Questions regarding Hawking radiation

[Buzz Bloom]

The following are a few questions to help me understand the variability of views about Hawking radiation held by various knowledgeable PF QM physicists.

1. Do you personally believe that Hawking radiation is a real phenomenon rather than a only a theoretical possibility?
2. What percentage of the world's QM physicists do you guess believe that Hawking radiation is a real phenomenon rather than only a theoretical possibility?
3. Am I correct in my understanding that to date no astronomical observations/measurements of radiation or particles have been made which have been reliably reported as possible evidence of Hawking radiation?
4. Assuming I am correct re (3), and assuming re (1) you believe Hawking radiation is a real phenomenon, what is your guess about how far in the future it will be before astronomical observations/measurements of Hawking radiation will be confirmed?
​

I found the insight Article "The Vacuum Fluctuation Myth" by A Neumaier

https://www.physicsforums.com/insights/vacuum-fluctuation-myth/​

very informative and entertaining. By rational reasoning it confirmed for me a personal insight that as a lay reader I will never have any reliable intuitive grasp of quantum mechanics. Is spite of this, the article has encouraged me to make another try at seeking knowledgeable PF help to resolve some aspects of my confusion about Hawking radiation. The last two threads I participated in asking questions and seeking clarity did not work out for me.

https://www.physicsforums.com/threads/qs-re-hawking-radiation-part-i.873163/
https://www.physicsforums.com/threads/qs-re-hawking-radiation-part-ii.873353/​

I will much appreciate any and all responses.

Regards,
Buzz

 

[secur]

A few years ago I made an informal survey of physicists I know personally (not on the net) re. this question. FWIW here are the answers I got. They believe it is a real phenomenon not just theoretical possibility. Since it's so very weak there's no chance of observing it directly for the foreseeable future. A dozen or so physicists agreed with those points, there was no "variability of views". However the following more speculative items weren't so unanimous: It may be inferable from some indirect observations before too long. Or, less likely, created in a lab via some currently unknown process (creating an unstable mini BH). It's impossible to say how soon, or whether, that would occur. I doubt these opinions have changed much, and will be interested to see if PF experts agree.

 

[mfb]

I'm not aware of plausible models that do not predict Hawking radiation. The radiation is way too weak to detect it from black holes we know.

- if smaller primordial black holes exist, they might evaporate today. There is a chance to see the final explosion if it happens close enough.
- if there are small extra dimensions, the Planck mass might be much lower - potentially in reach of collider experiments. An unlikely scenario, however.

=> It probably exists, but it is unlikely that we can detect it in the foreseeable future.

It is possible to create effective event horizons, e. g. for sound. This has been done, and Hawking-like radiation has been detected.
"Observation of quantum Hawking radiation and its entanglement in an analogue black hole", Jeff Steinhauer, 10.1038/nphys3863, PDF

 

[Buzz Bloom]

Hi @secur and @mfb:

Thank you very much for your responses.

What puzzles me the most about Hawking radiation is my inability to understand any explanation of a mechanism that causes mass-energy from inside a black hole event horizon to escape away from the black-hole, thereby reducing the mass of the black-hole. I heard Hawking's open lecture at MIT (I believe this was in the 1970s) about what is now called Hawking radiation. At that time he explained the phenomenon in terms of virtual particles, which I understand he later changed to real particles. My confusion relates to two aspects of the story.

1. What is the source of energy and the mechanism that creates a pair of real particles outside the event horizon?
2. What mechanism causes a reduction of mass-energy inside the black hole event horizon corresponding to the escaping particle?​

I think that the usual explanation is that in-falling particle annihilates one of its antiparticles inside, and the resulting produced energy vanishes to balance the "borrowed" energy that created the external particle pair.

Is this a correct explanation of the phenomenon?

If so, my confusion relates to the timing of the events. In particular, I understand that there is a Heisenberg limit to the amount of time between the "borrowing" of energy to create a particle pair, and the return of the borrowed energy when the pair self annihilates, and this limit is inversely proportional to the total amount of energy borrowed. I have not been able to find anywhere any discussion of whether or not the time limit would be exceeded by the events of the Hawking radiation phenomenon.

Regards,
Buzz

 

[Nugatory]

Is this a correct explanation of the phenomenon?

No, although that description has been widely repeated in the popular press. There's a pretty decent laymen-friendly explanation here. The real thing is this paper, and if you take a look at page 4 you'll see that what you heard was the "heuristic" explanation for non-specialists.

 

[mfb]

a mechanism that causes mass-energy from inside a black hole event horizon to escape away from the black-hole

There is no such mechanism, and attempts to localize the energy of a black hole don't work properly.

What is the source of energy and the mechanism that creates a pair of real particles outside the event horizon?

There is no such thing. This is just a pop-science myth.

 

[secur]

... what you heard was the "heuristic" explanation for non-specialists.

Yes, Stephen Hawking says it's a heuristic, and he's right.

One might picture this negative energy flux in the following way. Just outside the event horizon there will be virtual pairs of particles, one with negative energy and one with positive energy. ... It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally.

There is no such thing. This is just a pop-science myth.

No, the particle-antiparticle explanation is a heuristic not a myth.

From the dictionary at https://www.merriam-webster.com :

heuristic: involving or serving as an aid to learning, discovery, or problem-solving

myth: an unfounded or false notion

A heuristic is not simply "unfounded" and "false". Instead it's a reasonable picture for a layperson, about the best you can do without being a specialist (i.e., in the present case, a physicist). Read Hawking's original paper for a good explanation of this particle-antiparticle heuristic. You'll see that it's founded, loosely, on the actual mathematics (roughly, positive energy solution corresponds to particle).

 

[ShayanJ]

A heuristic is not simply "unfounded" and "false". Instead it's a reasonable picture for a layperson, about the best you can do without being a specialist (i.e., in the present case, a physicist). Read Hawking's original paper for a good explanation of this particle-antiparticle heuristic. You'll see that it's founded, loosely, on the actual mathematics (roughly, positive energy solution corresponds to particle).

The only catch is that Hawking radiation is not produced at the black hole horizon and also the width of the wave-packets associated with the particles of the radiation, is much larger than the distance of the particle from the horizon.

 

[Nugatory]

No, the particle-antiparticle explanation is a heuristic not a myth.

When Hawking says it in the context of the paper that I linked, it's a heuristic. When science writers repeat it with neither context nor understanding, it becomes a myth.

 

[secur]

The only catch is that Hawking radiation is not produced at the black hole horizon and also the width of the wave-packets associated with the particles of the radiation, is much larger than the distance of the particle from the horizon.

I'm not sure these are the only problems with this heuristic, although indeed they are problems. But we already know it's inaccurate. If not, it wouldn't be a heuristic at all, but a fact, or a theorem. The question is whether it's properly called that, or a myth. The question is really in the realm of terminology - English language - not physics.

When Hawking says it in the context of the paper that I linked, it's a heuristic. When science writers repeat it with neither context nor understanding, it becomes a myth.

On the face of it this is a dubious proposition. As far as I've noticed almost all pop-sci writers repeat everything they say, valid or invalid, without "context or understanding". (Of course there are exceptions). That doesn't make it "unfounded" and "false". The principle of "ad hominem" can be seen as implying that the truth of a sentence depends only on that sentence, not on its author (or repeater). For example, suppose I saw some clouds in the sky that, amazingly and accidentally, appeared to spell "2+2=4". Clearly those clouds have no understanding of mathematics. Does that mean this basic fact of addition suddenly becomes a "myth"? No.

However, taking it as humor, I agree with you.

 

[Haelfix]

1. What is the source of energy and the mechanism that creates a pair of real particles outside the event horizon?
2. What mechanism causes a reduction of mass-energy inside the black hole event horizon corresponding to the escaping particle?​

I feel like this was just asked a few weeks ago. Anyway,

1) The source of energy is what else.. The gravitational field. Before you understand the specific case of black hole particle creation, learn about particle creation in gravitational fields. Better yet, learn about particle production in external fields in QFT. There are many good reviews. The black hole case is of course the most subtle. Very roughly, this is the analog of the Schwinger effect, where now instead of electric charge you have mass as a source. Note a few important differences though. In the Schwinger effect the electric field is homogenous, and there is a binary value for the source appearing in the exponential, which is of course electric charge (positive or negative). B/c the analog for the gravitational case is positive or negative mass, it must be the case that the solution only makes sense for timevarying fields.

2) The black hole case is as I said the most subtle, in a sense it is the existence of a Killing horizon that produces an effective time variation for modes that straddle the horizon, where now the negative mass source falls behind the horizon and is stretched apart from the source that is free to escape to future null infinity. This is what causes the mass loss, in a sense the gravitational field is absorbing negative energy. Note that interpreting them as particle pairs is somewhat dubious, as the typical wavelengths of the quanta are roughly the size of the black hole. So its far from a localized process, and of course would only make sense to an observer at infinity to view them as such..

 

[Buzz Bloom]

Hi @Haelfix:

I do much appreciate your effort to educate me by suggesting I seek out physics sources, even though I think it is unlikely I will be able to understand them. I hope you will be able to help me understand some content in your post that confuses me.

The source of energy is what else.. The gravitational field. Before you understand the specific case of black hole particle creation, learn about particle creation in gravitational fields. Better yet, learn about particle production in external fields in QFT.

I am guessing you intend this to mean that the "gravitational field" (GF) is a kind of quantum field, rather than in the action-at-a-distance classic Newtonian sense. Although my understanding of GR is limited, I understand that the GF is a property of the way (1) the shape of space time differs from (2) the flat space-time where there is no mass-energy producing accelerations due to gravity. On the other hand, you might intend that the GF might refer to a "field" of gravitational waves produced by the loss of potential energy among gravitating bodies in various orbits as these orbits gradually collapse, but I don't see how that would apply to the single black hole context.

If you do not have the QFT interpretation in mind for GF, I would very much like to better understand your intended meaning.

If you do have the QFT interpretation in mind for GF, would this not be part of a quantum theory of gravity, which as I understand the state of current theory, it is quite speculative rather than a confirmed valid interpretation of physical reality. If this is the case, would this not likely affect the validity of he answers in posts #2 and #3 to the 4 question is my post #1?

Regards,
Buzz

 

[Haelfix]

So when you deal with black holes, Hawking radiation and particle creation in gravity its useful to always remember a few different approaches/levels of approximation.

1) Quantum field theory in a fixed curved spacetime. This keeps the gravitational field completely classical, no different than in regular classical GR and there are quantum fields allowed to propagate on this fixed nondynamical background.

2) The Semiclassical theory (also sometimes called qft in curved spacetime somewhat confusingly). This is similar to the first, except that Einsteins field equations are modified by first order quantum gravity effects, there is some level of backreaction that takes place that you can compute, and in general you have to be careful to stay within the domain of validity of this approximation (eg when you have corrections that are far from being Planckian).

3) Gravitation as an effective field theory. Instead of truncating the effects of gravity to one loop as in 2, you can write down a new object, called the Wilsonian action which admits an energy expansion that formally has an infinite amount of undetermined constants. This is one very close to being a full theory of quantum gravity, except that it suffers from one fatal flaw, namely that it is nonrenormalizable in the power counting sense and loses predictivity in strong gravitational fields.

4) The full nonperturbative definition of quantum gravity. This is difficult to define, and it is not clear whether it even exists as a mathematical object (it could merely be an approximation of something else). Here presumably the full metric could be viewed as an operator in a Hilbert space of states, and it would be allowed to fluctuate as much as anything else.

Now... Particle creation falls under the approximation scheme of the 1st. It is a pretty safe regime which we understand to some extent, and vital for things like the theory of cosmic inflation, even though the full scheme of the approximation is poorly behaved in many regards (b/c it misses the properties that the other levels of approximation correctly incorporate). However to a good approximation, something like that must be true in general. In particular, the dynamics of the metric leads to what I was describing before, namely the analogue of the Schwinger effect.

Unfortunately to understand even the first level of approximation, you will need to have attended the first few graduate level classes in GR and quantum field theory.

 

[Buzz Bloom]

Unfortunately to understand even the first level of approximation, you will need to have attended the first few graduate level classes in GR and quantum field theory.

Hi @Haelfix:
Your quote above reconfirms my awareness that at my advanced years I will never reach any understanding about QM beyond the most elementary concepts.

Below I have tried to described what I think I have understood from your post. Please let me know if I got it right, or what corrections are necessary.

Hawking Radiation Theory (HRT) is based on a first approximation for quantum gravity theory (QGT) summarized in your (1), which I will abbreviate as QGT1. Although QGT1 is not sufficiently accurate to deal with phenomena at the Planck distance or time interval, it is accurate enough for useful calculations about HRT. This is the theoretical basis that have satisfied the majority of knowledgeable physicists that HRT describes a real physical phenomenon rather than just a plausible theory.​

It is also interesting that QGT1 has also been useful in analyzing aspects of inflation theory, perhaps by modeling the sequence of Standard Model particle creation events that take place during the inflation period. However, I guess that there must remain a good reason why inflation theory has not yet become generally accepted to become a "standard" extension of the Standard Model.

New question: Does QGT1 lead to physical predictions which have been, or are likely in the relatively near future to be, confirmed by observations?

Regards,
Buzz

 

[Haelfix]

So it is certainly not hopeless. Physics isn't some cloistered art, it's available to anyone with the discipline and interest to understand it. It just takes a little bit of effort to go through two or three textbooks before you hit Birrel and Davies or Wald (which are the canonical textbooks dealing with this subject). There are so many online lecture series now that you can can pretty much learn through several years worth of graduate level programs in physics.

Also, Hawking radiation comes from qgt2 (to borrow that lingo), b/c it allows for backreaction (this is what shrinks the black hole and allows it to evaporate). Particle production due to gravitation comes from qgt1 and so is on an even firmer foundation (in some sense). So while the effects are absolutely tiny and would not be directly observable, this sort of mechanism is absolutely *crucial* for the theory of inflation. So in some sense evidence we accumulate for the latter serves as indirect evidence for the former.

Incidentally, the same thing holds true for particle production by external fields in the case of electromagnetism and other forces. These effects have never been observed, but are so deeply intertwined with standard theory that they are almost universally believed.

 

[Imager]

now the negative mass source falls behind the horizon and is stretched apart from the source that is free to escape to future null infinity. This is what causes the mass loss

Why is it that the negative goes into the black hole and not the positive? Or to ask another way, why isn't "it" absorbed in equal positive and negative amounts?

 

[Nugatory]

Why is it that the negative goes into the black hole and not the positive? Or to ask another way, why isn't "it" absorbed in equal positive and negative amounts?

The references in post #5 of this thread explain this.

 

[A. Neumaier]

I understand that there is a Heisenberg limit to the amount of time between the "borrowing" of energy to create a particle pair,

There is no borrowing of energy. The (real) particle pair can be created only if the energy density of the gravitational field (which every black hole has) provides this energy.

When Hawking says it in the context of the paper that I linked

In his ground-breaking paper on the subject, Hawking says on p.2462 (left) that ''One can interpret such a happening as being the spontaneous creation in the gravitational field of the black hole of a pair of particles, one with negative and one with positive energy with respect to infinity. The particle with negative energy would fall into the black hole [...] The particles with positive energy can escape [...]''. (Note that only energy differences are meaningful, hence Hawking's reference to (zero energy in flat space at) infinity that gives meaning to the sign of the energy. No "virtual pairs" of particles and antiparticles that pop in and out of existence!

the "gravitational field" (GF) is a kind of quantum field, rather than in the action-at-a-distance classic Newtonian sense.

it doesn't matter whether the gravitational field is treated by classical or quantum mechanics; this only gives extremely tiny corrections to the exact rates. Calculations are usually done semi-classically, i.e., treating gravitation as classical external field. But getting essentially the same results from quantum gravity is considered as one of the tests that a quantum theory of gravity must pass to be regarded as a serious candidate.

 

[stevendaryl]

I'm not sure these are the only problems with this heuristic, although indeed they are problems. But we already know it's inaccurate. If not, it wouldn't be a heuristic at all, but a fact, or a theorem. The question is whether it's properly called that, or a myth. The question is really in the realm of terminology - English language - not physics.

At the risk of being too off-topic, the original meaning of "myth" was not "falsehood". They were stories that people told to explain how the world works, and how things came to be the way they are. The connection with falsehood is just that all the classical myths were actually false. But something doesn't have to be false to be a myth.

 

[Buzz Bloom]

'One can interpret such a happening as being the spontaneous creation in the gravitational field of the black hole of a pair of particles, one with negative and one with positive energy with respect to infinity.

Hi @A. Neumaier:
I am getting an inkling about what the above quote means, but I have no confidence that my inkling is correct. If it is wrong, I hope you will correct me.

I interpret "with respect to infinity" to refer to a mass-energy that is somewhat like gravitational potential energy. That is, the actual mass-energy of both of these particles has no meaning, except with respect to some arbitrary reference level, and for the purpose of this phenomenon (also like for gravitational potential energy) it its convenient to choose a zero value for the sum of the two energies at infinity as the reference.

At the point where the pair is created, both may be considered to have a negative energy (like potential energy), but at infinity, their energy will be equal in absolute value but opposite in sign. The particle which at infinity would have positive energy escapes, and the other particle goes into the black hole where it's net negative energy subtracts from the mass at the center. By "net" energy I mean the remaining negative energy after some of it's negative energy is converted to positive kinetic energy as it falls to the center of the black hole.

Regards,
Buzz

 

[Ilja]

The only catch is that Hawking radiation is not produced at the black hole horizon and also the width of the wave-packets associated with the particles of the radiation, is much larger than the distance of the particle from the horizon.

What you see if you look at a black hole is the surface of the collapsing star. It is that collapsing star which creates the radiation. This can be easily proven - if the collapse would stop, no matter how close to the horizon, Hawking radiation would stop after this. Stable stars do not Hawking-radiate.

 

[Buzz Bloom]

What you see if you look at a black hole is the surface of the collapsing star. It is that collapsing star which creates the radiation.

Hi @Ilja:
I find the above confusing, and I hope you can clarify it for me.

I understand the black hole (BH) does not yet exist if the matter comprising the BH with mass M is not entirely within the event horizon. If for convenience we assume no rotation and a spherically symmetric mass, then this means that all the mass must be within the sphere radius R where the escape velocity equals c. Do you agree with this?

If so, then this seems to mean that the still collapsing matter is entirely within the BH in order for Hawking radiation to occur. Do you agree with this?

If so, then this seems to mean that you won't be able to see the BH matter collapsing since it is inside the event horizon. Do you agree with this?

Also, I am confused by what the meaning is of someone at a distance detecting the Hawking radiation, since the time within the black hole as seen at a distance on the outside is warped in a way I don't understand. Can you explain what you have in mind?

Regards,
Buzz

 

[Ilja]

I understand the black hole (BH) does not yet exist if the matter comprising the BH with mass M is not entirely within the event horizon.

If so, then this seems to mean that you won't be able to see the BH matter collapsing since it is inside the event horizon. Do you agree with this?

Also, I am confused by what the meaning is of someone at a distance detecting the Hawking radiation, since the time within the black hole as seen at a distance on the outside is warped in a way I don't understand. Can you explain what you have in mind? .

1.) I have emphasized the key words of your first point. Essentially, the key word is "yet". What does it mean? If you have an SR course, you have heard about about relativity of simultaneity, and in a GR course you would have heard that contemporaneity is even more relative in GR because arbitrary coordinates are allowed. So, any arbitrary time-like function is as good as any other.

Ok, only time-like functions count. But so what? For a black hole which is the result of a gravitational collapse we can always define time in such a way that the black hole does "not yet exist" according to your definition.

And, note: Once the time coordinate is a time-like function, the idea that it really defines what is now is completely consistent. There is no causal influence from the future into the past.

2.) What you see from the outside if you look at a black hole after the collapse is something one can compute, and it does not depend on the freedom of choice of the time coordinate. Take the full solution (inclusive the collapsing star before horizon formation). Fix some point outside, the event of the external observer looking at the black hole - say, the remains of some collapse which happened last year. How to compute what he sees? It is a light ray which arrives, from this direction. So, you can trace it back, this is the same geodetic equation, only into the past. The answer where it comes from is unique - it comes from the surface of the collapsing star, at a moment before horizon formation.

3.) The whole Hawking radiation business is about a radiation which a distant observer is claimed to see. What happens for a distant observer is much less confusing, so I would recommend to use this as a starting point. Anyway, in the case of Hawking radiation it is also the end point. He sees it only because it has been radiated away. And, once it is the end point, it is no problem if the time inside the horizon is confusing - it does not matter anyway. Because, once you choose an appropriate time coordinate, the BH does not exist now. It radiates because you see (2) a collapsing star, and collapsing stars radiate.

 

[ShayanJ]

What you see if you look at a black hole is the surface of the collapsing star. It is that collapsing star which creates the radiation. This can be easily proven - if the collapse would stop, no matter how close to the horizon, Hawking radiation would stop after this. Stable stars do not Hawking-radiate.

1) You can have Hawking radiation from eternal horizons, i.e. horizons that were not created by the collapse of a star.

2) For an observer falling with the same speed as the surface of the star, the surface will pass the horizon. Its just for an observer at infinity that it takes an infinite time for the surface of the star to fall into the horizon.

3) Because of the infinite redshift at the horizon, signals sent by the star surface will be farther apart in time from each other, until the last signal reaches the observer at infinity at the infinite time of that observer. So there can be no continued radiation of any kind.

4) The explicit calculation of the Hawking radiation is pretty clear on what exactly the radiation is.

 

[Ilja]

1) You can have Hawking radiation from eternal horizons, i.e. horizons that were not created by the collapse of a star.

Feel free to think so, I have doubt that this is a valid result. I would say that there exist some regularizations which will show Hawking radiation. This is what has to be expected if the regularized picture is non-static. Instead, regularizations where the regularized black hole is static do not show Hawking radiation.

2) For an observer falling with the same speed as the surface of the star, the surface will pass the horizon. Its just for an observer at infinity that it takes an infinite time for the surface of the star to fall into the horizon.

The point being? Once we talk about Hawking radiation, we talk about radiation observable to a far away observer. So, why would the nearby infalling observer matter at all?

3) Because of the infinite redshift at the horizon, signals sent by the star surface will be farther apart in time from each other, until the last signal reaches the observer at infinity at the infinite time of that observer. So there can be no continued radiation of any kind.

A nice argument that there cannot be any Hawking radiation for a longer period of time.

4) The explicit calculation of the Hawking radiation is pretty clear on what exactly the radiation is.

Yes. And that it uses quite nonsensical assumptions about the validity of the calculation in horribly trans-Planckian regions is completely clear too.

 

[ShayanJ]

Feel free to think so, I have doubt that this is a valid result. I would say that there exist some regularizations which will show Hawking radiation. This is what has to be expected if the regularized picture is non-static. Instead, regularizations where the regularized black hole is static do not show Hawking radiation.

What regularization are you talking about?

The point being? Once we talk about Hawking radiation, we talk about radiation observable to a far away observer. So, why would the nearby infalling observer matter at all?

The point being that the surface of the star actually falls behind the horizon, its just that the observer at infinity can't observe this because of his peculiar time.

A nice argument that there cannot be any Hawking radiation for a longer period of time.

Hawking radiation doesn't originate at the horizon!

And that it uses quite nonsensical assumptions about the validity of the calculation in horribly trans-Planckian regions is completely clear too.

Outside the horizon of a black hole is not a trans-Planckian region. Its not even a high curvature region if the black hole is massive enough.

 

[ShayanJ]

Don't cry.

I let this inappropriate behavior slide this time!

It originates in a region arbitrary close to the horizon. This can be proven, my modifying the classical background, replacing it with a collapse which stops at the radius rS+εr_S + \varepsilon with arbitrary small ε\varepsilon. In this case, the Hawking radiation stops once the stable state is reached. See https://arxiv.org/abs/0906.1768v2 for details. If we have Hawking radiation in one case and no Hawking radiation in the other case, the origin is the region where they differ. The two solutions differ only below rS+εr_S + \varepsilon, so, the origin is this region.

The paper is pretty clear on what its talking about and it doesn't at all support what you claim. Its about the thermal radiation from quantum fields while the star is still collapsing. If the collapse doesn't result in a horizon, the radiation will stop. But if it does result in a horizon, the radiation will continue and that's the famous Hawking radiation. Just read the conclusion part of the paper.

 

[ShayanJ]

My point is that this difference is sufficient to identify the origin of Hawking radiation. The origin cannot be in a region where above solutions do not differ, because in this case the radiation would be the same. It has to be originated in a region where they differ. And the region where they differ, and which can causally influence the observer at infinity (which is done by having Hawking radiation or not), is the exponentially thin region between rSr_S and rS+e−105lPlr_S + e^{-10^5} l_{Pl} one second after the collapse of a solar-sized BH.

The presence of the horizon matters. Its not like we need a special place for Hawking radiation, we need the horizon itself.
In fact it has been proven that the Hawking radiation originates from a region around the horizon whose size is comparable to the size of the horizon itself. Also, the wavelength of this radiation is larger than the radius of the horizon so you can't pinpoint an infinitesimal region where the radiation originates.

 

[fresh_42]

I let this inappropriate behavior slide this time!

I don't.

 

[Ilja]

The presence of the horizon matters. Its not like we need a special place for Hawking radiation, we need the horizon itself.

Not good for Hawking radiation being a reliable thing if it depends on this. This would mean that we have to know the future to find out if there is Hawking radiation or not. Because you can easily define a time-like coordinate so that the horizon is formed only in the future. Schwarzschild time would do it.

In fact it has been proven that the Hawking radiation originates from a region around the horizon whose size is comparable to the size of the horizon itself.

Thank you for the link. A Physics Letters paper which can easily shown to be wrong is good news for getting a Physics Letters paper refuting it.

Also, the wavelength of this radiation is larger than the radius of the horizon so you can't pinpoint an infinitesimal region where the radiation originates.

As if this would prove anything.

Hm, let's try. Take a charge and move it, up and down, at home once in a second. What will be the wavelength of the EM wave created by this moving charge? What does this tell us about the size of the origin of this wave?

 

[ShayanJ]

Not good for Hawking radiation being a reliable thing if it depends on this. This would mean that we have to know the future to find out if there is Hawking radiation or not. Because you can easily define a time-like coordinate so that the horizon is formed only in the future. Schwarzschild time would do it.

I don't quite understand what you're trying to say.

As if this would prove anything.

Hm, let's try. Take a charge and move it, up and down, at home once in a second. What will be the wavelength of the EM wave created by this moving charge? What does this tell us about the size of the origin of this wave?

Here we're talking about particles. If there is an electron with de Broglie wavelength of the order of a stadium, it doesn't make sense to say where in the stadium that electron is.

 

[Ilja]

I don't quite understand what you're trying to say.

Hm, let's try again. I think a theory which predicts that I observe / do not observe radiation in dependence of some fact which happens only in the future, with everything which has already happened in the past, and up to now, being equal, would have a big problem with causality.

This holds for every time-like coordinate. If I have a time-like coordinate, and the fact if I observe Hawking radiation or not depends on something which is, according to this time coordinate, in the future, this sounds like a problem for Einstein causality, not?

For every event for an observer at infinity, who observes Hawking radiation, one can easily find a time-like coordinate where the horizon is not yet formed. Outside the collapsing body, standard Schwarzschild time will define one such coordinate. So, your claim
"The presence of the horizon matters. Its not like we need a special place for Hawking radiation, we need the horizon itself."
suggests me that such a position has a serious problem with Einstein causality.

In my opinion, all what can matter for the prediction of Hawking radiation at some far away event is what is part of the past light cone of this event. And this part does not contain any horizon, for all those events horizon formation is yet only future, so that it may be not even certain if a horizon will form or not.

Here we're talking about particles. If there is an electron with de Broglie wavelength of the order of a stadium, it doesn't make sense to say where in the stadium that electron is.

Sorry, no, I'm not talking about particles. I'm talking about radiation. And I know that to attribute a position to a photon is not unproblematic, so I do not talk about such positions. I was talking about the region which has caused the radiation. My example suggest that such a region may be much smaller than what the wavelength suggests.