MadSci Network: Physics

Re: Why is it impossible for a particule with a negative energy to escape a BH?

Date: Wed Sep 24 14:59:06 2003
Posted By: Benjamin Monreal, Grad student, Physics, MIT
Area of science: Physics
ID: 1064008156.Ph

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."


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