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

[Frame Dragger]

loldudes? You described particle tunnelling in the same way that I describe (to myself) quantum creation probabilities. If the question wasn't clear, I was asking how my interpretation differs from what got said, considering people like haelfix were saying the tunneling dual-particle analogy was wrong.

The argument I saw (considering I posted only fragments of the entire conversations) was circular, I was merely asking for clarification on what you consider the difference between the wording of my interpretation and your own. (let's ignore we are talking about hawking radiation as I kind of went off topic and started talking about particle black hole ownership and administration)

Thumbs down to your attempt to troll a perfectly good question, FrameD.

You really should read that link. The strong implication is that education in the fields in which the ignornace exists can effectively reverse the effect.

 

[TcheQ]

This is the part where I got confused:

Tunneling from inside to outside the event horizon is equivalent to a particle tunneling outside its own future light cone

HR is (quantum evaporation through) single particles tunneling

Don't bother. I will research it myself how both these statements can be in agreement with each other, but also conflict with my own wording.

The [mathematics and established physics] are very technical and [would require dedicated research] before you can even attempt to explain it.

 

[Frame Dragger]

The answer is that Haelfix is right, and the rest is all a matter of approximation. HR is pure math, and pure theory. That doesn't lend itself to a realistic explanation, just semi-conflicting analogies from QM formalism and Interpretations that try to explain in familiar terms what the math is saying.

 

[bcrowell]

feynman once said that if you cannot explain something to a layperson in terms they can understand, then you really do not understand it yourself...

I agree with the sentiment, but I believe it's usually attributed to Einstein, not Feynman. I've heard various versions, including either "barmaid" or "intelligent eight-year-old" as the person who you're supposed to be able to explain it to.

I read the Baez page, and didn't find it very clear or convincing. He says we should be talking about Bogoliubov transformations rather than particle-antiparticle pairs, and he says they may be equivalent, he's not an expert, but he doesn't see any reason to think they're equivalent. He then references Wald as a source of more detailed information. If you read the treatment in Wald, Wald explicitly states that the technical shenanigans with the Bogoliubov transformations *can* be interpreted as particle-antiparticle pairs.

My previous experience with the Bogoliubov transformations was in nonrelativistic nuclear physics, where we use the quasiparticle approximation to describe particle-hole excitations in the presence of a residual interaction that causes pairing between time-reversed orbits. Although I'm not familiar with the relativistic version, it seems qualitatively similar. Instead of filled and empty orbitals, you have a Dirac sea of filled negative-energy states and an empty spectrum of positive-energy states. A particle-hole excitation should clearly be interpreted as a particle-antiparticle pair.

Considering that Baez admits he's uncertain, and his references appear to contradict what he says, I would tend to discount his statements that there's anything wrong with the particle-antiparticle interpretation.

One of the interesting things about the Bogoliubov approximation is that the eigenstates are not states of definite particle number. In nuclear physics, this means that you can try to describe some isotope like 168Er, but the wavefunction you're calculating is an average over various nearby isotopes like 167Er, etc. This is all in a nonrelativistic context, where it's clearly wrong to have a variable particle number, and you can only hope that the resulting errors average out to zero. I assume that the Bogoliubov wavefunctions also have this property in the relativistic case, but I don't know what the interpretation is.

 

[jnorman]

bcrowell - the quote apparently is:
" 'If you can't explain it to a six year old, you don't understand it yourself.'

i found the quote attributed to feynman here:
http://quotes.ethanbloch.com/post/133216421/if-you-cant-explain-it-to-a-six-year-old-you

and i also found it attributed to einstein in a number of locations, so it probably was einstein who said it first. i think i may have remembered reading it in "surely you must be joking, mr feynman", and thought it was his own comment.

that said, feynman was always right up front with comments about what physics understands and what it does not. QED is filled with remarks like:
"you see, my physics students don't understand it either. that is because i don't understand it. nobody does." and:
"the more you see how strangely nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. so theoretical physics has given up on that."

which is why i keep posting comments like "nobody knows what a field is" and "nobody knows how a field works." which always upsets someone who responds with "of course we know what a field is - a field is a domain...blah blah" which explains exactly nothing about the nature of a field or how it operates.

i believe it is inherently very important for physicists to be upfront not only with laypersons, but also with themselves, that we truly do not understand even the simplest phenomena, such as how a magnet works, or what happens when two particles interact, etc.

 

[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.