Hawking radiation

[Schmelzer]

I dare say even Professor Unruh would not understand that.

Try to learn the meaning of analog gravity. It is about the sound waves of classical condensed matter. The speed of sound is, in this analogy, what corresponds to the speed of light. So, this analogy is the completely classical ether - which is a material such that the speed of light is its speed of sound. And, of course, Unruh knows this very well. By the way, he cites Jacobson, who openly uses the e-word.

By the way, here is the explicit quote where Unruh assumes a preferred frame, and tells us which it has to be:
W.G. Unruh, R. Schutzhold, On the Universality of the Hawking Effect, Phys. Rev. D 71, 024028 (2005), arXiv:gr-qc:0408009

A) If we assume that the usual local Lorentz invariance is broken at the Planck scale via the introduction of preferred frames (where preferred frames are the frames in which Planckian physics displays maximal symmetry under time-inversion, for example) then the freely falling frame should be preferred (instead of the rest frame of the black hole, for example).

And he also knows that if these conditions fail, there may be no Hawking radiation.

As an example, in which the aforementioned set of assumptions fails and which does not reproduce Hawking radiation, let us consider the following fluid model:

This is, by the way, the main problem which prevents me from writing a paper: The claim that if the preferred frame would be the rest frame of the black hole there would be no Hawking radiation would be nothing really new. It would be only yet another illustration of a fact mentioned already in this paper.

 

[paddoboy]

It would be only yet another illustration of a fact mentioned already in this paper.

Except that there are no facts, which I have no trouble admitting or realising...Only anologues that may or may not support a particular scenario, and that which most see as more likely than other possibilities.

 

[OnlyMe]

And I believe he has shown this.
I won't comment on the rest of your post and your ether as you know my thoughts, and the thoughts of the general mainstream academia on this matter, suffice to say, as I have mentioned before, the onus is on you to support your overall cosmological claims as against those generally accepted.

I don't think so.

The first line of one of his paper's abstracts begins,

It is argued that Hawking radiation has indeed been measured...

... But that paper goes on to describe an analogue of what he, Unruh and the coauthors of his earlier paper, interpret the process Hawking predicted, to be - in a purely classical setting. So what the paper actually argues is that how sound waves act in a moving fluid is similar to the escape process Hawking predicted for Hawking radiation. But even that is a stretch because admittedly no classical environment duplicates the conditions that are predicted to exist at an event horizon in the case of gravity... And Unruh's analogues deal only with how waves in a moving medium seem to simulate what would be expected of EM radiation or particles escaping a black hole from near its event horizon.

The third paper involving ultrashort laser pulses (Unruh was not a contributor), again did not produce any conclusive evidence even though they did observe photon emissions unlike other photon known emissions. From that paper note the last sentence quoted below.

... we report experimental evidence of photon emission that on the one hand bears the characteristics of Hawking radiation and on the other is distinguishable and thus separate from other known photon emission mechanisms. We therefore interpret the observed photon emission as an indication of Hawking radiation induced by the analogue event horizon.

Again even in this case they were not working under conditions involving the extreme gravitational fields associated with black holes.., and they don't make any explicit claims that any separation of virtual particle pairs is involved. All they are really saying is that they have observed photon emission, where the mechanism of emission cannot be readily explained, but fits with their assumptions about the process Hawking predicted.

In the papers presented so far it has been only a simplification of the Hawking process, to classical conditions, that has been explored. Nothing that duplicates the extreme gravitational filed conditions required.

BTW playing only the role of devil's advocate, in these papers it is unclear whether the authors are talking about an emmision process limited to massless photons or ultimately virtual particles that become real massive particles escaping.., and the bigger issue of whether the counterpart photon or particle captured by the black hole represents some negative mass in any real sense. Basically what the whole process depends on, in an over simplified way, is that the captured half of the virtual "particle" pair is always an antiparticle (or maybe some sort of unknown anti-photon?), that ultimately some how reduces the mass of the black hole..? Since both energy and mass contribute to the gravitational field in GR and neither can escape a black hole across an event horizon, even the energy of an anti-particle/photon should add to the gravitational field of the black hole. When particle/antiparticle pairs annialte, they each contribute half of the resulting released energy. Even if half of that energy cannot escape the black hole it adds to the black hole's total energy... At least as long as both mass and energy contribute to a gravitational field.

 

[paddoboy]

I don't think so.

I said it earlier, Hawking Radiation certainly is not on as firm ground as is SR or GR for example.
What I'm saying is that the anologues do support the likelyhood of Hawking Radiation. Nothing more and nothing less.
And just as obviously if the anologues did not support the concept, then its detractors would certainly be using that in their arguments.
My opinion based on that is that Hawking Radiation appears a reasonably logical concept and for that reason, is generally accepted.

Basically what the whole process depends on, in an over simplified way, is that the captured half of the virtual "particle" pair is always an antiparticle (or maybe some sort of unknown anti-photon?), that ultimately some how reduces the mass of the black hole..? Since both energy and mass contribute to the gravitational field in GR and neither can escape a black hole across an event horizon, even the energy of an anti-particle/photon should add to the gravitational field of the black hole. When particle/antiparticle pairs annialte, they each contribute half of the resulting released energy. Even if half of that energy cannot escape the black hole it adds to the black hole's total energy... At least as long as both mass and energy contribute to a gravitational field.

I'm not sure how to answer that, but I did find the following answers which may help in that regard.

http://physics.stackexchange.com/qu...awking-radiation-cause-a-black-hole-to-shrink

The following answer at
http://physics.stackexchange.com/questions/30597/black-holes-and-positive-negative-energy-particles

There are two ways to approach your question. The first is to explain what Brian Greene means, and the second is to point out that the "particles being swallowed" explanation is a metaphor and isn't actually how the calculation is done. I'll attempt both, but I'm outside my comfort zone so if others can expand or correct what follows please jump in!

When a pair of virtual particles are produced there isn't a negative energy particle and a positive energy particle. Instead the pair form an entangled system where it's impossible to distinguish between them. This entangled system can interact with the black hole and split, and the interaction guarantees that the emerging particle will be the positive one. NB "positive" and "negative" doesn't mean "particle" and "anti-particle" (for what it does mean see below), and the black hole will radiate equal numbers of particles and anti-particles.

Now onto the second bit, and I approach this with trepidation. When you quantise a field you get positive frequency and negative frequency parts. You can sort of think of these as representing particles and anti-particles. How the positive and negative frequencies are defined depends on your choice of vacuum, and in quantum field theory the vacuum is unambiguously defined. The problem is that in a curved spacetime, like the region near a black hole, the vacuum changes. That means observers far from the black hole see the vacuum as different from observers near the black hole, and the two observers see different numbers of particles (and antiparticles). A vaccum near the event horizon looks like excess particles to observers far away, and this is the source of the radiation.

 

[paddoboy]

Here is another explanation by Steve Carlip:
http://www.physics.ucdavis.edu/Text/Carlip.html#Hawkrad
Hawking radiation
There are a number of ways of describing the mechanism responsible for Hawking radiation. Here's one:
The vacuum in quantum field theory is not really empty; it's filled with "virtual pairs" of particles and antiparticles that pop in and out of existence, with lifetimes determined by the Heisenberg uncertainty principle. When such pairs forms near the event horizon of a black hole, though, they are pulled apart by the tidal forces of gravity. Sometimes one member of a pair crosses the horizon, and can no longer recombine with its partner. The partner can then escape to infinity, and since it carries off positive energy, the energy (and thus the mass) of the black hole must decrease.

There is something a bit mysterious about this explanation: it requires that the particle that falls into the black hole have negative energy. Here's one way to understand what's going on. (This argument is based roughly on section 11.4 of Schutz's book, A first course in general relativity.)

To start, since we're talking about quantum field theory, let's understand what "energy" means in this context. The basic answer is that energy is determined by Planck's relation, E=hf, where f is frequency. Of course, a classical configuration of a field typically does not have a single frequency, but it can be Fourier decomposed into modes with fixed frequencies. In quantum field theory, modes with positive frequencies correspond to particles, and those with negative frequencies correspond to antiparticles.

Now, here's the key observation: frequency depends on time, and in particular on the choice of a time coordinate. We know this from special relativity, of course -- two observers in relative motion will see different frequencies for the same source. In special relativity, though, while Lorentz transformations can change the magnitude of frequency, they can't change the sign, so observers moving relative to each other with constant velocities will at least agree on the difference between particles and antiparticles.

For accelerated motion this is no longer true, even in a flat spacetime. A state that looks like a vacuum to an unaccelerated observer will be seen by an accelerated observer as a thermal bath of particle-antiparticle pairs. This predicted effect, the Unruh effect, is unfortunately too small to see with presently achievable accelerations, though some physicists, most notably Schwinger, have speculated that it might have something to do with thermoluminescence. (Most physicists are unconvinced.)

The next ingredient in the mix is the observation that, as it is sometimes put, "space and time change roles inside a black hole horizon." That is, the timelike direction inside the horizon is the radial direction; motion "forward in time" is motion "radially inward" toward the singularity, and has nothing to do with what happens relative to the Schwarzschild time coordinate t.

The final ingredient is a description of vacuum fluctuations. One useful way to look at these is to say that when a virtual particle- antiparticle pair is created in the vacuum, the total energy remains zero, but one of the particles has positive energy while the other has negative energy. (For clarity: either the particle or the antiparticle can have negative energy; there's no preference for one over the other.) Now, negative-energy particles are classically forbidden, but as long as the virtual pair annihilates in a time less than h/E, the uncertainty principle allows such fluctuations.

Now, finally, here's a way to understand Hawking radiation. Picture a virtual pair created outside a black hole event horizon. One of the particles will have a positive energy E, the other a negative energy -E, with energy defined in terms of a time coordinate outside the horizon. As long as both particles stay outside the horizon, they have to recombine in a time less than h/E. Suppose, though, that in this time the negative-energy particle crosses the horizon. The criterion for it to continue to exist as a real particle is now that it must have positive energy relative to the timelike coordinate inside the horizon, i.e., that it must be moving radially inward. This can occur regardless of its energy relative to an external time coordinate.

So the black hole can absorb the negative-energy particle from a vacuum fluctuation without violating the uncertainty principle, leaving its positive-energy partner free to escape to infinity. The effect on the energy of the black hole, as seen from the outside (that is, relative to an external timelike coordinate) is that it decreases by an amount equal to the energy carried off to infinity by the positive-energy particle. Total energy is conserved, because it always was, throughout the process -- the net energy of the particle-antiparticle pair was zero.

Note that this doesn't work in the other direction -- you can't have the positive-energy particle cross the horizon and leaves the negative- energy particle stranded outside, since a negative-energy particle can't continue to exist outside the horizon for a time longer than h/E. So the black hole can lose energy to vacuum fluctuations, but it can't gain energy.

 

[brucep]

I don't think so.

The first line of one of his paper's abstracts begins,



... But that paper goes on to describe an analogue of what he, Unruh and the coauthors of his earlier paper, interpret the process Hawking predicted, to be - in a purely classical setting. So what the paper actually argues is that how sound waves act in a moving fluid is similar to the escape process Hawking predicted for Hawking radiation. But even that is a stretch because admittedly no classical environment duplicates the conditions that are predicted to exist at an event horizon in the case of gravity... And Unruh's analogues deal only with how waves in a moving medium seem to simulate what would be expected of EM radiation or particles escaping a black hole from near its event horizon.

The third paper involving ultrashort laser pulses (Unruh was not a contributor), again did not produce any conclusive evidence even though they did observe photon emissions unlike other photon known emissions. From that paper note the last sentence quoted below.



Again even in this case they were not working under conditions involving the extreme gravitational fields associated with black holes.., and they don't make any explicit claims that any separation of virtual particle pairs is involved. All they are really saying is that they have observed photon emission, where the mechanism of emission cannot be readily explained, but fits with their assumptions about the process Hawking predicted.

In the papers presented so far it has been only a simplification of the Hawking process, to classical conditions, that has been explored. Nothing that duplicates the extreme gravitational filed conditions required.

BTW playing only the role of devil's advocate, in these papers it is unclear whether the authors are talking about an emmision process limited to massless photons or ultimately virtual particles that become real massive particles escaping.., and the bigger issue of whether the counterpart photon or particle captured by the black hole represents some negative mass in any real sense. Basically what the whole process depends on, in an over simplified way, is that the captured half of the virtual "particle" pair is always an antiparticle (or maybe some sort of unknown anti-photon?), that ultimately some how reduces the mass of the black hole..? Since both energy and mass contribute to the gravitational field in GR and neither can escape a black hole across an event horizon, even the energy of an anti-particle/photon should add to the gravitational field of the black hole. When particle/antiparticle pairs annialte, they each contribute half of the resulting released energy. Even if half of that energy cannot escape the black hole it adds to the black hole's total energy... At least as long as both mass and energy contribute to a gravitational field.

What you think is irrelevant since you're pretty much confused. Read the entire Unruh paper on the analog experiment. What he said was the original derivation that Hawking wrote down had some issues. Then in 1980 he had the idea to use the analog because the analog experiment domain resolves the issues that he had with the original derivation. From there they designed the experiment which Professor Unruh claims they measured Hawking radiation. He also made it clear that the experimental analysis doesn't include a analysis of a domain, he defines, that might be included in further experimental analysis. They measured the Hawking radiation because the experiment met the original conditions for an analog experiment. Tell us why you think you understand the experiment well enough to say all they measured was the speed of sound. Read the paper which describes the experiment in detail if you can't figure the relationship between the experiment components and why the Hawking radiation should be present. Then you can say what you really mean that analog experiments can't tell us anything about the physics.

 

[OnlyMe]

What you think is irrelevant since you're pretty much confused. Read the entire Unruh paper on the analog experiment. What he said was the original derivation that Hawking wrote down had some issues. Then in 1980 he had the idea to use the analog because the analog experiment domain resolves the issues that he had with the original derivation. From there they designed the experiment which Professor Unruh claims they measured Hawking radiation. He also made it clear that the experimental analysis doesn't include a analysis of a domain, he defines, that might be included in further experimental analysis. They measured the Hawking radiation because the experiment met the original conditions for an analog experiment. Tell us why you think you understand the experiment well enough to say all they measured was the speed of sound. Read the paper which describes the experiment in detail if you can't figure the relationship between the experiment components and why the Hawking radiation should be present. Then you can say what you really mean that analog experiments can't tell us anything about the physics.

Bruce, where did you get the idea I was saying anything about the speed of sound? What I was pointing out is that the analogue experiment could be conducted specifically because it did not involve the conditions that would exist in a strong gravitational field....., a black hole event horizon....

The reference to sound was from,

Thus the creation process for modes of the white hole analog horizons in our experiment will create modes with short wavelengths, which turn out to be about 20cm in our case.

A 20 cm wavelength is within the wavelength range of sound waves.

Black hole event horizons as you imagine them to be remain prediction..., that is at present they are not real things known to exist. Even while many theorists believe that they do. What observational evidence we have for the existence of black holes falls far short of confirming event horizons. Which leaves the Hawking radiation as it involves black holes..., speculation about how an unconfirmed prediction of GR might interact with the unconfirmed virtual particles of quantum theory.

None of your references, the ones you presented in response to my questioning your use of the word "fact" in reference to Hawking radiation, prove your assertion or use of the word. Stop once in a while and think! Even read your own references and quote the specific place they present evidence, with regard to black hole Hawking radiation. That's where this started!

I don't usually get into discussions involving things like the Big Bang or Hawking radiation because they require blind acceptance of too many unproven assumptions. The intent of my posts here has been on the certainty that an obviously lay discussion has been putting on what is theoretical at best and the way I read the papers referenced mostly speculation.

There is no scientific consensus about virtual particles as real components of the vacuum, at best you might get some consensus about an EM spectrum component.., so any speculation about how they (virtual particles) interact with anything, is as I said at best theoretical and most times speculation.

 

[OnlyMe]

Then you can say what you really mean that analog experiments can't tell us anything about the physics.

I never said analogue models or experiments cannot tell us something about physics... But it is foolish to forget that they do not reproduce the conditions, in this case existing at a black hole event horizon, and so while they may provide some limited insight into the process being discussed, they cannot be expected to be taken as proof of anything that happens at or near a black hole event horizon, or even that Hawking radiation does in fact occur. And is the fact that I was questioning.

 

[tashja]

Hi Q. Apologies for the delay. Here's Prof. Unruh's response to your #76:

Right here I have an issue. Not with the renormalization bit but with the assumption of zero net energy of thermal radiation.

It is not an assumption. In flat spacetime We are referring to the vacuum
state. That state has zero energy. The accelerated observer sees that state as
having thermal particles in it. Ie if he uses a particle detector, that
detector will tell him that there are thermal particles around with
temperature proportional to the acceleration. But it is still the same state,
the Minkowski vacuum state, and still has the same energy, zero. Thus the
state that the observer sees as having thermal particles also has zero energy.

The picture has it that enormous tidal g gradients 'tear apart' zero-point EM fluctuations so as to create real photon quanta - yes? How is that not a net gain in energy - given as I pointed out earlier this thread, photons are their own anti-particle? Or put it another way, what *physical sense* can there be to the notion of real -ve energy EM quanta?

Nope, wrong picture. It is more complex than that. In flat spacetime there is
not "enormous tidal g gradients" And near the horizon, the usual observer for
whom the Schwarzchild time is proportional to his own proper time, the situation is
almost like in flat spacetime-- namely this out and in flux, but in this case
where is a bit less in flux than out. That subtraction is what gives the
negative energy flux inward. Sorry that you find it hard to imagine.

Energy density is after all a parametric function of field strength - or it was when I went to school. I can see that mathematically putting an 'i' in front of an E or B could do such a trick, but is that not just mathematical trickery? Explaining what an actual -ve energy EM quanta 'looks like' seems problematical to me.

No "i". The quantum energy naively interpreted is infinite. If you subtract
that infinity, then anything with less energy is negative.

Again, I question the 'must have' there. Take the case of Schwinger 'vacuum polarization' expected when very intense E fields are generated. Owing to the opposite signs of charge for electron-positron virtual pairs, just a uniform E of sufficient strength is all that's needed to 'tear apart' such virtual pairs so as to create real electron-positron pairs. No-one suggests there the net energy of such real pairs is other than large and positive. How then is that same general condition not true when the 'tearing apart' is owing to tidal g gradients rather than an applied E? Is it not so net positive energy is first required then created in such pairs in either case? Of course for Schwinger vacuum polarization, the resulting current quickly neutralizes the E source. In the BH case though, it gets back to that EM quanta don't surely have opposite 'gravitational charge'. And if one gives them such by mathematical fiat declaration, one is left to actually explain how '-ve gravitational charge' could logically allow such to be other than violently expelled - with only +ve energy quanta capable of being trapped inside EH. At the end of it, if you wish to insist the energy book is balanced and have real +ve energy quanta ejected, real -ve energy quanta have to be trapped/swallowed somehow - DESPITE THEIR IMPLIED NEGATIVE GRAVITATING MASS!

See above.

Well thanks for taking the time and effort there to 'unconfuse me', and maybe the fine details somehow add up to a sensible and consistent final picture. As per above comments though, I still have serious reservations.

You have made a model for yourself in your mind, and then, when the facts
differ from the consequences of your model, you argue with the facts. I really
cannot do more than show you what the calculations of quantum field theory
give and to try to give you a model to understand them. That it differs from
your prejudices is surely a learning opportunity for you, rather than an
opportunity to argue that anything that violates your prejudices must be
wrong.

Yes, energy is conserved. Yes, there is a negative energy flux into the black
hole.

If it makes you feel better you can think of the vacuum state as seen by the
accelerated observer as having a huge negative energy vacuum polarization, and
that the thermal positive energy momentum tensor cancels it out, and if there
is a little bit too little of the positive thermal flux, then it is not
entirely cancelled and one gets a net negative flux. The problem with that
image is that that accelerated vacuum diverges at the horizon and is clearly
non-physical.

The problem is that the notion of particles is not an invariant notion but
depends on the state of motion of the observer. Exactly the same state that
one person will say has no particles in it, the other will say there are lots
of particles in it, as measured by a particle detector. Particles in a quantum
field theory, are an epiphenomenon, not something fundamental to the theory.


William G. Unruh | Canadian Institute for|
Physics&Astronomy

I also sent Prof. Polchinski your posts. Here's his reply:

For those of us who are not versed in QFT but do exercise the faculty of critical thinking, that ostensibly standard account has some evident issues.

Maybe QFT can actually make sense of the notion that negative frequencies = negative energies, but it's use elsewhere has no such exotic inference - e.g.:
http://www.bitweenie.com/listings/negative-frequency/
Nothing more or less than an arbitrary coordinate dependent designation of forward vs reverse propagation direction. Actual energies always positive. Hence E = h|f| is what's physically significant, regardless of any mathematical convention where f < 0 is used. A similar thing could be said for the convention of 'complex frequencies'.

Brings me to another troubling aspect of that piece - always referencing HR to particle/anti-particle pairs. The anti-particle always having negative energy somehow. Yet an assumed initially stellar mass BH would have an exceedingly low effective T for the vast bulk of it's slowly shrinking existence. The assumed radiation would be EM, not e.g. electron-positron and higher energy particles.
It's well known a photon is its own anti-particle. Hence both necessarily having positive E = hf energy. By what seeming magic then does an intrinsically positive energy 'anti-particle' photon somehow 'go negative' once it crosses the dreaded EH? Oh yeah, that's right - 'space becomes time, and time becomes space' there. Really? Well gee, if that's truly the case in a physically sensible way, one has to ask why nobody suggests that dropping say a positive energy stone into a BH has that mass magically turning negative and reducing the overall exterior M value of BH. Something special about photons then?

One could go on and e.g. question the logic behind assertion that somehow only the 'negative energy partner' is selected for swallowing. The above though is probably enough to stimulate possible doubts in those not given to unquestioning devotion to orthodoxy. Maybe a QFT expert can now step in and graciously alleviate my doubtlessly unwarranted scepticism.

Standard HR narrative has that negative energy particles are always swallowed by BH hence never observed. Only inferred indirectly as a supposed BH mass loss. However, as a supplement to my last point in #15:
, it may be more pointedly asked why on earth the selection process would not in fact exclusively select the supposed -ve energy particles for expulsion.
Since -ve energy surely logically equates to -ve gravitating mass! Hence, one might reasonably conclude, impossible for a -ve energy particle to ever reach EH let alone sink without trace.

Anyone else think there may be more than a whiff of insanity with the standard narrative? I do NOT apologize if this makes devoted followers of consensus position hurt in their heads.

An important issue is the relativity of energy: different observers measure different energies. The energy being referred to here is the energy associated with the external time-translation symmetry. Now, behind the horizon, this becomes a spatial translation, so it is perceived by a local observer as a momentum, which can have either sign. For an inward directed motion this quantity is positive, while for an outward directed motion it is negative.

Energy is conserved, so for a particle thrown into the black hole, it remains positive (inward directed motion). The particles that have negative energy are outward directed, forming in the pair creation event, but since they are behind the horizon they just hit the singularity. The conserved energy is manifestly positive for particles outside the horizon, so it is clear that no negative-energy particle could escape.

Incidentally, the particle description is clumsy, one always uses the field description in a precise calculation, but the issues raised in your note can be answered in the particle description.

Best,
Joe

 

[tashja]

I'm very grateful to both Prof. Unruh and Prof. Polchinski for their informative replies, and also to Prof. Adam Helfer for addressing Q's questions/concerns. Here's his reply:

For those of us who are not versed in QFT but do exercise the faculty of critical thinking, that ostensibly standard account has some evident issues.

Maybe QFT can actually make sense of the notion that negative frequencies = negative energies, but it's use elsewhere has no such exotic inference - e.g.:
http://www.bitweenie.com/listings/negative-frequency/
Nothing more or less than an arbitrary coordinate dependent designation of forward vs reverse propagation direction. Actual energies always positive. Hence E = h|f| is what's physically significant, regardless of any mathematical convention where f < 0 is used. A similar thing could be said for the convention of 'complex frequencies'.

Brings me to another troubling aspect of that piece - always referencing HR to particle/anti-particle pairs. The anti-particle always having negative energy somehow. Yet an assumed initially stellar mass BH would have an exceedingly low effective T for the vast bulk of it's slowly shrinking existence. The assumed radiation would be EM, not e.g. electron-positron and higher energy particles.
It's well known a photon is its own anti-particle. Hence both necessarily having positive E = hf energy. By what seeming magic then does an intrinsically positive energy 'anti-particle' photon somehow 'go negative' once it crosses the dreaded EH? Oh yeah, that's right - 'space becomes time, and time becomes space' there. Really? Well gee, if that's truly the case in a physically sensible way, one has to ask why nobody suggests that dropping say a positive energy stone into a BH has that mass magically turning negative and reducing the overall exterior M value of BH. Something special about photons then?

One could go on and e.g. question the logic behind assertion that somehow only the 'negative energy partner' is selected for swallowing. The above though is probably enough to stimulate possible doubts in those not given to unquestioning devotion to orthodoxy. Maybe a QFT expert can now step in and graciously alleviate my doubtlessly unwarranted scepticism.

Standard HR narrative has that negative energy particles are always swallowed by BH hence never observed. Only inferred indirectly as a supposed BH mass loss. However, as a supplement to my last point in #15:
, it may be more pointedly asked why on earth the selection process would not in fact exclusively select the supposed -ve energy particles for expulsion.
Since -ve energy surely logically equates to -ve gravitating mass! Hence, one might reasonably conclude, impossible for a -ve energy particle to ever reach EH let alone sink without trace.

Anyone else think there may be more than a whiff of insanity with the standard narrative? I do NOT apologize if this makes devoted followers of consensus position hurt in their heads.

Dear Tashja,

Thanks for your question.

The short answer is that explanations of Hawking radiation in terms of positive-/negative-energy particle/antiparticle pairs give a sort of general feel for what is going on, but are not really adequate for understanding the physics in detail. For the Hawking process, there are difficulties with talking too casually both about particles and about positive and negative energies.

Here's more detail:

As you may know, there are also questions about how credible Hawking's description of black-hole radiation is, but I'll leave that issue aside as far as I can. Since a lot of what follows is a bit technical, let me first block out the main things we know and how your questions fit in:

(a) Hawking's calculation does predict a flux of particles coming from the region around black holes (strictly speaking, around black holes formed by collapse -- eternal black holes would be another question).

(b) Arguments for how the energy of the hole should decrease as a result of this process are indirect and we do not have a very specific understanding of that.

It is for (b) that the issue of negative energies is more central -- and so I am cautioning you that you may find I can answer some of your questions (resolve certain concerns) but no one really has a full answer.

A lot of people, in discussing Hawking radiation, use the term "particle" for something which has many of the mathematical properties of a particle but is not actually a physical particle. I'll keep to the physical meaning. Then particles should be particular kinds of excitations, with specific properties, of the quantum state.

In a curved space-time (that is, when gravitational effects are important), in many cases it is not hard to say what a quantum particle is, but in other cases it does become problematic. One main difficulty comes when the wavelengths of the quantum excitations are around the local radius of curvature of the space-time. This is exactly the situation for the region around a black hole which Hawking quanta are supposed to emerge from. Far enough away from the hole, the radius of curvature is small, it is unproblematic to speak of particles, and we can say that the computation predicts a particle flux. But in the vicinity of the hole, while there is some sort of excitation of the quantum state, that cannot be viewed in any simple way as a collection of particles. This is one reason why the Hawking process would be a non-local phenomenon.

As for the negative energies, I should begin by saying that "negative energy particle" is almost always a short-hand for a mathematical and not a physical notion of particle. (It goes back to Dirac's idea of a "negative energy sea," ca. 1930. While that idea did help to develop the theory, it is rejected as a physical concept by the more modern formulation, that is, quantum field theory.) Unfortunately, even the professional literature is not always very clear about this!

Discussions of energy become tricky when we bring in general relativity, even if we leave aside quantum issues. While locally any particle will have a well-defined energy-momentum four-vector (and energy would be the component measured by an observer at that point), the curvature of space-time prevents there from being a simple way of comparing the energy-momenta at different points. For a quantum excitation which is not really localized to begin with, discussions of energy are especially problematic. (And one reason Hawking's original result surprised so many people is that it depended partly on rejecting an "obvious" approach to measuring energy in the problem!)

Now, a main argument for the plausibility of Hawking's calculation is that it doesn't seem to require one to confront tough questions about how quantum effects act back on the geometry of space-time: the quantum fields are taken to be just "painted on" the space-time. This seems at least superficially o.k. because the black hole is a macroscopic object and Hawking radiation is supposed to perturb that only slightly (at least, unless we wait very long times).

However, when we ask how the black hole loses mass to compensate for the Hawking radiation (assuming it does lose mass -- by conservation of energy), we lose this advantage, for now we are asking just how these quantum effects generate changes in the space-time geometry. We simply have no real theory of this at present.

A plausible approach would be to assume that in some sort of average sense the quantum field contributes a source term to Einstein's equations, a stress-energy tensor. There is partial success in constructing a plausible such object, and, insofar as the success goes, it does seem that the object contributes a negative energy flux across the horizon. But none of that can really be interpreted in any simple way in terms of physical particles.

There has been a lot of work in the past fifteen years or so in which people try to give arguments for Hawking radiation based on "negative energy particles." I haven't followed all of it, but every so often I look at. A number of interesting ideas have been introduced, but at least so far I'm not aware of any work which really overcomes the conceptual issues involved (if what one is looking for is a treatment which is based on conventional quantum field theory and physical definitions of particles). This is not always clear in the papers, because of the loose use of the terms "particle" and "negative energy."

I hope this helps!


— Adam Helfer



--

Adam Helfer

Department of Mathematics

University of Missouri

Columbia, MO 65211

U.S.A.

 

[The God]

I'm very grateful to both Prof. Unruh and Prof. Polchinski for their informative replies, and also to Prof. Adam Helfer for addressing Q's questions/concerns. Here's his reply:

Hi Q. Apologies for the delay. Here's Prof. Unruh's response to your #76:




I also sent Prof. Polchinski your posts. Here's his reply:

You have made a model for yourself in your mind, and then, when the facts
differ from the consequences of your model, you argue with the facts. I really
cannot do more than show you what the calculations of quantum field theory
give and to try to give you a model to understand them. That it differs from
your prejudices is surely a learning opportunity for you, rather than an
opportunity to argue that anything that violates your prejudices must be
wrong

Thanks Tashja..

Prof Adam clearly and candidly explains that things around HR are not so clear and thus questionable. Under the circumstances claiming that HR is measured in Analogue experiments etc may not be applicable in BH domain. I am not disputing the analogue experiment but its extension. I fully agree and believe that HR is extremely speculative idea, and present interpretation available from various sources which loosely talks of particles and negative/positive energy is highly simplistic and confusing...

What surprises me the tinge of exasperation and rudeness in Unruh's response to Q-reeus argument. Q-reeus argument is valid and air of confusion gets over only with the candid response of Prof Adam. There are at least two posters here who claim HR to be a near certainty, but thats not so as clear from Prof Adam's response. Prof Unruh seems to be taking a different stand, kind of pushing HR valiantly.

 

[paddoboy]

I'm very grateful to both Prof. Unruh and Prof. Polchinski for their informative replies, and also to Prof. Adam Helfer for addressing Q's questions/concerns. Here's his reply:

I believe the forum as a whole is grateful to you also for your efforts tashja.
I seem to get more "ignores" sometimes the occasional reply.
Might be a gender/age thingy......ie, answering a pretty young lady rather then replying to some old bastard! [tic mode on of course]

 

[paddoboy]

There are at least two posters here who claim HR to be a near certainty,

If you are referring to me [which you do fanatically] then that is entirely wrong
In fact what I have said [if you are referring to me] is

I said it earlier, Hawking Radiation certainly is not on as firm ground as is SR or GR for example.
What I'm saying is that the anologues do support the likelyhood of Hawking Radiation. Nothing more and nothing less.
And just as obviously if the anologues did not support the concept, then its detractors would certainly be using that in their arguments.
My opinion based on that is that Hawking Radiation appears a reasonably logical concept and for that reason, is generally accepted.

The nature of Hawking Radiation is still rather less than certain as per the near certainty of GR say, but again as I have said, appears as a rather logical extension imho of quantum theory.

I believe all our professional replies have supported that concept.
Sorry, but the need to correct you once again is for the benefit of highlighting the truth as against your misinterpretations, errors and unjust claims.

 

[The God]

If you are referring to me [which you do fanatically] then that is entirely wrong
In fact what I have said [if you are referring to me] is




I believe all our professional replies have supported that concept.
Sorry, but the need to correct you once again is for the benefit of highlighting the truth as against your misinterpretations, errors and unjust claims.

Dishonesty cannot be cured without punishment. You are expert in changing track and that diameter dance proved that.

Now let see this changing HR stand of yours...

You were so passionately in argument (supporting HR) with at least 3 of us, schemelzer, Q-reeus and myself with a brief interlude with OnlyMe. Schmelzer declared you 'Uneducable', Q-reeus declared you 'illiterate cretan' and I have proved you a 'liar' and now your dishonesty will be further proved..

Hawking radiation as supported by many reputable links, and in line with particle pair production is most certainly a reasonably logical scenario to envisage...

I say it again, Hawking radiation although a quantum effect, is based on good logic and what we already theorise.

In the course of discussion, you started playing safe and conveniently started blowing varied temperature air...the present change of stand after prof Adam's reponse is part of your usual dishonest ways without admitting.

Now see, below post by Schmelzer..

This picture of Hawking radiation with a virtual particle pair is quite popular but misleading.

Correct observation, which gets confirmed by Prof Adam, if you knew anything about HR realistically then you would not have made below comment...now you are changing to align with Schmelzer without acknowledging his original stand on HR. Is it not dishonesty ?

Why is it misleading?
You have expressed your doubts re hawking Radiation and I have offered reputable links supporting the HR concept.

I see HR as reasonably logical as many other reputable physicists also find.
Yes it is still rather theoretical and has not been validated, but it is based on already accepted cosmology of particle pair creation.

I know you will come up with some wierd argument to justify your change of stand without admitting it, but thats how you are scripted. I am getting convinced that rationality and reasonableness do come from education also. Lack of education may make a person irrational.

 

[Q-reeus]

Hi Q. Apologies for the delay. Here's Prof. Unruh's response to your #76:...

Many thanks again tashja for quietly getting down to business and eliciting useful feedback - from three different Profs this time.
There are a number of statements made by Prof Unruh that I'm inclined to question if not outright challenge, but see no point in keeping the ball rolling. He is a well recognized professional physicist convinced of the correctness of his model and has sizable support for it, which I guess explains to some extent an exasperated tone in that reply.

I also sent Prof. Polchinski your posts. Here's his reply:...

Prof. Polchinski's answer seems to reflect a very formal approach relying in part on the 'weirdness' of interior Schwarzschild coordinates. For me, it's enough to note that owing to sqrt(g_tt) -> 0 at BH EH, any notion of energy -> momentum etc. or any physical 'process' occuring for r < 2M that could have real consequences for exterior r > 2M is just absurd and self-contradictory. But that's me. It was while participating in a thread elsewhere dealing with (attempted) metric matching across a spherical shell, the pathological nature of Schwarzschild metric became evident and soon after I became a fan of 'fringe' Yilmaz gravity. For which there can never be issues of HR or e.g. bizarre 'spacetime swapping'. That's enough to stir righteous indignation in some so enough of that talk.

 

[Q-reeus]

I'm very grateful to both Prof. Unruh and Prof. Polchinski for their informative replies, and also to Prof. Adam Helfer for addressing Q's questions/concerns. Here's his reply:...

Again, not interested in keeping the ball rolling here, but will state I do have a preference for Prof Helfer's 'warts and all' explanation over that of the other two above. His response does imo acknowledge there are consistency issues, although it's also fair to say he believes that HR is more likely real than not.

Thanks again tashja.

 

[paddoboy]

Dishonesty cannot be cured without punishment. You are expert in changing track and that diameter dance proved that.

The only thing dishonest is you and your posts as most already know, along with your other questionable "god like" qualities.

You do realise that people are laughing at you don't you?
I don't need to say much more, as like I said previously you are totally and seriously unable to accept what a total fool you have made of yourself, due to your arrogant self delusional nature, and of course your peers on this forum will be the judge of who has lied in near every post, and I'll gladly stand by that judgement.

 

[The God]

The only thing dishonest is you and your posts as most already know, along with your other questionable "god like" qualities.

You do realise that people are laughing at you don't you?
I don't need to say much more, as like I said previously you are totally and seriously unable to accept what a total fool you have made of yourself, due to your arrogant self delusional nature, and of course your peers on this forum will be the judge of who has lied in near every post, and I'll gladly stand by that judgement.

So you agree that HR prevalent concept with virtual particle pair is misleading?

 

[OnlyMe]

I'm very grateful to both Prof. Unruh and Prof. Polchinski for their informative replies, and also to Prof. Adam Helfer for addressing Q's questions/concerns. Here's his reply:

Tashja, once again....

I believe that Professor Helfer's response is the better of the three for a lay oriented discussion, because it clearly conveys the theoretical nature of the subject. That does not mean that I believe the earlier two responses are faulty in any way, only that in those responses, I prefer to believe, that the professors assume the theoretical character of the discussion is taken for granted.

Even when we discuss theory or our favorite speculations, we tend to do so in a way that projects some measure of certainty. In a peer to peer professional discussion that should present little problem. In a lay discussion it can sometimes be misleading. It is that tendency for the way a discussion is phrased that often draws my attention... And one reason why I prefer Professor Helfer's response.

Once again good work in obtaining these comments and responses.

 

[OnlyMe]

Dishonesty cannot be cured without punishment. You are expert in changing track and that diameter dance proved that.

Paddoboy has been clear in his position, at least where his own words are involved. It appears to me that you confuse.., or perhaps better interpret his many quoted references, as representing his personal opinion.

Almost all references presented in these discussions carry with them some bias of the author. As I mentioned, in different words, an earlier post.., as long as all parties understand whether they are discussing the physics of what is known to be real or the physics of theory and/or speculations, debate should be a matter of discussing differing interpretations of the implications....

Some of your criticism and even mine, might be the result of paddoboy's habit of not putting articles and references in the QUOTE function, which would create a clear separation between what he is quoting and what he is saying hisself... But that would just make it easier for those of us reading to see the change of voice. The fact that he does not use the quote function as often as I would like does not justify misreading his own words.

So you agree that HR prevalent concept with virtual particle pair is misleading?

As pointed out by the responses tashja, just posted.., in lay discussion reducing the virtual particles of quantum field theory to particles as commonly defined in a lay context, is what is misleading.., and yet almost a necessity in a lay discussion.

BTW it should be clear that there is no real prevalent or mainstream consensus, when it comes to the exact nature of virtual particles as any kind of real component of the vacuum. They are a useful part of a theoretical model that is often extended beyond any practical description of observable reality.