Suppose the LHC managed to create a microscopic black hole. The black hole would fly out of the earth within a second, and also out of our solar system -- if it didn't annihilate in a burst of Hawking radiation.
Why?
As a collider, the LHC would ideally collide equal-energy protons flying in the opposite direction. The center of mass would be stationary, so that the full energy would be available for interactions. How close does it realize that ideal in a particular collision? If the two energies differ by about 1% (and we ignore that the collision won't be fully 100% head-on), about one part in 40,000 of the energy would be unavailable.
Is there any kind of chance that the two energies would be less than 1% apart? Let's take them that far apart: E1 = 1.01 E2. Then the total energy is E = E1 + E2 = 2.01 E2, and the total momentum (100% head-on) is pc = E1 - E2 = 0.01 E2.
The speed of the object is pc2/E = 0.01 E2c/2.01 E2, approximately .005c or over 900 miles/second. The collision occurs horizontally, not vertically, so it will leave the earth in well under a second.
Who told us there was no danger? The experts in the field. Who were terrified of the danger, to the point of even calling to take out the LHC with a nuclear weapon? Ignorant laymen.
Let's further ground ourselves with an estimation based on general relativity, of the event-horizon radius of a Planck-mass black hole. In Planck units (specifically, hbar=c=G=1), R=2m, and also m=1. A Planck-mass (or Planck-energy) black hole would have R=2 Planck lengths or about 3x10-35 meters. The Planck energy is two billion Joules, or about 1015 times the LHC interaction energy.
The LHC is 15 orders of magnitude away from producing a black hole, by conventional theory. Sure, quantum effects, inflation, dark energy, or something might decrease the energy required by several orders of magnitude, but that still leaves us with plenty of orders of magnitude to play with.
No, there never was any danger, as the past decade-plus has shown.
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