers per second. That’s slow by astronomical standards, but not by human ones. To get an idea of how fast 10,000 kilometers per second is, let’s run a marathon.

At the same moment, the following things leave the start line: Usain Bolt at full sprint (10 m/s), me in my car (magically accelerating from 0 MPH to 100 MPH in zero seconds), a rifle bullet traveling at 1 kilometer per second (a .50-caliber BMG, if you want to be specific), the New Horizons probe traveling at 14 km/s (about as fast as it was going when it passed Pluto), and a supernova shockwave traveling at 10,000 km/s.

Naturally enough, the shockwave wins. It finishes the marathon (which is roughly 42.195 kilometers) in 4.220 milliseconds. In that time, New Horizons makes it 60 meters. The bullet has traveled just under 14 feet (422 cm). My car and I have traveled just over six inches (19 cm). Poor Usain Bolt probably isn’t feeling as speedy as he used to, since he’s only traveled an inch and a half (4.22 cm). That’s okay, though: he’d probably die of exhaustion if he ran a full marathon at maximum sprint. And besides, he’s about to be killed by a supernova anyway.

T + 569 seconds

If you’re at a safe distance from a supernova (which is the preferred location), the neutrinos won’t kill you. If you don’t have a neutrino detector (Ha ha!), when a supernova goes off, the first detectable sign is the shock breakout: when the shockwave reaches the star’s surface. Normally, it takes in the neighborhood of 20 hours before the shock reaches the surface of its parent star. That’s because supernovas (at least the core-collapse type we’re talking about) usually happen inside enormous, bloated supergiants. If you put a red supergiant where the Sun is, then Jupiter would be hovering just above its surface. They’re that big.

The Sun is much smaller, and so it only takes a couple minutes for the shock to reach the surface. And when it does, Hell breaks loose. There’s a horrific wave of radiation trapped behind the opaque shock. When it breaks out, it heats it to somewhere between 100,000 and 1,000,000 Kelvin. Let’s split the difference and say 500,000 Kelvin. A star’s luminosity is determined by two things: its temperature and its surface area. At the moment of shock breakout, the Sun has yet to actually start expanding, so its surface area remains the same. Its temperature, though, increases by a factor of almost 100. Brightness scales in proportion to the fourth power of temperature, so when the shock breaks out, the Sun is going to shine something like 56 million times brighter. Shock breakout looks something like this:

Sun Shock Breakout.png

But pretty soon, it looks like this:

Sun Supernova.blend

Unsurprisingly, this ends very badly for everybody on the day side. Pre-supernova, the Earth receives about 1,300 watts per square meter. Post-supernova, that jumps up to 767 million watts per square meter. To give you some perspective: that’s roughly 700 times more light than you’d be getting if you were currently being hit in the face by a one-megaton nuclear fireball. Once again: However big you think a supernova is, it’s bigger than that.

All the solids, liquids, and gases on the day side very rapidly start turning into plasma and shock waves. But things go no better for people on the night side. Let’s say the atmosphere scatters or absorbs 10% of light after passing through its 100 km depth. That means that, after passing through one atmosphere-depth, 90% of the light remains. Since the distance, across the Earth’s surface, to the point opposite the sun is about 200 atmosphere-depths, that gives us an easy equation for the light on the night side: [light on the day side] * (0.9)^200. (10% is approximate. After searching for over an hour, I couldn’t find out exactly how much light the air scatters, and although there are equations for it, I was getting a headache. Rayleigh scattering is the relevant phenomenon, if you’re looking for the equations to do the math yourself).

On the night side, even after all that atmospheric scattering, you’re still going to burn to death. You’ll burn to death even faster if the moon’s up that night, but even if it’s not, enough light will reach you through the atmosphere alone that you’ll burn either way. If you’re only getting light via Rayleigh scattering, you’re going to get something like 540,000 watts per square meter. That’s enough to set absolutely everything on fire. It’s enough to heat everything around you to blowtorch temperatures. According to this jolly document, that’s enough radiant flux to give you a second-degree burn in a tenth of a second.

T + 5 minutes to 20 minutes

We live in a pretty cool time, space-wise. We know what the surfaces of Pluto, Vesta, and Ceres look like. We’ve landed a probe on a comet. Those glorious lunatics at SpaceX just landed a booster that had already been launched, landed, and refurbished once. And we’ve caught supernovae in the act of erupting from their parent stars. Here’s a graph, for proof:

breakout_sim-ws_v6.png

(Source. Funnily enough, the data comes from the awesome Kepler planet-hunting telescope.)

The shock-breakout flash doesn’t last very long. That’s because radiant flux scales with the fourth power of temperature, so if something gets ten times hotter, it’s going to radiate ten thousand times as fast, which means, in a vacuum, it’s going to cool ten thousand times faster (without an energy source). So, that first bright pulse is probably going to last less than an hour. But during that hour, the Earth’s going to absorb somewhere in the neighborhood of 3×10^28 Joules of energy, which is enough to accelerate a mass of 4.959×10^20 kg. to escape velocity. In other words: that sixty-minute flash is going to blow off the atmosphere and peel off the first 300 meters of the Earth’s crust. Still better than a grisly death by neutrino poisoning.

T + 20 minutes to 4 hours

This is another period during which things get better for a little while. Except for the fact that pretty much everything on the Earth’s surface is either red-hot or is now part of Earth’s incandescent comet’s-tail atmosphere, which contains, the plants, the animals, most of the surface, and you and me. “Better” is relative.

It doesn’t take long for the shock-heated sun to cool down. The physics behind this is complicated, and I don’t entirely understand it, if I’m honest. But after it cools, we’re faced with a brand-new problem: the entire mass of the sun is now expanding at between 5,000 and 10,000 kilometers per second. And its temperature only cools to something like 6,000 Kelvin. So now, the sun is growing larger and larger and larger, and it’s not getting any cooler. We’re in deep dookie.

Assuming the exploding sun is expanding at 5,000 km/s, it only takes two and a quarter minutes to double in size. If it’s fallen back to its pre-supernova temperature (which, according to my research, is roughly accurate), that means it’s now four times brighter. Or, if you like, it’s as though Earth were twice as close. Earth is experiencing the same kind of irradiance that Mercury once saw. (Mercury is thoroughly vaporized by now.)

In 6 minutes, the Sun has expanded to four times its original size. It’s now 16 times brighter. Earth is receiving 21.8 kilowatts per square meter, which is enough to set wood on fire. Except that there’s no such thing as wood anymore, because all of it just evaporated in the shock-breakout flash.

At sixteen and a quarter minutes, the sun has grown so large that, even if you ignored the earlier disasters, the Earth’s surface is hot enough to melt aluminum.

The sun swells and swells in the sky. Creepy mushroom-shaped plumes of radioactive nickel plasma erupt from the surface. The Earth’s crust, already baked to blackened glass, glows red, then orange, then yellow. The scorched rocks melt and drip downslope like candle wax. And then, at four hours, the blast wave hits. If you thought things couldn’t get any worse, you haven’t been paying attention.

T + 4 hours

At four hours, the rapidly-expanding Sun hits the Earth. After so much expansion, its density has decreased by a factor of a thousand, or thereabouts. Its density corresponds to about the mass of a grain of sand spread over a cubic meter. By comparison, a cubic meter of sea-level air contains about one and a quarter kilograms.

But that whisper of hydrogen and heavy elements is traveling at 5,000 kilometers per second, and so the pressure it exerts on the Earth is shocking: 257,000 PSI, which is five times the pressure it takes to make a jet of abrasive-laden water cut through pretty much anything (there’s a YouTube channel for that). The Earth’s surface is blasted by winds at Mach 600 (and that’s relative to the speed of sound in hot, thin hydrogen; relative to the speed of sound in ordinary air, it’s Mach 14,700). One-meter boulders are accelerated as fast as a bullet in the barrel of a gun (according to the formulae, at least; what probably happens is that they shatter into tiny shrapnel like they’ve been hit by a gigantic sledgehammer). Whole hills are blown off the surface. The Earth turns into a splintering comet. The hydrogen atoms penetrate a full micron into the surface and heat the rock well past its boiling point. The kinetic energy of all that fast-moving gas delivers 10^30 watts per second, which is enough to sand-blast the Earth to nothing in about three minutes, give or take.

T + 4 hours to 13h51m

And the supernova has one last really mean trick up its sleeve. If a portion of the Earth survives the blast (I’m not optimistic), then suddenly, that fragment’s going to find itself surrounded on all sides by hot supernova plasma. That’s bad news. There’s worse news, though: that plasma is shockingly radioactive. It’s absolutely loaded with nickel-56, which is produced in huge quantities in supernovae (we’re talking up to 5% of the Sun’s mass, for core-collapse supernovae). Nickel-56 is unstable. It decays first to radioactive cobalt-56 and then to stable iron-56. The radioactivity alone is enough to keep the supernova glowing well over a million times as bright as the sun for six months, and over a thousand times as bright as the sun for over two years.

A radiation dose of 50 Gray will kill a human being. The mortality rate is 100% with top-grade medical care. The body just disintegrates. The bone marrow, which produces the cells we need to clot our blood and fight infections, turns to sterile red soup. 50 Gray is equivalent to the deposition of 50 joules of radiation energy per kilogram. That’s enough to raise the temperature of a kilo of flesh by 0.01 Kelvin, which you’d need an expensive thermometer to measure. Meanwhile, everything caught in the supernova fallout is absorbing enough radiation to heat it to its melting point, to its boiling point, and then to ionize it to plasma. A supernova remnant is insanely hostile to ordinary matter, and doubly so to biology. If the Earth hadn’t been vaporized by the blast-wave, it would be vaporized by the gamma rays.

And that’s the end of the line. There’s a reason astronomers were so shocked to discover planets orbiting pulsars: pulsars are born in supernovae, and how the hell can a planet survive one of those?

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All kinds of explosions.

As you’ve probably worked out by now, I’m a big fan of explosions. Since this ridiculous blog began, I’ve blown up rabbits (don’t worry–hypothetical rabbits), stellar-mass balls of gold, grains of neutronium, and I’ve nearly blown up the earth with an ultrarelativistic BB gun. As you’ve probably also figured out, I’m a big fan of bizarre thought experiments, thought experiments based on ideas boiled and distilled down to their absolute essentials. With that in mind, let’s blow some more shit up!

But before we can get started, we have to decide what an explosion is. For the purpose of this thought experiment, we’re going to use a one-meter-diameter sphere of space anchored to the surface of the Earth, just touching the ground. The explosions will consist of energy (in the form of photons of an appropriate wavelength) magically teleported into this sphere. (I still haven’t decided what symbol to use for the magic teleporter in my Feynman diagrams.) With that cleared up, let’s get blastin’.

The smallest possible explosion.

It’s pretty difficult to decide on the lower limit for the size of a one-meter-diameter explosion. First of all, that one-meter sphere is already full of all kinds of energy: solar photons, the kinetic energy of air molecules moving at high speeds, the rest-mass energy of those air molecules, et cetera. But even if the sphere were completely evacuated, quantum mechanics tells us that the lowest amount of energy that a volume of space can possess is greater than zero: its zero-point energy or vacuum energy.

To simplify things (and to keep me from having to learn the entirety of gauge field theory while writing a blog post), we’re going to say that the lowest-energy explosion we can create has the energy of the longest-wavelength (and therefore lowest-energy) photon we can fit in the sphere: 1 meter. That’s towards the high-frequency (short-wavelength) end of the radio spectrum. It’s not quite a microwave (those have wavelengths on the order of a centimeter), but it’s shorter than the photons used to transmit FM radio signals. Needless to say, it would impart a pretty much un-measurable quantity of energy to our sphere of air. A 1-meter photon carries 1.986×10e-25 joules of energy, the same energy as an oxygen molecule puttering along at a grandmotherly 6 miles per hour (10 kph).

The most efficient possible explosion.

But while we’re using our magic vacuum-fluctuation laser (lots of magic in this article…), we might as well see how big an explosion we can make with a single photon. We know the minimum is 1.986×10e-25 joules. But what’s the highest-energy photon we can stick in there? (Sounds like a plot to a horrible science porno…) I’m not a physicist, but I would guess that it’s a photon with a wavelength of 1 Planck length. Here’s my logic: the Planck length is the smallest length that makes sense according to our current laws of physics. To carry energy, an electromagnetic wave must change over time (or space, which work out to be part of the same thing). In order to take two different values, the wave’s crest and trough must be at least 1 Planck length apart. Of course, weird things happen on the Planck scale, so who knows if an electromagnetic field varying by a large quantity over 1 planck length would even make sense, or even behave like a photon, but you can say this with some certainty: a photon with a wavelength shorter than that doesn’t make a lot of sense.

A photon with a wavelength this short would be off-scale, as far as the electromagnetic spectrum goes. By definition, it would be a hard gamma ray, but that’s only because we humans don’t have access to the high-energy regions of the spectrum, so we say “Anything with a wavelength between A and B is an X-ray. Anything with a wavelength between B and zero is a gamma ray. Stupid gamma rays. Who needs ’em?”

This is a gross oversimplification, but photons tend to prefer to interact with objects that are roughly their same size. Visible photons interact with the electron clouds of  large molecules (like chlorophyll, which is good if you like oxygen). Infrared photons interact with large molecules directly, making them rotate or move. Radio-frequency photons interact only with big crowds of mobile electrons, like you find in plasma or radio antennas. In the other direction, ultraviolet photons interact with atoms and their bonds, either knocking outer electrons loose or breaking the bonds. X-ray photons interact with the tightly-bound electrons in lower energy states (I’m afraid to say “closer to the nucleus,” because that’s not quite right, and people smarter than me will make fun of me; but we’ll pretend that’s how it works to speed things along). Gamma-ray photons interact with the nucleus directly. They can push the nucleus into strange high-energy states or, if they’re the right wavelength, pelt protons and neutrons loose.

The physics of extremely short-wavelength gamma rays is much more complicated. That’s partly because, once a gamma ray passes an energy greater than 1022 keV (the kinds of energies you get when you heat something to several billion Kelvin) have enough mass-energy that they can spontaneously turn into matter: a 1023 keV gamma ray can briefly become an electron and a positron, which rapidly annihilate to re-form the gamma ray. The higher your photon’s energy gets, the more important these bizarre transformations become. Basically, once you get above 1022 keV, your photons start behaving less and less like light and more and more like matter.

Our Planck-length photon would (probably) be small enough to pass through all ordinary matter. It might pop a quark loose of a proton or a neutron, but I don’t really know. This photon would carry an energy far greater than 1022 keV. Indeed, its energy wouldn’t be measured in the peculiar particle-physics unit of the electronvolt, but rather in freakin’ megawatt-hours. This photon would add as much energy to our sphere as the explosion of three tons of TNT, which would form a cube large enough to contain our sphere with room to spare. From one…single…photon. Physics is scary.

Explosions, both conventional and nuclear (ain’t I posh?).

If you Google the phrase “largest conventional explosion,” you’ll probably dig up an article on Operation Sailor Hat, in which the U.S. Navy built a 500-ton Minecraft-style sphere of TNT:

It made a real mess of the decommissioned test ships anchored just offshore, and left a crater in Hawai’i that still exists to this day. It remains one of the largest intentional non-nuclear explosions humans have ever created. This isn’t relevant to our thought experiment, but I’m easily distracted by 500-ton piles of TNT.

In everyday life, a “conventional explosion” is one created by a chemical reaction of some kind. This ranges from the rapid burning of a lot of wheat dust in a grain silo to the bizarre high-tech cube-shaped molecule octanitrocubane. An explosion that gets most of its power from the fission of radioactive elements (or the fusion of light elements) is a nuclear explosion. Simple.

But you can think of it another way: the difference between conventional chemical explosions and nuclear explosions is a matter of temperature. Explosives like TNT produce gases with temperatures of thousands of degrees Kelvin. Nuclear explosions produce temperatures in the million to hundred million Kelvin range.

Since we’ve got a magic sphere of air we can pump energy into (how convenient!), let’s make one of each kind of explosion!

For the conventional explosion, we’ll heat the air to a temperature of 5,000 Kelvin (about as hot as the surface of the sun). Our sphere has a volume of 0.52 cubic meters, and air has a volumetric heat capacity of about 0.001 joules per cubic centimeter per Kelvin. Therefore, heating the air to 5,000 kelvin will require 2.6 million joules. We’re talking about a decent-sized bang here, equivalent to just over half a kilogram of TNT. Not exactly spectacular, but certainly not the kind of explosion you want to hold in your hand. (Actually, thinking about it, why would you want to hold any explosion in your hand? That was silly of me.)

For the nuclear explosion, we’ll heat our sphere to 10 million Kelvin, which is a compromise, since nuclear explosions are complicated beasties and their temperature varies very rapidly in the span of microseconds. I should point out that I’m still using a volumetric heat capacity of 0.001 joules per cubic centimeter per Kelvin, which is absurd. At these temperatures, we’re not just making molecules move faster–we’re breaking them apart. And blasting electrons off the individual atoms. Both of these things take energy, so heating the plasma to 10 million Kelvin will actually require more energy input than my idealized equation suggests. But I digress. We’re looking at an explosive energy of about 5.2 billion Joules, which is about one and a quarter tons of TNT. I’m disappointed. Even the smallest nuclear weapon ever made had a yield larger than that. (Incidentally, the smallest nuclear weapon ever made (by the U.S., at least) was the W54 warhead. This is what they used in the “Davy Crockett,” which was a nuclear warhead launched from a fucking bazooka. Think about that.)

But the real temperature of a young nuclear fireball (good name for a band) is probably higher than this. After the fission of the nuclear material is complete, there’s a brief period where the nuclear explosion is mostly made up of high-energy nuclear radiation (hard x-rays, gamma rays, and particles). Then, it gets absorbed by the evaporating bomb casing and the surrounding air and (mostly) turns into heat. It’s not unreasonable to assume that the temperature in a baby nuclear fireball (bad idea for a child’s doll) is closer to 100 million Kelvin, which works out to almost twelve and a half tons of TNT. Still not nuclear in the traditional sense, but certainly more than enough to bust up a whole city block.

Turning it up to 10.

I’m tired of messing around. I want a real boom. We’re sticking a full megaton into that sphere, and damn the consequences!

Well, with energy densities this high, you can’t really even pretend that the volumetric heat capacity equation applies. Even at 100 million Kelvin, we were getting into the region where atoms are stripped of most or all of their electrons, which is where matter stops behaving even remotely the way it does at ambient temperatures. Much hotter, and we’re going to start splitting the atoms themselves.

Instead, to describe the conditions in our magic sphere when 1 megaton is pumped into it, I’m going to make two assumptions: the energy is deposited over the course of 1 nanosecond, and the superheated sphere radiates like a thermodynamic blackbody, which is to say the same way red-hot steel does and stars (mostly) do.

An energy release of 1 megaton over 1 nanosecond gives us 4.184 trillion trillion watts of radiated power. The sphere will very briefly shine as bright as a small star, and will have a surface temperature of 69 million Kelvin. Then, ba-boom, say goodbye to your city. Next time you build a city, don’t go letting people like me build magic energy-spheres in the middle. I hope you’ve learned your lesson.

This thing goes to 11.

Sorry. Couldn’t help myself.

Let’s stick in 50 megatons now. That’s about the energy released by the Tsar Bomba, a Soviet hydrogen bomb that produced a mushroom cloud that rose above the top of the stratosphere. For comparison, really impressive explosions and big thunderstorms and volcanic eruptions and such are lucky if they can make it into the stratosphere at all, let alone breaking all the way through the damn thing.

I can do all the math here just like before: 210 trillion trillion watts, a temperature of 185 million Kelvin, yadda yadda yadda. The thing is, as I wrote in “A Piece of a Neutron Star“, up to a point, an explosion is an explosion. The energy of an explosion gets spread over a large volume fairly quickly, and ordinary fluid dynamics and thermodynamics take over. Ever notice how a conventional explosive produces a mushroom cloud that looks an awful lot like the mushroom from a nuclear explosion? That’s because both are powered by the same thing: a rising plume of hot air. While it’s true that in the nuclear explosion there’s a lot more air and it’s a hell of a lot hotter, it’s easy to see that the two are related. They’re part of the same spectrum. A nuclear explosion is like a conventional explosion, only it’s larger, and it produces a lot more radiant heat.

This thing goes to 111.

This scaling law (which real physicists have investigated in great detail) seems to hold for larger and larger energies. Small asteroid impacts create explosions that are very much like nuclear explosions (with some extra effects from high-velocity ejecta and from the entry trail and so on). Even impacts like Chicxulub (which may or may not have helped kill off the dinosaurs, but certainly ruined everybody’s day for several thousand years) produce a fairly ordinary shockwave, and then a fireball that reaches an enormous, but reasonable, size before cooling to ordinary temperatures. The excellent Impact Effects Calculator tells me that a Chicxulub-like impact would produce a visible fireball with a radius of about 66 kilometers. This would reach up through the stratosphere, and about halfway to the edge of space, so it would probably be flattened, with a blurry, undefined edge at the top, but it would still be very much like what it is: a 100 million megaton explosion.

But like all scaling laws, the explosion spectrum eventually gives out. Once you start imagining blasts with the same kinetic energy as, say, a 100-kilometer-wide stone asteroid, you’ve passed over a threshold. Beyond this threshold, the assumptions that let us imagine our earlier explosions break down. Assumptions like “Shockwaves and heat plumes travel through the atmosphere, but the atmosphere doesn’t go flying off or anything” and “The crust is firmly attached to the rest of the Earth.” (It’s nice that we live in a time when we can make assumptions like that. Not that we could live in a time when the crust wasn’t attached, but it’s nice to know we (probably) have that kind of stability). We move out of the realms of meteorology and geology and into the realms of astrophysics. When you talk about 100-kilometer asteroid impacts, you’re no longer talking about “an asteroid hitting the Earth.” You’re talking about “two celestial bodies colliding.” Things like organic life and atmospheres crumble (and burn and evaporate) before energies like this.

Which is a (very) roundabout way of saying that a 90-billion-megaton explosion isn’t really an explosion anymore. It’d blow the atmosphere off a pretty big portion of the planet, peel back the crust, and pave some or all of the Earth in magma. Larger explosions could put sizeable dents in the Earth, or blow off enough material to push it into a different orbit. Not that we care: we’ll all be dead. Again. Sorry. Planet-killing is a bad addiction to have.

Hey! Where’d my explosion go?

This transition from fluid dynamics to astrodynamics has an ultimate limit. You can only squeeze so much energy into a 1-meter-diameter sphere and have it come back out. For this, you have Albert Einstein and Karl Schwarzschild to thank.

Energy and mass are equivalent. Not only can one be converted into the other, but they also produce and react to gravity in the same way. Because of this, if you try to cram more than 3.029e43 Joules (7239 trillion trillion megatons) of energy into a sphere 1 meter across, you won’t get an explosion at all. Your energy, no matter what form it’s in, will vanish behind an event horizon. This is bad news for the Earth. Partly because this energy will weigh 56 times as much as the Earth (over a fifth the mass of Jupiter), and will therefore screw up its orbit and either freeze us or boil us. Of course, the slow and painful destruction of the entire human race, all of our infrastructure and achievements, everything you and I and everybody else cares about, and also all life on earth, is the least of our problems. Because now we’ve got a 1-meter black hole sitting in the middle of a public park somewhere (I moved it away from downtown, to be nice. Sorry.) The Earth will swirl into the hole like a sinkful of water down a drain. That’s not just me failing to be poetic, that’s about how it’ll be. The whole Earth wont’ fall into the hole in an instant, nor will it be instantly spaghettified. Remember that, until you get close to it, a black hole behaves like any other object of the same mass. So the bulk of the Earth will fall towards the hole (thereby putting the hole at the middle of the planet) and everything else will collapse around it. We will, briefly, have a planet cracked and hollowed like a broken Kinder egg. Then we will have a ball of incandescent gas around a tiny black hole. Then we will have an accretion disk whose molecules do not resemble the farmers, sailors, priests, road signs, eggs benedict, and fire ants they were once part of. This is the point at which the explosion stops being an explosion. This is the limit.

Hey, this thing goes to 10.999.

That’s no fun. Well, I tell a lie–black holes are great fun to play with. (From a large distance.) But we want explosions, not black holes! We can talk about black holes some other time (hint hint). What if we put a little less than 3.029e43 Joules into our magic sphere? If that happens, boy oh boy do we get some fireworks!

The first thing that’ll happen is that the spacetime around the sphere will go from the gentle curvature (gravity) produced by the Earth, Sun, and other celestial bodies to a violent light-bending time-warping curvature. This does not end well for us. (why would you think it would? You’re silly.) A single powerful pulse of gravity waves races out at the speed of light, turning the Earth to gravel in a few milliseconds. Right on its heels comes a wave of radiation with almost the power of a supernova (almost, as in, 0.3 times as energetic as a supernova. Serious shit.) The Earth does not have time to fall into the region of ridiculous energy density and turn it into a black hole. That’s because the Earth is busy turning into a pancake of purple-white plasma and racing outwards at high speed. If the pancake hits anything, the flash will destroy the solar system. (Which sounds like it should be a line from Spaceballs). If it doesn’t hit anything, the supernova will destroy the solar system.

The moral of today’s story is: Don’t trust a man who says he has a magic sphere. He might kill everything.

The other moral of today’s story is: If you study a little physics, you can take any thought experiment to its absolute logical limit. Which, as I’m discovering, is pretty damn fun.

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Exploding rabbits.

(Courtesy of Wikipedia.)

I have a thing against rabbits. I don’t like them. They fill me with contempt. There’s absolutely no reason for this. It’s an utterly irrational hatred. Because of this particular neurosis, during a conversation with a friend, I happened to say something about vaporizing a rabbit. That sent my loony swamp-bog brain spinning off on another of its tangents, and I started to wonder What would happen if you vaporized a rabbit?

For the sake of this thought experiment, I’m going to start off assuming that a rabbit weighs 1 kilogram. That’s within the mass range listed by Wikipedia, but Wikipedia can’t always be trusted. But by virtue of the fact that they exist, we know that rabbits weigh more than 0 kilograms, and by virtue of the fact that we don’t inhale rabbits and get horrible nibbling-rabbit pneumonia, we know that they probably weigh more than 0.000 000 000 000 001 kilograms (1 picogram, which is about the mass of a bacterium). And from this oft-referenced report from the BBC, of Ralph the Unthinkably Large Bunny (who I must admit is kinda cute), we know that rabbits can reach 7.7 kilograms. So 1 kilogram is not unreasonable.

Now that we’ve got that bit of pedantic obsessiveness out of the way, we can proceed.

Most organisms contain quite a lot of water. The density of a human being is similar to the density of water. (If you can float in a pond or a swimming pool, your density is less than that of water, meaning less than 1,000 kilograms per cubic meter. If you have to tread water, your density is higher than 1,000. For the record, I float.) So, for the sake of simplicity, let’s pretend that our 1-kilogram bunny is made entirely of water, like a really disappointing version of those chocolate Easter bunnies. Let’s also assume that it starts out at typical rabbit body temperatures: 100 Fahrenheit, 38 Centigrade, or 311 Kelvin. In order to vaporize this all-water rabbit, we have to add enough heat-energy to it to raise its temperature to the boiling point, which is 212 Fahrenheit, 100 Centigrade, or 373 Kelvin (Have you noticed that we have way too many fucking temperature units? It’s a pain.) That’s a difference of 62 Kelvin. To find out how much energy we need to boil this rabbit (and make some extremely watery rabbit stew), we need water’s specific heat capacity, which happens to be about 4.18 Joules per gram Kelvin.

Specific heat capacity is one of those nice units that just makes sense. Newton’s gravitational constant is measured in units of (Newtons * square meters) / (square kilograms). What the fuck is a square kilogram? Well, the constant is one of those universal constants that tells you, in a vague way, just how weak a force gravity is. Specific heat capacity, though, makes intuitive sense. Water has a specific heat capacity of 4.18 Joules per gram Kelvin (Not to be confused with Jules per Graham Kevin, who is the president of the Earth in the alternate reality where Canada became a totalitarian superpower). That means that, to increase the temperature of one gram of water by one Kelvin, you have to add 4.18 Joules of heat energy to it. The units tell you exactly what they mean, which is nifty.

Anyway, in order to heat our rabbit-shaped mass of water to boiling temperature, we need to add 259,200 Joules of heat energy. But notice that I said “to heat our rabbit-shaped mass to boiling temperature.” That’s not the same as actually making it boil. For that, we need to add extra energy. This extra energy won’t increase the temperature at all, but it will get the water over the hump and vaporize it. This extra energy is quantified by another constant: the specific heat (or enthalpy) of vaporization. For water, this is 2,260,000 Joules per kilogram. That means we need 2,260,000 more Joules to turn our rabbit-shaped water balloon into a rabbit-shaped cloud of steam. So, all told, we’re concentrating 2,500,000 Joules into a volume on the order of 1,000 cubic centimeters. 2,500,000 Joules is about the energy released in the explosion of half a kilogram of TNT, which seems to me (citation needed) like a decent fraction of a stick of dynamite.

Unfortunately, energy alone isn’t going to get us the explosion we’re looking for. Just because we have the equivalent of a stick of dynamite doesn’t mean we’re going to have the same explosion as a stick of dynamite. That energy is all bound up in the rabbit-shaped cloud of steam.

What will get us the explosion we’re looking for, however, is the fact that we’ve got a cloud of hot gas compressed to the density of water and eager to expand. From the ideal gas law (and assuming a rabbit volume of 1,000 cubic centimeters), the cloud will begin at a pressure of 1,699 atmospheres (172.19 megapascals). That’s about half the pressure generated by the burning gunpowder in a .357 magnum cartridge. Maybe not enough to kill you, but certainly enough to make your ears ring. And enough to make you stand in the meadow blinking while a fine mist of rain falls around a little crater in the grass, asking yourself what the hell just happened.

But you know what? Rabbits aren’t just made of water. They’re made of all sorts of weird shit like water, tubulin, hemoglobin, cadherin, vitamin D, collagen, phospholipids, and more rabbit-semen than anybody wants to think about. And from cooking (and from that one scene in The Lord of the Rings) we know that heating a rabbit up to boiling won’t destroy all of its chemical bonds.

I want to make sure this rabbit is gone. I mean gone. Vaporized. I want to rip its fucking molecules apart, so that there’s no trace of fucking rabbit left. I should probably talk to my therapist about this. But for now, I’ll finish what I started.

As it turns out, I can still reasonably assume that the whole 1-kilogram rabbit is made of water, because the hydrogen-oxygen bonds in water are some of the strongest you’ll find in ordinary materials (carbon-hydrogen bonds are stronger, but not by much; nitrogen-nitrogen bonds are much stronger, but there’s not a lot of gaseous nitrogen floating around in a rabbit’s tissues, so we don’t need to worry about it). We’re looking at 55.56 moles of rabbit (NOT 55.56 moles of rabbits; disgusting shit happens when you try to assemble a mole of small mammals). The bond-dissociation energy for the hydrogen-oxygen bond in water is a shade under 500,000 Joules per mole, and there are two such bonds in every water molecule, so the total energy will be about 1,000,000 joules per mole. That means that completely vaporizing a rabbit will require something like 55,500,000 Joules, which is (roughly) equivalent to the detonation of 10 kilograms of TNT. 10 kilograms of TNT works out to just over 6 liters, so imagine two three-liter soda bottles (or six big liter-size beer steins, or a 1-gallon jug and a half-gallon jug) filled to the brim with TNT. That’s more explosives than you find in some artillery shells. You know what that means?

ExplodingRabbit

KAAAAA-BOOOOOOOOOM! 

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A piece of a neutron star.

In the previous article, I talked about neutron stars, and like pretty much everybody else who’s ever tried to describe a neutron star’s absurd density, I explained that a piece of a neutron star the size of a 500-micron grain of sand would weigh as much as a small cargo ship.

That’s the kind of scientific example I like: it uses to comprehensible objects to illustrate something that would otherwise be pretty much impossible to visualize. I know the mass of a cargo ship isn’t exactly intuitive, but it’s more intuitive than saying 2e17 kilograms per cubic meter.

But one thing such examples gloss over is just how hard it is to pack this much mass so close together. In order to reach the pressures and temperatures necessary for fusion, we need the mass of the entire Sun, and that still only compresses the Sun’s core to 1.5e5 kilograms per cubic meter. It takes a truly massive star that has no way to maintain its internal temperature to compress matter the rest of the way and keep it there.

Neutron stars are supported almost entirely by neutron-degeneracy pressure, which, to seriously oversimplify matters, is a product of the fact that neutrons don’t like to occupy the same quantum state, and therefore don’t like to be brought too close together. It produces a lot of pressure. Enough to support 1.38 solar masses or more against a surface gravity of 100 billion gees. It also means that if we got really literal and took an actual piece out of a neutron star, it would not end well.

Let’s say we teleported a cube of neutron fluid, at a density of 2e17 kilograms per cubic meter and 3,000,000 Kelvin, into the air a meter over an empty field on Earth. The pressure exerted by all those neutrons packed too close together is complicated to calculate, but would probably be in the neighborhood of 5e33 pascals, or about 5e18 atmospheres. That’s a million trillion times higher than the pressure during the detonation of a hydrogen bomb.

That’s a lot of energy in one place, but as we’ve learned while trying to kill humanity with a BB gun and contemplating killer asteroids, even when you deposit a ridiculous amount of energy into a small volume, if there’s enough matter around it, eventually, it’ll be converted into a more ordinary form. This is another way of saying that, up to a certain limit, all explosions are going to behave a lot like scaled-up nuclear explosions.

But a whole lot of interesting shit is going to happen very rapidly before we get to that point. First, our grain of neutronium (which, admit it, sounds way cooler than “neutron superfluid,” cool as that one is) will expand rapidly. This will cause its pressure to decrease, and so it’ll be a lot like ascending through the layers of a neutron star, moving from outer core to crust. When the pressure drops low enough, many of the neutrons will decay into protons, emitting electrons and neutrinos. Neutrinos are infamous for carrying off energy, and also for refusing to interact with things. They might heat the ground below them by a few fractions of a degree, but considering that they pass right through the Earth without difficulty, they’re probably not important, except in the fact that they’ll cool the nuclear matter down.

Now, our grain of neutronium is a slightly larger grain of protons and neutrons all mashed together. Without the surrounding pressure to force them unnaturally close, the protons will naturally repel each other. They’ll still be attracted to each other and to the neutrons via the strong force, but once again, without the ridiculous pressures provided by the bulk of a neutron star, their clustering will be limited by the short range of the strong force. That is to say, they’ll stop being a soup of nucleons and go back to being atomic nuclei.

These nuclei will start out quite heavy, but the falling pressure will cause them to rapidly fission and give off a lot of radiation. There’ll be a lot of gamma rays, a lot of stray protons and neutrons, a lot of alpha particles, and probably a lot of beta decays producing protons and electrons from neutrons. It’d take a particle physicist to tell you exactly what elements to expect in the fallout, but I’d wager it’d mostly be lead, iron, hydrogen, and helium, with a smattering of lighter and heavier elements.

By now, we’re dealing with energies too low for massive neutrino emission, so the only way this expanding sphere of plasma can lose energy is by emitting traditional electromagnetic radiation and by expanding. It is now, for all intents and purposes, an extremely hot and extremely small version of a nuclear fireball.

How big would the fireball ultimately get? That depends on a lot of things: first, on how much energy was initially contained in our deadly granule. Second, on how much of that energy got carried off by the snobbish non-interacting neutrinos. It’s hard to be certain how much potential energy would have been in the grain to start with, but I’ve read that the neutron degeneracy pressure of neutronium is one third of its mass density. E = m * c^2, so mass density is just energy density. One third of the energy density of our grain of neutronium comes out to about 7.5e23 joules, which is of the same order of magnitude as the Chicxulub impact. So, even though we’re dealing with a very exotic explosion, we know that it’s not the kind of explosion that’s going to blow off the entire atmosphere or boil all the oceans. And actually, since so much energy is likely to be lost to neutrinos (neutrinos carry off 99% of the energy in supernovae, which considering that they still shine as bright as 10 billion suns, is horrifying to contemplate), it could be an almost-ordinary thermonuclear explosion. But, because I don’t know exactly how much energy we’re losing to neutrinos here, I’m going to assume the whole 7.5e23 joules is going to get deposited in the atmosphere.

Using this number, we can estimate the relevant parameters by using the excellent Impact Effects program, written by some very nifty folks. This program is, as far as I’m concerned, justification enough for the existence of the Internet all by itself. By assuming a stony asteroid 12 kilometers across, impacting perpendicular to the ground at 22 kilometers per second, we get an impact energy in the right ballpark.

The fireball would grow to massive proportions. As we learned from nuclear tests, hot plasma is pretty much completely opaque to radiation, since it’s got electrons flying around loose, and since photons like to bounce off of electrons. An initial burst of gamma rays would escape, but much of the radiation from our exploding grain of neutronium would be trapped in the plasma bubble, bouncing around while the bubble expanded at high speed. This bubble would reach a radius of 95 kilometers, reaching vertically to near the edge of space and pushing a massive shockwave out in front of it. Anything that happened to be caught within the fireball wouldn’t be destroyed. It wouldn’t even be vaporized. It would be flash-ionized into hot plasma. But, once the bubble had expanded to 95 kilometers in radius, it would finally have cooled enough to de-ionize and become transparent to ordinary radiation again.

This is very briefly good news for the people in the surrounding area, since it means they’re not going to get smacked in the face with a wall of plasma at 5000 degrees. Then, it becomes very bad news, since there’s a lot of thermal energy in that fireball that can now suddenly escape. The fireball would be visible from 1,100 kilometers away, and possibly farther, if you’re unlucky enough to be in an airliner or on a mountain. And if this fireball is visible to you, that pretty much means you’re dead. We’re looking at flash-fires and third-degree burns for five hundred miles in every direction.

About an hour later, the people at 1,200 kilometers, for whom the fireball was below the horizon, would stop being lucky: the blast wave would arrive, bringing overpressures of almost 2 atmospheres (enough to blow down just about any building) and wind speeds of 610 miles an hour (enough to blow down just about any building).

But the disaster would only just be beginning. Here, the peculiar origin of the explosion would make itself apparent: there would likely be a lot of radioactive fallout, and it would be made of peculiar isotopes generated in a flash when those protons and neutrons were separating into nuclei again. Not only that, with all the ionizing radiation, there would be even more nitric oxide in the plume than usual. Imagine if you will a pancake-shaped incandescent cloud hundreds of kilometers across–the size of a country. This cloud glows from within a larger, dark-red cloud of nitric oxide, ozone, iron, lead, and radioactive dust. Over the course of hours, the upper half of the cloud collapses downward as it cools, while the other half rises buoyantly upward. Within days, there’s a sheet of opaque vapor thousands of kilometers across, trapped in the stratosphere, blowing with the winds, fed from below by a firestorm of a kind not seen for 65 million years. Smoke and dust circle the planet within weeks. Temperatures drop far below freezing. People and animals are poisoned by toxic gases. With the sunlight blotted out, plants die. People starve. There’s a mass extinction. Only the hardiest species survive. After the dust settles out and the climate rebounds, new creatures populate the Earth. The only reminder of the catastrophe is a thin layer of exotic elements, and a crater 160 kilometers across and 2 kilometers deep. Perhaps if Earth ever spawns another species that spawns paleontologists, they will think the crater came from an asteroid impact. But it didn’t. It was created by an object the size of a grain of sand.

So take this as a grim warning: Under no circumstances should you take a useful scientific analogy so literally that you actually remove a piece of an exotic compact star and transport it to a planet. And they say you can’t learn anything from psychotic bloggers!

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Decibels of DEATH!

Ear Protection

When I see the word “decibel,” I think two things. First, I think “Noise.” Then, I think “Oh god, decibels confuse the hell out of me…”

Well, I think I finally understand the decibel. It’s kind of a weird unit, but it’s also nifty, and it showcases one of the coolest things in mathematics: the logarithm.

Here’s how you compute the decibel-level of a sound. First, you figure out the acoustic power of that sound, probably using a microphone (or using a sound engineer who has a microphone and understands better than I do the difference between “acoustic power” and “sound amplitude.”) The acoustic power tells you the maximum pressure the sound wave exerts on things (say, your eardrums). Most of the time, you measure that sound pressure in pascals. Take that sound pressure and divide it by 20 micro-pascals. 20 micro-pascals is a semi-arbitrary reference point. It’s about the sound pressure where a 1000-Hertz sine wave first becomes audible to a human ear. It’s not a lot of pressure. The pressure 10 meters underwater is about twice what it is at sea level, which means the overpressure is about 1 atmosphere (1000 hectopascals. I’d like to note that Hectopascal would be a good name for a movie villain.) Well, the depth of water it would take to get an overpressure of 20 micropascals is 2 nanometers, which is about the diameter of a strand of DNA. Did you know human ears were that sensitive? I didn’t.

Anyway, you can use decibels to express a wide range of noise levels without using too many digits (Because, let’s face it, we all start zoning out after you get beyond about six digits, give or take.) To get the decibel number, you divide your sound pressure by 20 micropascals, take the base-10 logarithm of that, and multiply the result by 20. For example: a sound pressure of 20 micropascals gives you 20 * log10(20/20) = 20 * log10(1) = 20 * 0 = 0 dB.

With a title like Decibels of Death, you knew this article was going to be all about extremes. The quietest officially-measured place in the world is the anechoic chamber at Orfield Laboratories. It’s a room encased in a foot-thick concrete vault. The room itself sits on I-beams which are on springs to isolate external vibration. The inside of the room is full of wedge-shaped foam blocks which prevent echoes and dampen the sound from outside even further. The Guinness Book of World Records measured the sound level in the Orfield anechoic chamber at -9.4 decibels. That works out to a sound pressure level of 6.8 micropascals. To produce an overpressure that small, you’d only need a layer of water 0.612 nanometers thick. At that point, it’s less a puddle and more a molecular stack. That’s pretty damn quiet.

It’s actually intolerably quiet, apparently. The longest anybody’s ever spent in the chamber is 45 minutes, according to that Daily Mail article I linked above. I’ve heard stories about people who freaked out in the chamber because, all of a sudden, they can hear their heartbeats. And some people have auditory hallucinations when deprived of sound long enough, which probably makes the Orfield chamber even scarier.

So -9.4 dB is quiet enough to make you crazy. 0 dB is the threshold of hearing. 10 dB is about the quietest environment you or I will ever experience, and that’s only if we don’t breathe too loud. 25 dB is a very quiet room. According to a funky app I’ve got on my smartphone, the noise level at this desk is 51 dB. The EPA (the US environmental agency) recommends your everyday environment not exceed 70 dB. 85 dB can cause hearing damage over the long-term. 130 dB is painful. 150 dB can rupture your eardrums. This is what I was talking about earlier: logarithmic scales allow you to convert numbers orders of magnitude apart into nice numbers with low digit counts, which makes it easier to compare them side-by-side. When we started out, back at -9.4 decibels, the pressures were so low they were almost impossible to measure. Now, they’re so high they’re doing organ damage.

And speaking of organ damage… The strength of a blast wave is measured by its overpressure, just like the strength of a sound wave. In this fascinating and unnerving paper, some doctors report the effects of 62,000-pascal blast waves on rats. They speak of “minimal to mild alveolar hemorrhages,” as though there were such a thing as a mild case of bleeding fucking lungs. The upshot of all this is that, although 150 dB may burst your eardrums, 189.9 decibels (which is the decibel equivalent of 62,000 pascals overpressure) can actually damage your guts.

But if you’re catching a 190-decibel blast, you’ve got more serious things to worry about than bleeding lungs. Yes, really. There are a lot of reports of soldiers who have been hit by blasts from roadside bombs and car bombs and other such nasty things. Some of these soldiers, although they didn’t hit their heads on anything and nothing hit them in the head, developed serious cognitive problems: difficulty concentrating and short-term memory loss, enough to pretty much spoil their day-to-day lives. In another experiment, rats exposed to a blast overpressure of 20 kilopascals (180 decibels) experienced similar symptoms, and when they were dissected, had lots of dying brain cells. Which is all really pretty damn sad.

As it turns out, there’s actually technically a maximum sound pressure, at least if you want an undistorted sound wave. A pure tone has the shape of a sine wave: the pressure rises a certain amount above atmospheric, drops in a graceful sinusoidal curve, falls that same amount below atmospheric pressure, returns to atmospheric pressure, rinse and repeat. The thing about these kinds of sine waves is that, after their maximum overpressure, they have to drop that far below atmospheric pressure. And if the sound pressure of your sine wave happens to be greater than atmospheric pressure, that can’t happen: pressure is a number that doesn’t go any lower than zero, which is a vacuum. So a sine wave with a sound pressure larger than 1013 hectopascals (1 atmosphere) will sound all right when the pressure goes up, but will get cut off (“clipped,” the sound-engineer people call it) when it goes down. (And when I say “Will sound all right” I mean “Will rupture your aorta, destroy your lungs, tear your limbs off, and knock your house down,” as we learned from nuclear tests.) The maximum for unclipped sound, therefore, is 194.1 decibels.

But since we’re already blowing everything up, why worry about a little distortion? You know the Barrett M82? The big-ass .50-caliber sniper rifle? That one from that movie The Hurt Locker? The big scary one? Well, when that thing fires, its cartridge sees a blast wave of 265.5 decibels, which is just one more reason not to live in a rifle barrel.

You would experience 270 decibels if you were standing about 100 meters (350 feet) from a 1-megaton nuclear bomb when it went off. I use “experience” loosely here, since you wouldn’t have long to enjoy the racket before you were spread over an alarmingly large area.

Now, let’s say you were standing on the surface of a star just as it went supernova. Well, you’d be exposed to a blast pressure of something in the (very rough) neighborhood of 476 decibels, which I’m pretty sure the EPA would classify as “potentially hazardous.”

As it turns out, there’s a maximum pressure that is still physically meaningful, at least according to our current understanding of physics. It’s called the Planck Pressure, and it’s very large. It’s the kind of pressure you get inside black holes. It’s the kind of pressure the universe experienced (we think) right after the Big Bang. The Big Bang had a noise rating of 2,367.3 decibels. The explosion that set the current universe in motion had a pressure which can be quantified in five significant digits.

That’s what I mean about logarithmic scales being awesome. They turn unimaginable cosmic numbers into nice, manageable, comprehensible numbers. You’d better believe I’m going to be playing with logarithmic scales again soon. Which sounds way dirtier than I intended.

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