Slashdot Mirror
Micro-Black Holes Make Poor Planet Killers
astroengine writes "Physicists are getting excited about the possibility of micro-black holes (MBH) being produced by the LHC and an international group of researchers have done the math to see what kind of impact they could have on the Earth. Unfortunately, if you're a megalomaniac looking for your next globe-eating weapon, you can scrub MBHs off your WMD list. If a speedy MBH is produced, flying through our planet, it will only have a few seconds to accrete the mass of a few atoms. It would then be lost to space where it will evaporate. If a slow MBH is produced, dropping into the Earth where it sits for a few billion years, the results are even more boring."
I guess I know what kind of girl to look for now ;)
U+F8FF
Well, the key isn't just mass, but also radius. Gravity (I'll go newtonian, just because I'm lazy) increased linearly with mass, but decreases with the square of the radius. So for example, if you packed something the mass of Earth in just half the size of Earth, the gravity on the surface would be 4 times that of Earth. Squeeze it into a quarter of the size of Earth and get 16 times the gravity on the surface. Squeeze it small enough and you have a black hole.
If you do the proper maths, the Schwarzschild radius of a black hole with the mass of Earth is about 9mm.
Which really means, don't think something that will suck matter and bend light spectacularly all the way to Alpha Centauri. It means that if light happens to go within 9mm of that singularity, it ain't coming out. But farther away, it's still a body with the mass of Earth. The moon's orbit will still have the same radius for example.
A polar bear is a cartesian bear after a coordinate transform.
"Calculating how quickly a micro-black-hole would accumulate mass strikes me as a great undergrad tutorial question."
Which implies using existing theories to calculate it. What I think the grand parent post is saying is that we don't know for sure our current theories are all correct. After all, if we knew it all 100% correctly, there wouldn't be any need to build the LHC.
Scientific evidence accumulates over time. In science, its extremely hard to say 100% correct and be very careful of anyone who claims different.
Our current theories are our best current understanding of the universe and they do indeed work well. But we cannot be 100% sure. In the case of creating a black hole we won't know for sure until we create one under the conditions in the LHC (which due to the grouping of particle collisions in the LHC is different from a single high speed collision happening in the upper atmosphere).
Throughout the history of science we can see time and time again where theories were overturned. We therefore cannot assume all our current theories are correct under all possible conditions. There could be factors we are so far ignoring.
The problem is, the creation of a black hole in the LHC is kind of a unique experiment, as most wrong answers in science don't have such horrific results if our current theories are wrong.
There are 10 kinds of people in the world... those who understand binary and those who don't.
Have you considered religion?
# cat
Damn, my RAM is full of llamas.
In principle, any mass, if packed densely enough, could become a black hole. For each mass - from a cluster of atoms to an entire galaxy - there is a calculable quantity called the Schwarzschild radius. If you could somehow pack the mass so that it fit inside a volume smaller than that mass's Schwarzschild radius, the force of gravity would invariably overcome all other forces and cause the mass to become a singularity. The Schwarzschild radius also defines the "edge" of the black hole - if anything, including light, gets closer than one Schwarzschild radius from the central mass, it will not be able to escape. In other words, at the Schwarzschild radius, the escape velocity is the speed of light.
It is easy to see how the core of a really big star could collapse on itself in a supernova - there's just so much mass, coupled with the force of the explosion. However, our own sun could become a black hole - if some as-yet unknown physical process could squeeze its entire mass into a 6-km diameter sphere. The Schwarzschild radius of one solar mass is about 3 km.
It is important to note that, were this to happen tomorrow, the Earth and the other planets would continue to orbit the black hole sun exactly as they have done for billions of years. The gravity of the sun hasn't changed, because its mass hasn't changed. If you were, however, unfortunate enough to come within 3 km of the center of the black hole sun, that's the last the universe would ever see of you. (As a practical matter, you'd be doomed long before then, simply because no rocket would be powerful enough to bring you away once you got closer than a few thousand kilometers. To escape the black hole sun once you were, say, 3.1 km away, you would need to somehow achieve a speed near to the speed of light, which we simply can't do.)
It is also important to note that you would not be sucked into a black hole if you came within 3 km of the center of the sun as it exists today, shining hot and bright. This is because 99.999% of the mass of the sun lies outside of that 3 km radius and so "doesn't count" in terms of the force of gravity. Aside from instantly transforming into plasma from the heat, you would actually feel far less gravity than you would on the Moon. (For reasons why, see here.) Remember: a black hole would exist only if you could compress the whole mass of the sun into that 3-km radius spherical volume. This can be applied to just about any mass. The Schwarzschild radius of the Earth is about 9 mm - smaller than a grape. This gives you a sense of how densely you'd have to pack things if you wanted to make an Earth-mass black hole. For a pair of protons smashed together at high energies - as in the LHC - I think you need to bring in other areas of physics than just general relativity. Suffice to say the Schwarzschild radius would be much, much, much smaller than the size of a proton, which in turn is much, much, much smaller than the size of an atom, which is much smaller than the distance between atoms in most solids. So in order for a micro-black-hole to accumulate mass, it would need to pass very close, on the order of its Schwarzschild radius, to the nucleus of another atom. At the length scales we are talking about, that's about as likely as me randomly shooting off a bb gun and hitting a passing bird a kilometer away.
So rest easy, the world isn't about to end.
I apologize for the long answer, but I hope it has answered your question.
Particles. A hand-waving description of what happens is as follows:
Pairs of particles (one matter, one antimatter) form randomly near the event horizon. One quantum-tunnels out of the black-hole and so appears to an observer outside the black-hole to have been emitted. Therefore, to conserve energy, the other particle must have negative energy and thus the black-hole loses a tiny parcel of energy (and thus mass).
The main point is that, because the particle was formed near the event horizon and didn't come from the black-hole itself, it carries no information out - thus, while the black-hole loses mass, no information can escape.
The argument goes like this: There are plenty of cosmic rays which impact our atmosphere, the other planets in the solar system, the sun, other stars, everything, with energies across a huge spectrum, including LHC energies. Either the LHC will produce MBH or it will not. If it will, then cosmic rays also produce MBH, and do so without destroying any of the things we can see in the sky, so MBH from the LHC would similarly not destroy the earth. If the LHC will not produce MBH, then we have nothing to worry about in that regard anyway.
;)
This argument works for just about any Earth destroying LHC scenario, except, I suppose, the time traveling killer Higgs
SIGSEGV caught, terminating
wait... not that kind of sig.
There's no such thing as an anti-photon. In the case you are describing - pair production - both of the particles are virtual particles. They can be an electron and a positron (anti-electron), a quark and its anti-quark, etc - any particle/antiparticle pair. However a photon is its own anti-particle. And your explanation of the uncertainly principle is wrong. The time-energy formulation says (uncertainty in time) * (uncertainty in energy) = hbar, so the time limit for the life of the virtual particles is Planck's constant / energy (or Planck's constant divided by mass, since mass and energy are proportional and we measure the mass of these particles in units of electron-volts anyhow). Note that if it's mass * hbar, as you have above, then the higher the mass is, the longer the particles can stick around! That's exactly backwards. It's the tiny little particles that are flickering in and out of existence, not huge massive objects! If it were mass*hbar, you'd have virtual planets, stars and galaxies - the larger the object the more likely it would be to suddenly appear out of nowhere! This is an amusing thought but doesn't accurately describe the reality that we find ourselves living in.