How Do Particles with Negative Energy Contribute to Hawking Radiation?

[jnorman]

can someone please try to explain to me how a particle can have negative energy - specifically how one particle from spontaneous particle pair production near a BH EH can (must) have negative energy as it falls into the BH resulting in hawking radiation?

i am now trying to accept that everything i thought i knew is wrong. i was taught that a photon has no position between the time it is emitted and the time it is absorbed - apparently that is wrong, since people are now doing photon-photon collision testing. i was also taught that a photon cannot be accelerated - apparently that is wrong too (four-work?), though i don't get it. or how half of a particle pair can escape from near the EH of a BH when the other doesnt, when they are not created with anything near C velocity which they would have to have to escape anywhere near the EH, and they only exist for extremely short period of time to begin with...

 

[kuon]

At tree level photons don't interact. But at one loop they can interact through virtual electrons.

 

[humanino]

can someone please try to explain to me how a particle can have negative energy - specifically how one particle from spontaneous particle pair production near a BH EH can (must) have negative energy as it falls into the BH resulting in hawking radiation?

The negative is "as measured at infinity" where the other particle escapes, where by definition spacetime is "asymptotically flat" and simply put the zero of energy has been shifted by the gravitational potential.

 

[blechman]

it is a little misleading to think of a particle falling into the BH with negative energy. That is fine from the point of view of calculations (where you just follow your nose through the math) but if you want a more "physically appealing" description, you should really think in terms of the OBJECTS in the problem:

what is really happening is that a BH is shedding energy through radiation of particles. As it does this, it loses energy (i.e. mass). This sounds totally reasonable, right?

Now the fact that this occurs through a quantum process where the BH imparts energy onto a particle-antiparticle pair, allowing the particle to escape while swallowing the antiparticle (or vice versa) should not trouble you any more than the statement that you cannot measure position and momentum to infinite precision at the same time!

In other words: the swallowed particle is not "real" (it is what you would call a "virtual particle"). And as it has "negative energy" - when the BH swallows it, it LOSES mass, as it should.

Slightly oversimplified, but I hope that helps.