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How do virtual particles cause black holes to evaporate?

Stephen Hawking has stated that black holes disappear over time. My understanding is that because of the uncertainty principle there are vacuum fluctuations causing positive and negative energy particles to be produced at the event horizon. If the negatively energy particles fall into the black hole they reduce the mass of the object and over time the black hole evaporates. My question is don't these particles have a 50% chance of being of positive or negative energy? And if I'm right the same percentage of positive or negative energy particles will fall into the black hole, yielding no change to the object.

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Vacuum fluctuations cause virtual particle pairs to pop out of the vacuum and disappear again. The total energy of both particles is zero (because they appear out of "nothing"), so one particle has negative energy and the other positive energy. The black hole evaporates because the negative energy particles can fall into the black hole while the positive energy particles escape. This causes the total energy of the black hole to become less and, since energy is mass times the speed of light squared, the black hole loses mass.

The question is, why can't positive energy particles fall into the black hole while the negative energy particles escape? To explain this, it is necessary to understand how this business with virtual particles arises. This is not well explained in popular books. You probably know that quantum mechanics predicts that systems like atoms have energy levels. So, the hydrogen atom has a lowest energy state, a first excited state with higher energy, etc. but nothing in between those energies. It works ...

Solution Summary

We explain in a nontechnical way how the Hawking process causes black holes to evaporate. We also briefly explain some basics about quantum field theory and virtual particles.