The smallest mass of a black hole is theorized to be 10^16 kg and the mass of Earth is roughly 6^24 kg, so it would take a very significant portion of the whole planet to make a black hole, which is definitely not what CERN is doing with the LHC.

Would not the created black hole also be moving well beyond escape velocity?

@jmoreno Which would further imply that the LHC somehow imparts enough kinetic energy to accelerate 10^16 kg to 11 kilometers per second. It's too early in the morning for me to do math, but that seems like it'd take a lot of power even assuming 1:1 efficiency.

@Shadur 6,05 * 10^17 MJ if I am not mistaken. At 100% efficiency (Mass to energy conversion) that's about 6.7 * 10^6 kg. Global energy production is 6.19 * 10^5 MJ so it would take just about 10^12 years at the current output to reach that amount of energy.

@computercarguy I would not put much faith in that 10^16 kg limit (from a poorly sourced paragraph in Wikipedia). It is based on a speculative extensition of general relativity (Einstein-Cartan theory) and the baseless assumption that the black hole would have to formed from fermions.

@jmoreno The black hole would in principle be produced in the center of mass-frame of the collision. In the case of the LHC this means it can be produced with a very low velocity relative to the Earth. For Cosmic rays however, this means that the black hole would be produced at velocities well above the escape velocity.

@SirHawrk And at 99% efficiency that would produce enough waste heat to melt the bedrock of most of the continent into magma.

@TimRias Would a hypothetical black hole created by a cosmic ray be able to escape the Sun? If not, then there's the proof that it's not a threat. If it's a simple cross-section calculation, the lower density of the sun compared to a neutron star shouldn't matter.

@computercarguy: While such speculation can be conceptually interesting, it seems a bit too misleading.

@computercarguy Your numbers have the mass of the earth as 8 orders of magnitude larger than the smallest black hole. I'm not sure that .00000001 earth masses is significant.

@doneal24, 1 kg equals 0.26 gallons of water, so that means 10^16 kg is 2.6 billion gallons of water. That seems pretty significant to me. You are forgetting the math of large numbers in your statement.

@TimRias, well, the smallest black hole we've ever found is still 3.3x the mass of our sun. technologyreview.com/2019/11/01/65095/… And NASA says that black holes only form if a sun is 3-10 times the size of our sun. nasa.gov/vision/universe/starsgalaxies/Black_Hole.html On a speculative note, NASA does say black holes could be smaller, but still have the mass of a mountain. nasa.gov/audience/forstudents/k-4/stories/nasa-knows/…

@nigel222 The Sun still is not dense enough, but Neutron Stars are (see answer, and LSAG report linked).

@computercarguy And 6^24 kg is 1.6 septillion gallons of water. Yes, your number is large but it is insignificant when you're comparing it to a much larger number. Big, but still a very small fraction of the earth's mass.

@computercarguy 2.6 billion gallons is significant on the scale of a person. It isnt significant on the scale of the earth. Theres 1.386 billion km^3 of water on earth, and 0.00984 km^3 in 2.6 billion gallons, one trillionth of the Earths water...

@doneal24, it's significant to the sale of matter used at the LHC, which is what's actually relevant. symmetrymagazine.org/article/10-years-of-lhc-physics-in-numb‌​ers

@computercarguy Your comment was that the mass needed would take up a significant portion of the entire planet. Scale against LHC is large, scale against Earth's mass is very small.

@computercarguy Am I misreading it would take a very significant portion of the whole planet to make a black hole? I'm not quite sure how else to take this statement.

@doneal24, because you are forgetting the very important part about "which is definitely not what CERN is doing with the LHC". LHC doesn't deal in that much mass.

@computercarguy Your comment said that the mass required for a black hole was "a very significant portion of the whole planet". No one is saying it's not significantly more than what the LHC currently uses, but it's not a "very significant portion" of Earth's mass. In terms of Earth mass it's literally negligible. Our error on the estimates for Earth's mass is +/- 6^20 kg, the 10^16 mass of water is so insignificant that if we lost 1000 of them, it would fall into the error bounds of how accurately we know Earths mass.

Black holes get a bad rap, but false vacuum decay is scarier (and will affect the entire universe).

@computercarguy 10^16 kg is about half the mass of the water in the Baltic Sea. Nothing to sneeze at, but negligible on planetary scales. In any case, it is far beyond what CERN works with, which was your original point.