More Questions About Hawking Radiation

[Airbrush]

My questions about Hawking Radiation:  (1) When 2 virtual particles appear near the event horizon, how far apart are they?  It is hard to imagine how one of the pair enters the black hole, but the other one doesn't.  (2) How long would virtual particles exist before they merge and annihilate if they are nowhere near any black hole?  (3) How many of these virtual pairs can pop in and out of existence in a cubic meter of empty space during one second?

"...Close to the event horizon of a black hole, a local observer must accelerate to keep from falling in. An accelerating observer sees a thermal bath of particles that pop out of the local acceleration horizon, turn around, and free-fall back in. The condition of local thermal equilibrium implies that the consistent extension of this local thermal bath has a finite temperature at infinity, which implies that some of these particles emitted by the horizon are not reabsorbed and become outgoing Hawking radiation...."

Above may explain it but I don't understand it.  Can anyone explain this or answer my questions?

https://en.wikipedia.org/wiki/Hawking_radiation#Discovery

Any other questions about the production of Hawking Radiation?  All questions about the process of Hawking Radiation are permitted here.

 

Edited April 7, 2020 by Airbrush

[MigL]

While the Event Horizon of a BH is a mathematical construct, the limit it represents has to follow certain Physical laws.
Heisenberg says the EH radius cannot be a hard limit, because of the 'fuzzyness' inherent in the HUP.
Virtual particles can, in effect, manifest inside the EH limit and 'tunnel' out, through the 'fuzzy' EH limit.
Or you can choose to look at it differently. The virtual particles are 'fuzzily' spread over space, again because of HUP, and while one might have its 'probability sphere' inside the EH, the other might be have some part of its 'probability sphere' outside.
In both cases the quantum mechanical 'tunneling' effect is used.

Virtual particles are dependent on the local energy density.
In free space, that would be vacuum energy ( see Casimir effect and Lamb Shift ).
But they also constitute a 'halo' around normal particles ( due to their fields ), and makes calculating specific attributes ( mass, charge, etc. )of the particle very difficult ( see 'renormalization' ).
 

[Airbrush]

3 minutes ago, MigL said:

While the Event Horizon of a BH is a mathematical construct, the limit it represents has to follow certain Physical laws.
Heisenberg says the EH radius cannot be a hard limit, because of the 'fuzzyness' inherent in the HUP.
Virtual particles can, in effect, manifest inside the EH limit and 'tunnel' out, through the 'fuzzy' EH limit.
Or you can choose to look at it differently. The virtual particles are 'fuzzily' spread over space, again because of HUP, and while one might have its 'probability sphere' inside the EH, the other might be have some part of its 'probability sphere' outside.
In both cases the quantum mechanical 'tunneling' effect is used.

Virtual particles are dependent on the local energy density.
In free space, that would be vacuum energy ( see Casimir effect and Lamb Shift ).
But they also constitute a 'halo' around normal particles ( due to their fields ), and makes calculating specific attributes ( mass, charge, etc. )of the particle very difficult ( see 'renormalization' ).
 

Then the answers to my 3 questions are "we don't know"?  Any educated guesses?

[MigL]

Keep in mind that the 'virtual particle pair created on the edge of the EH' is an interpretation introduced by S Hawking in his book, A Brief History Of Time, and as such, is intended for laymen.
The actual paper describing the process is a little more involved.

https://www.brainmaster.com/software/pubs/physics/Hawking Particle Creation.pdf

12 minutes ago, Airbrush said:

Then the answers to my 3 questions are "we don't know"? 

While that might be true for yourself, and even myself, it obviously isn't for S Hawking and many others.
Not understanding =/= not knowing.