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Q & A: Hawking radation puzzler

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Most recent answer: 10/22/2007
Q:
Concerning the Hawking radiation, why is it impossible that the particle with a negative energy escapes if the one with a positive energy falls in the black hole?
- David (age 26)
Montréal
A:
Real particles which can be observed far away from black holes can only have positive energies. Quantum mechanics allows the creation and destruction of "virtual" particles with arbitrary energies, but virtual particles are not in the final state. They must finish their interactions before their energies can be measured, and the time scale is given by Heisenberg’s uncertainty principle, delta E * delta t >= h/2pi. Negative-energy particles cannot "propagate".

Not so inside the event horizon of a black hole -- the geometry is such that the radial coordinate behaves kind of like a time coordinate, and the time behaves more like a spatial coordinate. So ordinary kinds of particles, which "go forwards in time" must necessarily travel inwards towards the center of the hole. Just as you cannot go backwards in time, you cannot travel outwards from the center of a black hole once you are inside the event horizon. But this lifts the restriction on negative-energy particle propagation -- it’s perfectly legal inside the event horizon, as long as the particle in question travels inwards.

(I’m getting this from Bernard Schutz’s book, "A First Course in General Relativity", Cambridge University Press, 1985, 1988).

Tom

(published on 10/22/2007)

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