What's the mathematical underpinning that has everyone convinced of Hawking Radiation?

Question

Why is everyone convinced? I have no clue what it is, I'm not literate in astro physics obviously. Since this has never been observed in space or a natural environment.. What are the mathematical or physical underpinnings that make this theory accepted? And why is there still a substantial amount of skepticism?

This is primarily concerning the LHC?

I got into a debate this night with someone at a party over this. I've read that the collisions produced by cosmic rays that the Earth's been bombarded with on a daily basis since the beginning of time are far greater than anything the LHC is capable of. We're still here. My friend for some reason strongly disagrees with me.

He says that the unique properties of the LHC environment coupled with the fact that this is being done inside the Earth's atmosphere could cause some really bad stuff.

Maybe we're foolish to believe we can play with this stuff in a controlled environment.. Who knows.

Answer 1

The first user stole my answer :o).

Hawking Radiation is similar to radioactive decay. According to classical physics, no particle should have enough energy to escape the Coulomb barrier at the nucleus of an atom, yet we know they do. The Uncertainty Principle of quantum physics, however, allows a finite probability that the alpha particle could penetrate the barrier by the QM tunneling affect.

While some think there is a possibility of creating micro-black holes, the chances are extremely remote and even if it happened, they would be smaller than a proton, so small they would either evaporate immediately, or would pass through the Earth without hitting anything.

The physicists at CERN are trying to verify the existence of the Higgs boson, which is believed to be the mechanism that gives matter mass, one of the big puzzles in physics.

Although the energy achieved by the particle beams sounds immense, particles hit the atmosphere every day which are much more energetic. On October 15, 1991, the Fly's Eye in Utah detected a proton (called the OMG particle) with an energy of 3.2e20 ev. By comparison, the LHC will collide streams of protons at 7e12 ev each, 20 million times less.

The energy of the OMG particle was about 51joules. That of the 7e12 ev LHC particles is only 1.12e-6 joules.

http://www.fourmilab.ch/documents/OhMyGo...

Edit: Hawking radiation process is quantum tunneling effect, wherein particle-antiparticle pairs form from the vacuum and one tunnels outside the event horizon.

http://en.wikipedia.org/wiki/Hawking_rad...

http://www.iop.org/EJ/abstract/1126-6708...

Answer 2

Hawking Radiation is not due to tunneling.

It arises because of vacuum fluctuations outside the event horizon. We know these occur because they can be measured in a lab - the Casimir Effect is a famous example. In a vacuum fluctuation, particle-antiparticle pairs arise spontaneously but have life times that mean dEdT <= h/2pi. Normally the particle pairs are unobservable directly (they are virtual), but at the event horizon it is possible for one of the pair to be captured by the black hole.

The main objection to the idea is its impact on entropy. In effect, a know particle falling into the event horizon tells us something about the entropy of the black hole (conveys information) and this should not be possible.

Your friends is totally wrong re the LHC - he clearly has no clue. The supposed risk of the LHC is that it creates densities large enough to create a Schwartzchild metric (black hole) locally, but this would be infinitely tiny. The same math that shows this could happen also shows it would evaporate almost instantly - hence no risk.

Answer 3

Well, Hawking radiation is simply energy being emitted by black holes, basically through quantum tunneling.  Since we can prove quantum tunneling exists, Hawking radiation must also.

As far as your disagreement with your friend goes.  It is true that billions of high energy cosmic rays (photons) are passing thru you all the time, but they are very unlikely to ever interact with you.  The LHC is only a few times more powerful than previous colliders, so it isn't like it is vastly different than the things that have been done safely for years.  Any emissions from it powerful enough to pass thru the detector and shielding, are unlikely to be absorbed by anything we care about.

Answer 4

I don't see what Hawking Radiation has to do with your argument with your friend. Hawking used virtual particles in his discussion on black hole radiatation. Virtual particles do not exist in nature, for this reason I have no faith in his conclusions.