What are the unanswered questions about Hawking radiation and the Unruh effect?

[Frame Dragger]

I don't believe that most physicists believe they have the kind of insight you seem to think they do. When asked for explanations they give the best they have under the assumption that you, I, we, know they are not omniscient...

btw, a 6 year old's brain is functionally and structurally different from an adult's, or a teens, or a person of 40. Is that REALLY a smart and worthwhile quote just because of its possible source?

 

[Gatchaman]

Too bad there's a major flaw in Hawking's derivation. He makes a big assumption in that all wave equations that work in flat spacetime will work the same way in curved spacetime just by swapping the Minkowski metric with a general one. The consequence of this assumption is that there is no feedback effect to take the changes created by Hawking radiation and feed them back to the metric.

 

[Frame Dragger]

Too bad there's a major flaw in Hawking's derivation. He makes a big assumption in that all wave equations that work in flat spacetime will work the same way in curved spacetime just by swapping the Minkowski metric with a general one. The consequence of this assumption is that there is no feedback effect to take the changes created by Hawking radiation and feed them back to the metric.

How could there possibly be a way to refer feedback from HR to the original metric when it breaks unitarity?

 

[Gatchaman]

How could there possibly be a way to refer feedback from HR to the original metric when it breaks unitarity?

In Hawking's paper, at the outset, he assumes that there exists a time-translational Killing vector (KV), as is consistent with the S-vac, and with Birkhoff's theorem. This implies that there will be no time evolution of the spacetime. Working in this spacetime, and considering an in-falling spherical shell of matter enclosing a vacuum spherical region, Hawking proceeds to derive the HR, with some more or less hidden assumptions. The eventual result is that there is black-body radiation at infinity, at very late times, i.e. way out on the future extent of the event horizon. Thus, the spacetime evolves...this is the nature of a body that radiates. Given that it evolves, one thing is certain: there is no longer a time-translational KV, and we have arrived at a contradiction. It may seem just a small problem, but to me it is a huge problem. The very existence of the spacetime required the time-translational KV, and such a spacetime is not a "near approximation" of a dynamic spacetime. Furthermore, the event horizon has the various properties it has, which are important for the derivation, because it is a Killing horizon, and its based on the existence of the time-translational KV. To put it another way, the idea of approximate symmetries is inherently difficult, even for finite distant scales, but it becomes close to impossible to discuss approximate symmetries on infinite distance scales, such as the whole of the spacetime.

 

[Frame Dragger]

In Hawking's paper, at the outset, he assumes that there exists a time-translational Killing vector (KV), as is consistent with the S-vac, and with Birkhoff's theorem. This implies that there will be no time evolution of the spacetime. Working in this spacetime, and considering an in-falling spherical shell of matter enclosing a vacuum spherical region, Hawking proceeds to derive the HR, with some more or less hidden assumptions. The eventual result is that there is black-body radiation at infinity, at very late times, i.e. way out on the future extent of the event horizon. Thus, the spacetime evolves...this is the nature of a body that radiates. Given that it evolves, one thing is certain: there is no longer a time-translational KV, and we have arrived at a contradiction. It may seem just a small problem, but to me it is a huge problem. The very existence of the spacetime required the time-translational KV, and such a spacetime is not a "near approximation" of a dynamic spacetime. Furthermore, the event horizon has the various properties it has, which are important for the derivation, because it is a Killing horizon, and its based on the existence of the time-translational KV. To put it another way, the idea of approximate symmetries is inherently difficult, even for finite distant scales, but it becomes close to impossible to discuss approximate symmetries on infinite distance scales, such as the whole of the spacetime.

Do you find the same problems to be present with The Unruh Effect?

 

[Gatchaman]

Do you find the same problems to be present with The Unruh Effect?

Yes. The Unruh effect has a problem as well, and while slightly different, it is also related to the assumption of a symmetry that persists forever. In this case, the "detector" has been accelerating from infinite past and will accelerate into the infinite future, so there is an injection of essentially infinite energy, such that the spacetime cannot actually be the vacuum of Minkowski as was taken to originally be.

 

[Frame Dragger]

Yes. The Unruh effect has a problem as well, and while slightly different, it is also related to the assumption of a symmetry that persists forever. In this case, the "detector" has been accelerating from infinite past and will accelerate into the infinite future, so there is an injection of essentially infinite energy, such that the spacetime cannot actually be the vacuum of Minkowski as was taken to originally be.

Alright, well, from what I gather these are valid concerns about two somewhat radical and maybe untestable (in any near future) theories. I wouldn't call them fatal flaws, but rather open questions which remain to be adressed.