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Is this a fair description of Hawking radiation? Also, if I made an error, please correct it. Thank you.

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- Thread starter Chaos' lil bro Order
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- #1

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Is this a fair description of Hawking radiation? Also, if I made an error, please correct it. Thank you.

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A reader might ask which particles are radiated in this manner.

Also, it would be nice to include information about the entropy and temperature of black holes, and how that relates to Hawking Radiation.

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You see, if the virtual particle pairs occurring at the event Horizon were no different from the virtual particle pairs appearing everywhere throughout space-time, then the process of one virtual particle being trapped within the black hole while the other escapes would be a process by which the black hole

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How?

What is the importance of Hawking radiation? Why is it so sig?

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I think that one important thing about Hawking Radiation is that it is the first mechanism shown by which something from inside a BH (mass) can get out. Also, it is one of very few cases (mayeb the first case?) of a model that incorperates QM and GR into a single process, and accurately predicts the outcome of that process.

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That does not sound quite right.Also, it is one of very few cases (mayeb the first case?) of a model that incorperates QM and GR into a single process, and accurately predicts the outcome of that process.

I don’t think there has been any evidence to demonstrate that nature actually has Black Holes losing mass where some verifiable observation conclusively shows that mass inside a Black Hole uses some process to allow some of that mass to escape from inside the event horizon.

Observations that the total mass an individual Black Hole had in fact become smaller over time would certainly be a strong indicator – are you saying that such evidence has actually been observed.

I suspect it better to say the process of Hawking Radiation predicts an outcome many hope is true. But has yet to be confirmed as happening at all, let along that the actual rate of mass loss from a Black Hole "accurately" matches that projected by Hawking Radiation.

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using energy from the black hole. The inclusion or exclusion of this small phrase may seem a bit "nit-picky," but it is actually rather significant.

You see, if the virtual particle pairs occurring at the event Horizon were no different from the virtual particle pairs appearing everywhere throughout space-time, then the process of one virtual particle being trapped within the black hole while the other escapes would be a process by which the black holegainsmass. But, if both virtual particles in a pair are formed by energy from within the event Horizon, then the escape of one represents the loss of energy (and therefore mass) from the black hole.

That is not nit-picky at all Lurch. In fact I thank you heartily for pointing that out to me as I did not know it and its clearly a vital part of Hawking's theory. So thank you.

So to summarize, you said that virtual particles 'pop' up in greater abundance on the SR due to some kind of 'lending' of energy from the BH that increases the potential for virutal particle 'pop ups'. I was wondering then, is this a commonly accepted theory in particle physics? From what I know, or thought I knew, particle physicists give the same probability of a particle pair 'pop up' for all regions of space. Clearly this contradicts what you've said, so I was wondering if perhaps there is a reference you could provide to clear up my confusion.

What if the probability of each particle pair 'pop up' was equal for all regions of space, BUT, on the SR, energy leant from the BH goes, not into increases the total # of particle pair 'pop ups', but rather the energy leant from the BH goes into 'popping up' higher energy particle pairs. In other words, in all regions of the universe particle pairs 'pop up' at the same rate, but in very high energy regions of space like the SR of a black hole, the particles in each pair are simply 'bigger', so to speak, in terms of ev/C2.

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Yes, it solves the paradox of information appearing to be destroyed.I think that one important thing about Hawking Radiation is that it is the first mechanism shown by which something from inside a BH (mass) can get out.

:rofl: No, by "accurately predicts.." you probably just meant "consistent with other thought experiments from thermodynamics"?Also, it is one of very few cases (mayeb the first case?) of a model that incorperates QM and GR into a single process, and accurately predicts the outcome of that process.

Who said the vacuum boils harder under gravitational effects?I'm afraid I don't know the exact mechanism, only that VPP's occur everywhere in space, but [..] I've always heard it explained was that the space in that area "boils" more because of the tension between the sharply curved space inside and the relatively flat space outside.

Hawking's paper started a field of "QFT on curved space-times". As far as I understand it, the equation of the quantum field is generalised in the obvious/natural manner (much like Maxwell's equations) and solved globally on the manifold like any other PDE. This means that there usually isn't any explicit study of actual particle processes near the horizon, so those processes are (as per norm?) waftily explained with terms such as virtual particle pairs which (it must be stressed) are very different to the real particle/antiparticle pairs we're more familiar with (particularly, the virtual particles do not both have positive mass-energy.. and hence their separation would be quietly short-lived if it were not possible, through the turning of the horizon time-axis relative to infinitely distant observers, for only the negative mass-energy virtual particle to fall in whilst the escaping partner becomes real with respect to distant observers.. Baez probably elucidates further.) A problem of course, with this whole semi-classical approximation, is that there is no feedback into GR (ie. the shrinking of the black hole is theoretically just a guess, not a mathematical result, and it certainly can't be tested by astrophysical experiment yet).

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- #9

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Actually, I was talking about a headline I saw years ago which said something to the effect that a group of Itallian scientists had observed Hawking Radiation. Since this discussion began, I have gone over the Web looking for that article, only to find that they were lying through there cannoli holes. What actually happened was that this group of researchers produced a:rofl: No, by "accurately predicts.." you probably just meant "consistent with other thought experiments from thermodynamics"?

I'm pretty sure I read that one in "A Brief History of Time." It was in refference to the tension created by the curvature of spacetime at the EH.Who said the vacuum boils harder under gravitational effects?

I will look around and see if I can pinpoint the exact location.

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http://www.sciforums.com/showthread.php?p=1863857

I am not sure if this is true, but its along the lines of what Lurch was getting at (I think).

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First I should say I do not believe Hawking Radiation is correct.I found this description in another physics forums that was nicely put...

“… The only violation of this is when one of the pair falls inside the EH of a BH and leaves the other as a long lived real electron or positron in our universe. I.e. it is not a "virtual particle" but a real one …”

That said, I don't think HR expects particles when radiated from a black hole need be as large as electrons or positrons; photons alone are enough and more likely in that process. The key is when the virtual pair is created the net energy of both is Zero, assume one has a “

Since near a BH where the two VP’s may separate with one going it is a 50-50 shot as to which one is left behind why shouldn’t there be a even distribution of “-“ and “+” energy that nets to Zero outside the BH? The trick is whichever VP, “

Thus in order to obey conservation, all the individual VP’s drawn into the BH must resolve into “Negative Energy” where the net effect is Real Energy (and thus Mass) is erased inside the BH.

I don’t see the justification for one way exit of energy/mass in the process. It certainly is a well-designed mathematical hypothesis; I just don’t see the theoretical support in it (let alone the lack of observation evidence) for the scientific community to raise the idea to the importance of a “theory” over just an interesting piece of math. Just IMO.

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You probably know that quantum mechanics predicts that systems like atoms have energy levels. So, the hydrogen atom has a lowest energy state, a first excited state with higher energy, etc. but nothing in between those energies. It works in much the same way if you apply quantum mechanics to fields. What you find is different series of equally spaced energy levels. These energy levels are interpreted as states containing particles of various energies. I.e. particles are just excited states of fields.

Now, just like if an hydrogen atom is in its ground state you can't say that there is no hydrogen atom, the same is true for fields. If the electromagnetic field is in the ground state, then that means that there are no photons, but the electromagnetic field is still there. Now, I think you have read about quantum tunneling. Suppose, e.g. that you have a system that has three quantum states: X, Y and Z and that in X and Z it has the same energy while in Y it has a larger energy. If the system, when described classically, can only go from X to Z while passing through Y, then it cannot make that transition because that would violate energy conservation.

But according to quantum mechanics such transitions are possible. The fact that a "real" intermediary state Y exists connecting X to Z is enough to make transitions from X to Z possible, even though the system cannot be found in state Y because of lack of energy. We can qualitatively say that the system goes from X to Z by first making a virtual transition to state Y (by borrowing energy using the time energy uncertainty relation) and then from Y to Z and then paying back the borrowed energy used to make it to Y. What is crucial here is that X and Z do have the same energy, so energy is conserved.

In case of virtual particles it is much the same story, the intermediary state Y being an excited state of a field (i.e. a particle) for which there is not enough energy, but which nevertheless couples an initial state X to a final state Z. So, in case of the evaporating black hole you have:

X = black hole has energy E, field is in ground state and has energy zero.

Y = black hole has energy E, field is in an excited two particle state with energy 2q

Z = black hole has energy E - q, field has energy q, i.e. there is a particle with total energy q.

Clearly X and Z have the same energy: E = E -q + q. But Y has an amount 2q more energy. The transition from X to Z is still possible via quantum tunneling via Y. If the system had enough energy it could have made it to Y and paid for the two particles of energy q each, then it could have let one particle crash into the black hole and let the other escape. So, the state Y does indeed connect X to Z.

Because we don't have the 2 q of extra energy to pay for the two particles, the state Y is entered virtually with energy zero. One can then assign a total energy of zero to the two particles. But note that we already know how state Z must look like: Black hole ends up with energy E - q and the particle that escapes has energy q. You cannot write down a final state Z in which the black hole ends up with energy E + q and the escaping particle get's -q, because the field has an energy of zero at least (the ground state is the lowest energy the field can have).

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As I said HR is a “well-designed mathematical hypothesis” and would expect “extremely smart physicists and mathematicians” would agree with it on that basis. Nor do I need to wait until an “explanation has satisfied me”, that HR is correct.

A theory need not be completely correct or a “Law of Physics” to be useful enough or likely to be correct to justify calling it a theory.

I just don’t see HR as including the needed physical theoretical detail within the idea to merit the move past even a speculative mathematical hypothesis (worthy of study for sure) to upgrade it to being considered a theory within the science of physics.

IMO if HR was instead presented by someone without the scientific respect and charisma of Hawking I think would only be a hypothesis well worthy of study by other scientists. But not the important Theory that needs to be explained to the public as it is now treated.

I don’t think HR is bad (it is worth understanding it for what it is), just over rated and not likely to be correct.

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As I said HR is a “well-designed mathematical hypothesis” and would expect “extremely smart physicists and mathematicians” would agree with it on that basis. Nor do I need to wait until an “explanation has satisfied me”, that HR is correct.

A theory need not be completely correct or a “Law of Physics” to be useful enough or likely to be correct to justify calling it a theory.

I just don’t see HR as including the needed physical theoretical detail within the idea to merit the move past even a speculative mathematical hypothesis (worthy of study for sure) to upgrade it to being considered a theory within the science of physics.

IMO if HR was instead presented by someone without the scientific respect and charisma of Hawking I think would only be a hypothesis well worthy of study by other scientists. But not the important Theory that needs to be explained to the public as it is now treated.

I don’t think HR is bad (it is worth understanding it for what it is), just over rated and not likely to be correct.

While I agree with everything you just said, I as does the public, put our faith in physicists to give us answers. Perhaps if I were good at mathematics and could understand Hawking's derivation, I could form a valid opinion on the plausibility of HR, but as I am not, I take such things on faith (blindly, I'm not ashamed to admit).

As a funny little sidenote, I remember how Hawking and Feynman had a mini battle over who was smarter. To paraphrase, Hawking reminded Feynman that he could do complex calculus in his head without the aid of paper or calculator. While Feynman retorted that Hawkings' calculating power was all fine and well, but could he creatively pull a fundamental theory of nature out of the aether like QED? Perhaps HR was Hawkings' attempt to prove to the world and Feynman that even calculators could be creative.

Personally I think Feynman dwarf's Hawkings' professional accomplishments, but its just one opinion.

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The principle is simple - if the gravitational field changes in time, then the equations of QFT on such a background predict some radiation.

At a first look, this seems in contradiction with the view that a BH is a stable configuration. But the BH has been created by a collapse. And now take a look at the origin of the Hawking radiation. This origin is some event outside the BH horizon. As the origin of everything we can see outside. But it comes from the region where the BH is located. In fact, it arrives together with the extremely redshifted last information from the collapsing star. That means, it comes from a region of spacetime where the configuration of the gravitational field was not stable at all.

To add some facts about variants of Hawking radiation: A stable star (not BH) does not have HR. Instead, a collapsing star gives, during the collaps, radiates.

I would like to add that there are different levels of certainty for different parts of the theory. About the behaviour of quantum fields on a given (fixed) curved background there is not much doubt. Of course, no observational support at all (the effects are much too small), but no conflict of the fundamental principles, and the extension of known laws of physics into this domain is quite clear and unique.

A completely different question is the process of evaporation. This is an application of energy conservation which includes a notion of energy of the gravitational field, which is not defined in GR and contradicts their principles of covariance. In some sense, it is nonetheless a quite natural consequence, because, last not least, we have a preferred system of coordinates, especially a preferred time, for this particular situation (a Killing vector field). Therefore, we can use such non-covariant things like energy of the gravitational field, computing them in these coordinates. Nonetheless, the whole thing is already in contradiction with fundamental GR principles. (Even if people try to hide this as much as possible.) A non-covariant step is, especially, the renormalization of the energy-momentum tensor.

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If anything, the particle-antiparticle answer seems to be the most plausible one. This is where radiation matter gets "ripped apart" causing the anti-matter particles to get flown away at the BH's event horizon. Once again, us humans' inability to understand quantum mechanics and physics to it's truest form is the reason we will never be able to know the answer to this theory...but stay tuned.

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For state Z to exist, there must still be some mechanism for energy to be removed from the BH, no?

And if there is, why not go through state Y':

Y' = black hole has energy E - 2q, field is in an excited two particle state with energy 2q

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