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Hmm. To be honest, neither description is quite correct - both Prof.
Hawking and myself were oversimplifying a bit. Perhaps the most correct
description is the following: Let's say you start off with an empty
vacuum, with zero energy. (This is itself a simplification!) When a
particle-antiparticle pair pops into existence - a vacuum fluctuation -
suddenly there is a little extra energy. Both particles have mass, they
both have momentum and kinetic energy - so for a moment *conservation
of energy is violated*. Exactly what energy, mass, momenta do these
particles have? It's not well defined. This is quantum mechanics, after
all; energies and momenta and so on only take on exact values after you
measure them.

This can only persist for a very short time; usually the two particles
meet and annihilate, and the energy drops back to zero. (The question of
"what were the energies" is never answered, since the wavefunctions never
collapsed.) Near a black hole, however, sometimes one of the particles
gets sucked into the event horizon, while the other one escapes. This
sort of amounts to a "measurement" of the pair; just like any
quantum-mechanical wavefunctions, the particles decide what energies to
have *only* when the measurement is made.

One of the neat things about quantum-mechanics measurements is that they
will always give you a physically plausible answer. In this case, the
particle-antiparticle pair sort of "knows" that it has zero total energy.
When you measure the energy of one of the particles (by finding it far
away from the black hole) it *has* to have a positive energy.
Then, since the total energy was known to be zero, it always turns out
that a "negative energy" particle was the one that fell into the hole.
There was nothing weird or "negative" about this particle a priori, when
it was formed, but it must somehow "decide" to carry negative energy when
we measure the free particle to have positive energy. I know this sounds
a little strange! That's why Einstein didn't like quantum mechanics,
pointing out the famous "Einstein-Podolsky-Rosen" paradox.

Another way to look at it would be to draw a wavefunction - something
whose total energy is a little bit uncertain - *including* the
entire black hole as well as the vacuum fluctuations. Then you could
think of the "negative energy particle" as a sort of virtual state of the
whole black hole + ordinary particle system. I don't know enough about
general relativity (nor quantum field theory) to attempt to do this, but I
think Prof. Hawking might!

If I had to give a concise, correct, but wholly useless answer: Why is it impossible for a particle with negative energy to escape a black hole? "Because there is no such thing as a real particle with negative energy."

-Ben

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