Can we produce black holes by particle accelerators?

[Xforce]

TL;DR Summary

Thanks to CERN, we now have huge particle accelerators such as the LHC. We use them to enhance our understanding of quantum physics.

Summary: Thanks to CERN, we now have huge particle accelerators such as the LHC. We use them to enhance our understanding of quantum physics.

As everyone know,particle accelerators are huge machines that smashes atoms into pieces at near the speed of light. I have heard making antimatter by using them, which is an inefficient but the only known method. And I have heard the WIMP particles or Higgs-Boson particles that helps us study dark matter.
They are truly amazing stuff. But what about black holes? I heard that we can produce an artificial quantum-sized black hole by a particle accelerator. Of course it must be larger than LHC and the experiment will engage in space. The idea is, to accelerate a proton to such high energy that it’s wavelength shrinks to under The Planck’s length, which is 1.26*10^-35 meters(from Wikipedia). Another way is using the principal of special relativity, when the proton ‘s velocity makes its mass increases, and the Schwarzschild radius(which is 2Gm/c^2)becomes greater than the proton’s diameter(8.751^10^-16 meters). So is it feasible to make a black hole by particle accelerators?

 

[PeterDonis]

The idea is, to accelerate a proton to such high energy that it’s wavelength shrinks to under The Planck’s length

Another way is using the principal of special relativity, when the proton ‘s velocity makes its mass increases, and the Schwarzschild radius(which is 2Gm/c^2)becomes greater than the proton’s diameter(8.751^10^-16 meters)

These descriptions are not correct. Velocity is relative; just having a reference frame in which a proton is moving at a highly relativistic velocity cannot make it into a black hole.

Particle accelerators create high energy collisions by smashing beams of particles together that are traveling in opposite directions. Just making the particles move very fast does nothing by itself.

is it feasible to make a black hole by particle accelerators?

No. You would have to build an accelerator about the size of the observable universe for it to be able to smash together beams of particles with enough energy to do this.

 

[PAllen]

@PeterDonis , what you say is true for standard model and GR. However, for some hypothetical gravity theories, LHC could produce BH, and LHC looked for this, but none were found:

https://cms.cern/news/search-microscopic-black-hole-signatures-large-hadron-collider

 

[Xforce]

I have done some further research to this, and it turn’s out the energy of a particle collision required to generate a black hole is about 10^30 eV ( according to [The Universe in a Nutshell]), which is significant higher than LHC capacity, however, it is possible to build a particle accelerator as large as the solar system in a few centuries, because in the vacuum of space, no tube is required, we can just put a few million coils around the solar system in an arrangement. Plus, coils can be build larger and more powerful, because we don’t need to worry about to dig a big tunnel underground in space.

 

[PeterDonis]

the energy of a particle collision required to generate a black hole is about 10^30 eV ( according to [The Universe in a Nutshell]),

A pop science book is not a valid source. The truth is that we don't know for sure what this energy is because we don't know for sure what kind of physics might come into play at these energy scales. A rough guess would be that we would need roughly the Planck energy, $10^{28}$ eV; but that's just a rough guess.

which is significant higher than LHC capacity

Yes, 15 or more orders of magnitude above the LHC energy qualifies as "significant".

it is possible to build a particle accelerator as large as the solar system in a few centuries, because in the vacuum of space, no tube is required, we can just put a few million coils around the solar system in an arrangement. Plus, coils can be build larger and more powerful, because we don’t need to worry about to dig a big tunnel underground in space.

All of this is possible in principle, but whether it's doable in a few centuries is more problematic. Also, I don't think an accelerator the size of the solar system would be enough to reach the Planck energy.