While the following post doesn't quite get me to the point of understanding Hawking radiation, it gets me much closer to the point of understanding what Stephen Hawking was attempting to say in A Brief History of Time: now I know what he means by "virtual particles" and that I need to read up on Feynman diagrams to understand the argument.
Source: https://www.physicsforums.com/threads/higgs-field-and-the-casimir-effect.405738/#post-2736124
Graphically in a Feynman diagram a virtual particle is a particle that does not escape to infinity; so its line has two ends (two vertices) where it meets with another line or lines. Now draw a circle and two vertices on the circle. This is a vacuum fluctuation where at one vertex a pair of virtual particles is created out of nothing (vacuum); the two particles propagate to the second vertex where they annihilate into nothing (vacuum). Usually this is a mathematical [artifact] and is "subtracted" from the theory.
Near the event horizon something strange happens. One of the two virtual particles tunnels through the horizon whereas the other virtual particle is eventually sucked into the black hole. The particle outside the event horizon does not annihilate with the other particle, so it escapes to infinite and is therefore not a virtual particle. The confusion is due to the fact that we compare a process in flat space (with two virtual particles in a vacuum fluctuation) with another, different process in curved spacetime (with one real particle). That's why its strictly speaking not a virtual particle that becomes a real particle, but a particle that is created by tunneling (similar to the alpha particle that tunnels from a nucleus causing alpha decay).
The mathematical reason is difficult: in order to set up quantum field theory one must define a vacuum state. In curved spacetime this is no longer possible uniquely. So what we call virtual particle when its located inside the event horizon is a real particle when it is located outside the horizon. One can evaluate this vacuum ambiguity mathematically. In doing so one finds that one has to redefine the vacuum state outside the event horizon in such a way that is contains real particles with thermal spectrum.
A similar effect is the so-called Unruh effect. It simply says that if an observer at rest observes vacuum w/o particles then a constantly accelerated observer observes thermal radiation! So the same volume of space contains no particles at all or thermal radiation - depending on the observer. Again the very notion of vacuum is no longer unique. The two effects are closely related as in the Unruh case there is again a "kinematical horizon" which means there is a region of spacetime from which no signal can reach the accelerated observer. This is not due tothe eometry of spacetime but due to the acceleration only, but nevertheless it is a horizon.
Reference: https://www.physicsforums.com/threads/higgs-field-and-the-casimir-effect.405738/#post-2736124
Source: https://www.physicsforums.com/threads/higgs-field-and-the-casimir-effect.405738/#post-2736124
Graphically in a Feynman diagram a virtual particle is a particle that does not escape to infinity; so its line has two ends (two vertices) where it meets with another line or lines. Now draw a circle and two vertices on the circle. This is a vacuum fluctuation where at one vertex a pair of virtual particles is created out of nothing (vacuum); the two particles propagate to the second vertex where they annihilate into nothing (vacuum). Usually this is a mathematical [artifact] and is "subtracted" from the theory.
Near the event horizon something strange happens. One of the two virtual particles tunnels through the horizon whereas the other virtual particle is eventually sucked into the black hole. The particle outside the event horizon does not annihilate with the other particle, so it escapes to infinite and is therefore not a virtual particle. The confusion is due to the fact that we compare a process in flat space (with two virtual particles in a vacuum fluctuation) with another, different process in curved spacetime (with one real particle). That's why its strictly speaking not a virtual particle that becomes a real particle, but a particle that is created by tunneling (similar to the alpha particle that tunnels from a nucleus causing alpha decay).
The mathematical reason is difficult: in order to set up quantum field theory one must define a vacuum state. In curved spacetime this is no longer possible uniquely. So what we call virtual particle when its located inside the event horizon is a real particle when it is located outside the horizon. One can evaluate this vacuum ambiguity mathematically. In doing so one finds that one has to redefine the vacuum state outside the event horizon in such a way that is contains real particles with thermal spectrum.
A similar effect is the so-called Unruh effect. It simply says that if an observer at rest observes vacuum w/o particles then a constantly accelerated observer observes thermal radiation! So the same volume of space contains no particles at all or thermal radiation - depending on the observer. Again the very notion of vacuum is no longer unique. The two effects are closely related as in the Unruh case there is again a "kinematical horizon" which means there is a region of spacetime from which no signal can reach the accelerated observer. This is not due tothe eometry of spacetime but due to the acceleration only, but nevertheless it is a horizon.
Reference: https://www.physicsforums.com/threads/higgs-field-and-the-casimir-effect.405738/#post-2736124
-Max
--
I could not love thee dear, so much,
Loved I not honor more.
I could not love thee dear, so much,
Loved I not honor more.
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