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There are a lot of people worried that the world will end soon. This autumn, specifically, when the Large Hadron Collider (LHC) at CERN in Switzerland and France turns on and starts smashing protons together at velocities that are nearly the speed of light. The main concern is that these collisions will create a miniature black hole that will swallow the Earth and us with it.

Thankfully for human civilization, black holes just don’t work this way.

While the basic level of understanding of science in the United States should be much higher than it is, the science underlying black holes is pretty arcane. While everyone really should remember the basic biology, physics, cosmology, geology, chemistry, ecology, and even genetics that they were taught in high school and maybe college (alas, science is too “nerdy” or “geeky” for most to care, never mind that footballs follow a predictable ballistic trajectory determined by Newton’s Laws of Motion), the science of black holes is strange enough that it’s simply not fair to expect everyone to have much knowledge of them beyond the fact that they exist. Understanding why a LHC-created mini black hole won’t eat the planet requires a basic understanding of how black holes work, some of the weirder things they can do, and why those weird things mean that we don’t need to worry about a mini black hole eating the planet.

Our discussion of black holes starts with stars. Stars have a life cycle - they’re born, the live a long, long time, and then they die out. How massive a star is determines how long it lives and the various ways it can die. Stars like our sun, Sol, are pretty average stars, and average stars live 10-30 billion years or so, then blow up to be bigger than the orbit of Venus (some stars can become bigger than Mars’ orbit, some 227 million km, an increase of over 300x larger than the sun is now). Then they go nova, blow off the outer layers of their surface, and gradually shrink down to a dense, cold cinder called a brown dwarf. Big stars, however, live fast and die young, completing their entire life cycle in tens to hundreds of millions of years instead of billions of years. Big stars expand as they’re about to die just like average stars do, but then they go supernova.

To understand why a star goes supernova, let’s talk about gravity and fusion reactions. Stars keep their size because the explosive power of the fusion reaction that drives the star is equaled by the force of gravity holding the star together. As a star ages, there’s less and less hydrogen (the main fuel of fusion) to keep the reaction going in the core, so the star starts to collapse under its own weight. When the core of a big star gets too dense, it shrinks until something else stops it, and when that happens the energy released basically blows up the rest of the star - a supernova. The result of a supernova is one of two things, either a neutron star or a black hole. A neutron star is what’s left if the original star wasn’t quite big enough to collapse so far that the force of gravity overwhelmed light - a black hole is what’s left if the original star was so big that it’s core can capture even light.

Black holes are named such because the force of their gravity is so great that light, the fastest thing that can exist according to Albert Einstein’s Theory of General Relativity, cannot go fast enough to escape. The reason light can’t escape is essentially the same reason that rockets are huge to get the space shuttle off the Earth - it takes a certain amount of velocity (known as the “escape velocity”) to launch an object out of the Earth’s gravity altogether. When the escape velocity is greater than the speed of light, the body that creates that effect is called a black hole. The mathematical surface around the black hole’s center of mass where the escape velocity equals the speed of light is known as the “event horizon”.

Unfortunately, if light can’t escape past the event horizon, then neither can anything else - Einstein also proved mathematically that the speed of light is the universal speed limit, and no object made of matter can ever go any faster than that (in fact, nothing with mass can ever go that fast, but mass inflation and time dilation are topics for a different post). Anything that passes the event horizon is lost to this universe - only it’s gravity remains. So a black hole consumes matter and energy both.

There’s other ways to create black holes, though the collapsing star method is the only one that cosmologists are pretty sure they’ve directly observed. But Einstein also proved that energy and mass are equal, with a proportionality constant, using the equation e=mC², where E is energy, m is mass, and C is the speed of light in a vacuum (i.e. space). Which means that, if you’ve got smaller mass but that is traveling REALLY fast (fast things have more energy than slow things do), it might be able to convert enough of that energy into mass in a collision to create a black hole. And this is where the LHC comes back in again.

The LHC is a circular particle accelerator housed underground and straddling the border between Switzerland and France. Its purpose is to test the fundamental laws of physics, specifically the existence of certain types of sub-atomic particles (especially the Higgs boson) and how they interact with each other. To do that, though, it has to accelerate protons to extremely high energy, 7 TeV (tera-electron-Volts, a thoroughly inconvenient unit for anyone not used to working with semiconductor physics and/or particles) per proton. When a collision occurs, the protons will disintegrate into sub-atomic particles that will be indirectly detected and measured by the huge and complex science test equipment around the collision point.

It’s this collision that people are worried about. Since energy equals mass, there’s a chance that the 14 TeV collision will create a small black hole. And given that, as mentioned above, black holes eat matter and energy, a tiny black hole would be a threat to the Earth, right?

Wrong. But we’ll take a brief break here for a brief musical interlude so that everyone whose eyes have glazed over to regain their senses for another round of science content (although I’m most definitely not a “she”…)

Welcome back.

Einstein was a brilliant man, but he didn’t know everything. No person, however bright, can know everything, and Einstein hated the entire idea of quantum mechanics, rejecting it as “spooky action at a distance” and famously quipping that (paraphrased) “God does not play dice with the universe.” Unfortunately for Einstein, quantum mechanics has become as firmly entrenched in physics as general relativity, and it took another brilliant man, Stephen Hawking, to realize that the two sometimes interacted in really, really weird ways.

At the quantum scale (lengths of an atom or less, 10^-10 meters or shorter), recent theories of quantum mechanics say that space is foam of sub-atomic particles and antiparticles that pop in and out of existence due to the background energy of the universe. The equations of quantum mechanics say that this is possible so long as the total energy of this effect averages to 0 (zero), so for every particle that pops into existence another antiparticle (antimatter) also pops into existence. As weird as this sounds, scientists know that antimatter exists because particle physicists have created it in ultra-high vacuum chambers where it can’t interact with regular matter and annihilate itself. In fact, the medical PET scanner uses antimatter electrons known as positrons - PET stands for “Positron Emission Tomography”. Particles like this that pop in and out of existence are known in the science literature as “virtual particles” because they don’t hang around for long and their mass averages out to zero.

So, let’s propose that this foam of virtual particles is next to a black hole’s event horizon. Since particles and antiparticles can’t exist in the exact same spot without annihilating each other, the particle and antiparticle have to speed away from each other in opposite directions. Their movement makes it more likely that one will be lost into the black hole while the other will eventually escape the holes’ gravity. Because of conservation of mass and energy via general relativity, the particles (or antiparticles) that escape gradually reduce the mass of the black hole, effectively causing the black holes to evaporate. The emitted particles are known as “Hawking Radiation” after Stephen Hawking, and he also showed that bigger black holes evaporate more slowly than little black holes do.

So, if the LHC actually does create a mini black hole, then it will eventually evaporate into nothingness. And whether we need to worry about it or not will depend greatly on how fast it evaporates - if it evaporates faster than it can absorb new energy and/or mass and grow, then it’s ultimately harmless even if the LHC does create a mini black hole.

Let’s assume that the protons are each 7 TeV like the LHC FAQ says. Each 7 TeV proton then weighs about 1.2477 x 10^-23 kg. Using the equation for rate of evaporation from Wikipedia, we find out that a black hole created by two 7 TeV protons colliding will evaporate into a burst of sub-atomic particles within 1.306 x 10^-82 seconds. Or, if you prefer, 0.0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 01306 seconds.

The fastest laser pulses have been sub-femtosecond pulses, and those are only 10^-15, or 0.000000000000001 seconds, and those are fast enough to catch the location of an electron as they orbit an atomic nucleus. Even at 99.999991% of the speed of light, any itty-bitty black hole created would move about 3.92 x 10^-74 meters in that amount of time. That’s about 10^-59 the way across the diameter of an electron. So we can safely say that any mini black holes created will not escape the LHC itself.

The LHC expects about 600 million (6 x 10⁶) collisions like this per second, so there’s a small chance that two collisions could occur a the exact right time to combine. The chance of that happening, however, is roughly equivalent to the area of a proton collision compared to the area where the collision will occur. The LHC focuses the proton beams down to 64 microns (6.4 x 10^-5 m) across, or an area of 3.217 x 10^-9 m² (circular area assumed). The area of a proton is only 2.405 x 10^-30 m², so the probability of multiple collisions at the same spot in space is 7.476 x 10^-22. For comparison, this is a probability of about once every 100 billion lifetimes of the universe.

So, not only will any nano-black holes evaporate too fast to be a threat, the chance that the LHC beam will be able to create a nano black hole that MIGHT survive long enough to be a threat via the mechanism of multiple collisions at the same spot in space is so low that it probably hasn’t happened in the entire history of the universe to date, and probably never will. We certainly won’t be around to see it.

The real kicker here, though, is this: while the LHC is creating high energy protons artificially, the galaxy creates even higher energy particles (known as “cosmic rays”) all the time. We know that cosmic rays hit our atmosphere all the time because the shower of sub-atomic particles that the collisions create have been observed on the surface of the earth. If higher energy collisions are occurring all the time, then either a) nano black holes aren’t created by such collisions in the first place or b) those black holes evaporate harmlessly. And since the earth hasn’t been sucked up into a nano-black hole created by cosmic ray collisions yet, we can reasonably expect that the LHC won’t create a big enough black hole either.

Hopefully this science lesson has allayed your fears that the LHC will create a planet-eating black hole. It’s not the end of the world as we know it, but you should continue feeling fine.

UPDATE #1:

A few of the comments have suggested that the LHC will produce a stationary black hole if indeed it does create a black hole in the first place. This is not correct for primary non-elastic collisions, and I’ll explain why below. In addition, I’ll explain what happens in secondary collisions in Update #2. But first, a few quick definitions.

“elastic collision” - in an elastic collision, protons act like billiard balls, with the two protons bouncing off each other.
“Non-elastic collision” - if the two protons were billiard balls, a non-elastic collision would result in the explosion of both billiard balls or the fusion of both balls into a single ball.
“Primary collision” - the first collision of the two colliding protons as they pass through the collision region. In billiard terms, this would be the first time the cue ball hits another billiard ball.

“Secondary collision” - the second collision of a proton after an elastic collision with another proton. In billiard terms again, this would be the cue ball hitting a second ball after hitting the first, or the collision between a hit billiard ball and a second billiard ball.

First, if you look at the image at the LHC Collisions page, you see that Beams 1 and 2 do not intersect in a head-on collision. Because of this, there is no possible way that any resulting particle (and a nano black hole would be have mass and therefore be a “resulting particle”) from a primary collision can have zero velocity within the LHC. The image below shows two protons, A & B, heading toward a collision at the point that the two red arrows (vectors) intersect. Each of them is a 7 TeV energy proton traveling at 99.999991 % of the speed of light C. Notice if you will that they are traveling toward each other equally in the X-direction (left/right), but that because of the angle of their paths, they are both traveling in the negative Y-direction (down). If you’re familiar with vector mathematics, then the X velocity vectors are equal and opposite, but both have the same negative Y velocity vector.

This next image shows the two protons right before the non-elastic collision, when both are still traveling down, although they’ve both traveled to the intersection point.

The final image shows that nano black hole (particle C, composed of the dotted particles A and B) is all that’s left as a result of the non-elastic collision. Notice that the blue arrow, illustrating the direction of movement, is only pointing down. This is because the X-direction movement of A and B canceled each other out, but since there was no opposing force in the upward direction - both A and B were traveling downward - C must, according to the laws of conservation of mass and momentum, continue moving down.

Notice also that the speed of the resulting particle C is 99.9999996% of the speed of light, or even faster than the original two particles. This is due to the fact that the downward movement (negative Y velocity vectors) of the two particles A and B combine to produce a particle C that is moving even faster than either proton would be individually. According to Special Relativity and the gamma (γ) function as calculated using a 14 TeV mass for particle C.

Ultimately, though, what these three images show is that, since there is no opposing upward force (positive Y velocity vector) on particles A and B, particle C cannot come to a complete rest. So if particle C is a nano black hole, and if Hawking radiation doesn’t exist, then the nano black holes created by the LHC will pass through the Earth at very nearly the speed of light, never to return and eat the planet.

Update #2

In Update #1 above, I indicated that there could be secondary collisions, specifically if protons collided in an elastic (bouncing) fashion and the collided again. In this way, it’s actually possible to create a stationary particle. However, I’ll also show that a) the probability of a secondary collision being non-elastic is negligible.

The figure below shows the sequence of collisions that has to occur in order for our secondary non-elastic collision to produce a stationary particle.

The two green colored protons are from beam 1, the two magenta colored protons are from beam two. At positions A, the four protons are positioned so that they will collide in elastic collisions at point B. Because the collisions are elastic, the four protons bounce off each other at point B with the exact angles required (in three dimensions, although only two are shown for simplicity). Then two of the protons move to point C and collide in a non-elastic (destroying or fusing) collision that produces either the destruction of both protons or a single particle with a mass equal to the sum of the mass of the two colliding protons.

Because the momentum of the protons in both the X direction (left/right) and the Y direction (up/down) are equal and opposite, any resulting particle would be stationary. And if this were a nano black hole, and if Hawking radiation and evaporation didn’t occur, then it could become a problem over the long run. However, let’s talk about how likely this is.

According to the LHC collision page again, the number of collisions is defined by the the luminosity (10³⁴ protons*sec^-1cm^-2) multiplied by the elastic cross-section of a proton at 7 TeV, or 40 mBarn (40 x 10^-27 cm²). Using this number, I calculate that the number of collisions per second will be 10³⁴ x 40 x 10^-27, or 4 billion collisions per second (10x more than the LHC page calculates). Assuming my number is correct since it’s a worst-case situation, and dividing the number of collisions by the average number of proton clumps (2808) and further dividing that number by the number of cycles each bunch takes through the LHC every second (11245) and we have 127 elastic proton collisions per transition through a collision region.

However, we need to calculate the number of secondary non-elastic collisions, and for those, the luminosity (which used to be 10³⁴ protons is now the number of elastic collided protons, or 127. 127 x 60 x 10^-27 gives us 7.62 x 10^-24 non-elastic collisions per second. To put this number into perspective, if the LHC ran non-stop for 10 years (about 3.16 x 10⁸ seconds), we could expect .0000000000000024 collisions. Or, to put it another way, we could reasonably expect one collision of this type inside the LHC every 415 billion years.

And this assumes that the collision is exactly aligned right to produce a stationary combined particle. Given that a combined particle would have the default speed of 99.9999996% of the speed of light, if the alignment were off by one millionth of one percent, the particle would still go careening off harmlessly in some unpredictable direction at some slightly lower but still amazingly high percentage of the speed of light.

Image credits:
Valerio Mezzanotti for the New York Times
ParticlePhysics.ac.uk
Cern/Maximilien Brice, via the BBC

Source:

http://www.scholarsandrogues.com/2008/06/22/the-large-hadron-collider-will-not-eat-the-world/

Labels: The Large Hadron Collider will not eat the world