Can the CERN LHC Destroy Earth?

A calculation of the total energy density produced by protons in the Large Hadron Collider at CERN shows it is not likely to destroy Earth.

Paul A. Heckert - Sep 18, 2008

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Various popular media have been making much ado about the possibility that the tremendous energies to be produced by the CERN Large Hadron Collider (LHC) may destroy Earth. They speculate these energies could produce a small black hole that would eventually swallow Earth. Is there any scientific validity to this speculation, or is it much ado about nothing?

The fact that this article was written after the Large Hadron Collider was turned on provides very strong experimental evidence that it is indeed safe, but the physical reasoning behind physicists' conclusion that it is safe is instructive.

Arguments the LHC is Safe

Critics suggest that the LHC is unsafe because the high energy density and high energy collisions could produce an extremely low mass black hole that would eventually swallow Earth. The CERN - Large Hadron Collider Machine Outreach site argues the Large Hadron Collider is safe because:

1. Cosmic rays with greater energies strike Earth's atmosphere and have not yet destroyed Earth.
2. In the very unlikely event the LHC produced an extremely low mass black hole, the black hole would not have enough energy to do significant damage. Physicist Stephen Hawking predicts that very low mass black holes evaporate in a burst of gamma rays, but any produced by the LHC would release insufficient energy to do damage.

Energy Density in the LHC

An order of magnitude calculation shows how unlikely it is for the Large Hadron Collider to form a black hole. The LHC Outreach site states that protons will be accelerated to an energy of about 7e12 electron volts. (7e12 indicates 7 times 10 to the twelfth power.) Rounding that energy up to the nearest order of magnitude gives about 1e13 electron volts per proton.

It also states that the typical LHC beam will contain roughly 3e14 protons. Multiplying these numbers gives 3e27 electron volts in each beam of protons.

An electron volt is a unit of energy used in particle physics. Like most units used for studying subatomic particles, it is very small. 1 electron volt equals 1.6e-19 joules of energy, which rounds to 1e-19 joules.

Hence the 3e27 electron volts in the typical Large Hadron Collider beam equals a few hundred million (3e8) joules.

The key to forming a black hole however is compressing the matter or energy to a very high density. According to the LHC Machine Outreach, the LHC will compress these beams to a radius of about 1e-5 meters and a length of a few centimeters. Using the formula for the volume of a cylinder gives about 1e-11 for the volume of the LHC beam. Dividing the energy by the volume to get the energy density of the LHC beam gives a rough estimate of 1e19 to 1e20 joules/meter^3. (The ^ symbol indicates an exponent, so ^3 indicates something cubed.)

For a solar mass star to collapse into a black hole it must be compressed to an energy density of roughly 2e36 joules/meter^3. A smaller mass would have to be compressed to a higher density. Hence the energy beam in the Large Hadron Collider is many orders of magnitude away from being compressed into a black hole.

Energy in LHC Collisions

The LHC is expected to produce 6e8 proton collisions per second. Each collision between two protons with 7e12 electron volts should release twice that amount of energy. Multiplying 2X(7e12)X(6e8) gives about 1e22 electron volts/second, which is about 1000 joules/second. A joule per second is a watt, so the LHC collisions release about 1000 watts, which is equivalent to 10 light bulbs.

Don't Worry!