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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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Could you kill the human race with a BB gun?

As you might have guessed, this post is heavily influenced by xkcd’s brilliant weekly What-If blog

While pondering meteorites striking the earth with absurd velocities, I got to wondering whether or not you could actually kill the human race with a single BB. Because physics is a frightening place, the answer to questions like this is usually yes.

To simplify the first stage of calculations, we need to know how much energy is required to kill the human race. I will call this constant the “ohgod,” and I will set it equal to the kinetic energy of a 15-kilometer-wide stony asteroid traveling at 22 kilometers per second, which would be more than sufficient to cause a mass extinction which would almost certainly wipe out the human race. One ohgod is approximately 1.283 x 10^24 joules, or about 2.6 Chicxulubs (or, as people who fear the awesomeness of Mesoamerican words put it, 2.6 dinosaur-killers). 

The mass of a BB is surprisingly hard to find, although there is a very handy chart listing the masses of high-end BBs in grains, which can easily be converted to grams. By my reckoning, a standard 4.5-millimeter (0.177 caliber) BB should weigh about 0.4 grams. In order to figure out how fast a 0.4-gram BB would have to be moving to have 1 ohgod of kinetic energy, we must solve the relativistic kinetic energy equation for velocity. The relativistic kinetic energy equation is a little unwieldy:

E = [(1/sqrt(1-v^2/c^2)) + 1] * m * c^2

I actually had to get out pen and paper to solve this equation for v. Here’s my math, to prove that I’m not a lazy cretin:

Image

When I calculated v and plugged my numbers back into the relativistic kinetic energy formula on WolframAlpha, I was greeted with one of the most satisfying things a nerd can ever see: I got back exactly 1.283 x 10^24 joules, which means I didn’t have to do all that algebra again.

As it turns out, in order to have a kinetic energy of a species-killing asteroid, a BB would have to be traveling quite fast. I would have to be traveling at 0.9999999999999999999996074284163612948528545037647345 c, in fact. That speed is slower than the speed of light by only a few parts in 10^22, which is to say by only a few parts in 10 billion trillion. A few parts in 10 billion trillion equates to a bacterium-sized drop of water added to an Olympic-sized swimming pool. Feel free to insert your own joke about homeopathy here.

Our lethal BB would be traveling almost as fast as the fastest-moving particles ever detected. I’m thinking here about the Oh-my-God particle, which was (probably) a proton that hit Earth’s atmosphere at 0.9999999999999999999999951 c. The Oh-my-God particle is faster by a hair. But our BB is still traveling a ludicrous speeds. Light is fast. A beam of light could circle the Earth in 133 milliseconds, which, if you look at reaction-time data, is about half the time it takes a human being to detect a stimulus and for the nerve impulse to travel down their arm and make a muscle contract. Very few physical objects can hold their own against light. But our BB could. If you raced our BB and a beam of light head-to-head, after a thousand years, the BB would only be lagging 3 millimeters behind, which is about the diameter of a peppercorn, which is ridiculous.

But the question here is not “How fast would a BB have to be traveling to have the same kinetic energy as a humanity-ending asteroid.” The question is “Could you actually use a hyper-velocity BB to kill the human race,” which is much more interesting and complicated. 

First of all, the BB would have an insane amount of kinetic energy. E = m * c^2, of course, and from that, we know that our BB’s kinetic energy (its energy alone) would have a mass of 1.428 * 10^7 kilograms, which is about the mass of five Boeing 747 jet airliners. I would have to be a very gifted physicist to tell you what happens when you’ve got atoms with that kind of energy, but I suspect that there would be very weird quantum effects (aren’t there always?) which would conspire to slow the BB down. Because of quantum randomness, I imagine the BB would constantly be emitting high-energy gamma rays, which would decay into electron-positron and proton-antiproton pairs. Which is to say that our BB would be moving so fast that, rather than leaving behind a wake of Cherenkov radiation, it would leave behind a wake of actual physical matter, conjured seemingly from the ether by the conversion of its kinetic energy. 

As for what would happen when the BB actually hit the Earth, that’s beyond my power to calculate, on account of I don’t have access to a fucking supercomputer. But we can assume that the BB would pass straight through the Earth with no physical impact: all of its interactions with our planet would probably be on the level of ultra-high-energy particle physics. And from that, we can estimate its effects.

The BB would cut a cylindrical path 4.5 millimeters across and 1 earth diameter long. If it deposited all of its kinetic energy along this track, it would raise the temperature of the rock by 10^15 Kelvin, which would make it one million times hotter than a supernova, which would most certainly be more than enough to kill all of us and vaporize a significant fraction of the Earth.

But the BB would only spend 44 milliseconds passing through the Earth, and somehow I doubt that regular matter would stop it entirely. Let’s assume instead that only one tenth of its energy got deposited in its track. We’re still talking a temperature a hundred thousand times that in the center of a supernova, which is ridiculous and would, once again, kill us all and peel the skin off the planet.

What if the BB only loses one one hundredth of its energy as it passes through the Earth? Same result: the Earth is replaced by a ball of radioactive lava.

But if, because of its ridiculous speed, it only loses one one millionth of its kinetic energy interacting with Earth, it still heats its needle-thin track to 3 billion kelvin, which is hot enough to fuse Earth’s silicon into iron and produce a violent explosion that would spawn earthquakes and firestorms and might, in spite of the energy losses, kill us all anyway.

But when you consider how much energy even the mighty Oh-my-God particle (which was, let me remind you, moving so fast that light was having trouble staying ahead of it) deposited just by hitting the atmosphere, I’d say the BB would lose quite a bit more than one one-millionth of its kinetic energy on impact. And I’d say that that kinetic energy would be spread over a fairly wide area. I’m thinking it would leave behind a column of hydrogen-bomb-temperature fusion plasma in the atmosphere, then hit the crust and fan out within an ice-cream-cone-shaped volume of the mantle. The nastiness of the results depend entirely on how big an ice-cream cone we’re talking, but it’s likely to be fairly narrow and fairly long, so we’re probably looking at a near-supernova-temperature column of fusing rock plasma with a length measured in kilometers. The explosion would be worse than anything the Earth has ever seen and would, yes, almost certainly kill all of us. If the immediate radiation didn’t get us, then the explosion would expose the mantle and lift enough dust to darken the sky for years.

You know, at the start of this, I thought I had an idea I could pitch to Daisy Outdoor Products. Now that I think about it, I think I’ll put the proposal in a drawer and forget about it.

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