About hawking radiation

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Main Question or Discussion Point

1)when hawking first propounded this thermal radiation, he took into acount the the gravitational cllapse.
so I am not sure, if we consider a stationary system, then there won't be any particle creation. Is this the case? because I think there will not be any mixing of posive and negative frequencies.

2)From Unruh effect, we can also get the temperature.the freely-falling observer and the static observer on the event horizon will have different definition of vacuum, then the temperature can be deduced from the Bogolubov coefficients. But I cann't see why the event horizon is so significant in this case?
what happen on the event horizon exactly, when we consider Hawking radiation?
 
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  • #2
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when hawking first propounded this thermal radiation, he took into acount the the gravitational cllapse.
so I am not sure, if we consider a stationary system, then there won't be any particle creation. Is this the case? because I think there will not be any mixing of posive and negative frequencies.
1.) Remember that the event horizon changes the outcome for particles, not their initial behaviour. Pair creation is going to occur (if the BH is 'hotter' than the Background), and the theory doesn't take place in a stationary system.

2.) Do you mean static or stationary? A BH is neither. A Schwarzschild BH is non-rotating, not static or stationary.
 
  • #3
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1.) Remember that the event horizon changes the outcome for particles, not their initial behaviour. Pair creation is going to occur (if the BH is 'hotter' than the Background), and the theory doesn't take place in a stationary system.

2.) Do you mean static or stationary? A BH is neither. A Schwarzschild BH is non-rotating, not static or stationary.

What I know about Hawking radiation is that there are inequivalent vacuums, as Unruh effect. so, would you please explain in this respect to more details? Thank you so much!
 
  • #4
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while you are at it, please explain how a particle can have "negative energy".
 
  • #5
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I'm not advocating either theory, just pointing out some basics. The stuff about the Unruh effect was edited in by the OP after I posted. EDIT: To clarify, the quote in my first post was the OP's Original Post if you care for a reference.
 
  • #6
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while you are at it, please explain how a particle can have "negative energy".
The negative energy is to the infinite observer. In Penrose process, the negative energy is necessary to extract energy from a BH.
This negative energy is non-observable locally, according to Hawking's original paper.
 
  • #7
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I should add that negative energy of a single particle vs. negative energy densities in the region adjecent to the EH (part of the ergoregion) is not hard to imagine. I don't believe that QFT requires that individual particles have negative energy.

I don't know if what I said was accurate, so if a mentor or such wants to clarify this, I'd be happy to learn.
 
  • #8
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uhhh

a particle has a probability to be outside of the blackhole it is part of. When this probability is fulfilled, the particle radiates.

The end (?)
 
  • #9
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uhhh

a particle has a probability to be outside of the blackhole it is part of. When this probability is fulfilled, the particle radiates.

The end (?)
That isn't HR, or at least, that ignores many other factors such as the nature of the emission and the worldline of the emitted photon.
 
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i do not understand what you mean by an "infinite observer". seems a particle would represent some positive value of energy regardless of the location or ref frame of any observer.
 
  • #11
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i do not understand what you mean by an "infinite observer". seems a particle would represent some positive value of energy regardless of the location or ref frame of any observer.

Actually, this process is not quite clear to me , I may just as well refer to Hawking's paper
"Particle Creation by Black Holes", Commun.math.Phys.43,

"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. The negative particle is in a region which is classically forbidden but it can tunnel through the event horizon to the region inside the BH where the Killing vector which represents time translations is spacelike. In this region the particle can exist as a real particle with a timelike momentum vector even though its energy relative to infinity as measured by the time translation Killing vector is negative."
 
  • #12
JesseM
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uhhh

a particle has a probability to be outside of the blackhole it is part of. When this probability is fulfilled, the particle radiates.

The end (?)
Tunneling from inside to outside the event horizon is equivalent to a particle tunneling outside its own future light cone (i.e tunneling FTL)...I think it's debatable whether this can happen, certainly tunneling can't carry any information FTL (see this thread along with https://www.physicsforums.com/blog.php?b=1113 [Broken] for some discussion of the issue).
 
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  • #13
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Tunneling from inside to outside the event horizon is equivalent to a particle tunneling outside its own future light cone (i.e tunneling FTL)...I think it's debatable whether this can happen, certainly tunneling can't carry any information FTL (see this thread along with https://www.physicsforums.com/blog.php?b=1113 [Broken] for some discussion of the issue).
Thanks for those links. Heat transfer doesn't need to tunnel though (?). Normal photon or particle emission due to thermal sources can be described by quantum effects - does this mean the thermal emission from a black hole is un-quantum (strictly classical)? Or is HR only allowed in a classical blackbody mechanics?
 
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  • #14
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Here is how Wikipedia describes pair production:

In semiclassical general relativity, pair production is also invoked to explain the Hawking radiation effect. According to quantum mechanics, at short scales short-lived particle-pairs are constantly appearing and disappearing (see quantum foam); in a region of strong gravitational tidal forces, the two particles in a pair may sometimes be wrenched apart before they have a chance to mutually annihilate. When this happens in the region around a black hole, one particle may escape, with its antiparticle being captured by the hole.
http://en.wikipedia.org/wiki/Pair_creation

and also
Quantum foam is theorized to be created by virtual particles of very high energy. Virtual particles appear in quantum field theory, where they arise briefly and then annihilate during particle interactions, in such a way that they affect the measured outputs of the interaction even though the virtual particles are themselves never directly observed. They can also appear and annihilate briefly in empty space, and these "vacuum fluctuations" affect the properties of the vacuum, giving it a nonzero energy known as vacuum energy, a type of zero-point energy (however, physicists are uncertain about the magnitude of this energy
http://en.wikipedia.org/wiki/Quantum_foam

I assume participants here know that black holes are colder than our universe so Hawking radiation has NOT been observed....

From Unruh effect, we can also get the temperature.the freely-falling observer and the static observer on the event horizon will have different definition of vacuum, then the temperature can be deduced from the Bogolubov coefficients. But I cann't see why the event horizon is so significant in this case?
For one thing, the fee falling observer sees no event horizon...and passes thru that theoretical boundary without ever knowing it....and sees a perfect vacuum (no photons) and is surrounded by virtual photon pairs...in contrast the static observer near the horizon will be burned almost instantaneously by radiation which appears to her as thermal radiation...She sees a single thermal photon and has no way of knowing its one of a pair of virtual photons...

near the horizon the the separation into thermal and quantum depends on the observer
Leonard Susskind THE BLACK HOLE WAR, page 173...
 
  • #15
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Thanks for those links. Heat transfer doesn't need to tunnel though (?). Normal photon or particle emission due to thermal sources can be described by quantum effects - does this mean the thermal emission from a black hole is un-quantum (strictly classical)? Or is HR only allowed in a classical blackbody mechanics?
HR is a purely quantum effect that only MIMICS thermodynamic radiation. Really, it's... quantum evaporation through single particles tunneling: i.e. single particles with worldlines extending both into and outside of the event horizon, but carrying no information. The "trick" is that the portion within the EH is formulated as the past worldline of the "escaping" particle as part of a virtual pair. The part of the pair with "negative energy" from the POV outside the EH/Ergosphere, is the antiparticle that never escapes. EDIT: Clarification: it's also the same particle formulated as the past history of the "escaped" particle. It's very odd.

EDIT: @Naty1: Not to mention that for the HR to be detectable it would need to be a VERY low-mass bh and a COLD universe.
 
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  • #16
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Tunneling from inside to outside the event horizon is equivalent to a particle tunneling outside its own future light cone (i.e tunneling FTL)...I think it's debatable whether this can happen,
I agree..I have never seen that as a description...

seems a particle would represent some positive value of energy regardless of the location or ref frame of any observer.
My post above actually address this, but more can be understood by reading about the Unruh effect. Background DOES appear warmer to an accelerating observer!!!!

(which does seem rather crazy at first...and I don't think this has ever been experimentally verified...)
 
  • #17
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I agree..I have never seen that as a description...



My post above actually address this, but more can be understood by reading about the Unruh effect. Background DOES appear warmer to an accelerating observer!!!!

(which does seem rather crazy at first...and I don't think this has ever been experimentally verified...)
That would be one hell of an experiment! If you ever figure out how to do it... take pictures? :wink:
 
  • #18
Haelfix
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The negative energy is to the infinite observer. In Penrose process, the negative energy is necessary to extract energy from a BH.
This negative energy is non-observable locally, according to Hawking's original paper.
Yes, the positive energy particle escapes off to infnity, whereas the negative energy (relative to infinity) one is trapped on a timelike path , thus taking energy away from the gravitational field and consequently shrinking the hole (technically it is this absorption of negative energy, rather than emmission of quanta that shrinks the hole).

The average wavelength of this emission process is of order the mass of the blackhole, thus its inherently nonlocal as it makes no sense to try to localize the quanta, since the curvature of the hole is roughly the same magnitude as the wavelength of the particle. Here, the concept of a 'particle' is strictly speaking global in nature.

Heurestically we can speak of 'tunneling' but that is somewhat hazy. For one, this is not strictly speaking an instanton process, at least not in the traditional way. People have tried to make the identification, but there are analytic continuation problems that tend to crop up.
 
  • #19
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...And of course all of this leads to The Information Paradox. There is a lot of work yet to be done in this area, and with something as odd on its face as a BH, some odd theories have chances they wouldn't elsewhere.

I maintain that the study of earthbound analogues such as sonic BHs is the key to understanding HR if it eixsts. Beyond that, it's going to be just a theory hovering out there, until an understanding of quantum gravity changes the field.
 
  • #20
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i'm sorry, but i still have no idea what you mean when you say a particle has negative energy relative to infinity. when a spontaneous particle pair is created from the quantum foam, you have a particle and an antiparticle - not a positive energy particle and a negative energy particle.

also, it seems remarkably counterintuitive that when a particle pair is created near the EH of a BH, when they surely must have the same momentum and trajectory, and are exceedingly close together, that somehow, within a ridiculously small amount of time, one gets sucked in, while the other miraculously manages to escape the enormous gravitational field extant near a BH, when it cannot [possibly have enough momentum to do so.

i know all this must just be just so far beyond my poor little brain, but it just makes no rational sense to me whatsoever that hawking radiation can be a real thing.
 
  • #21
JesseM
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i'm sorry, but i still have no idea what you mean when you say a particle has negative energy relative to infinity. when a spontaneous particle pair is created from the quantum foam, you have a particle and an antiparticle - not a positive energy particle and a negative energy particle.

also, it seems remarkably counterintuitive that when a particle pair is created near the EH of a BH, when they surely must have the same momentum and trajectory, and are exceedingly close together, that somehow, within a ridiculously small amount of time, one gets sucked in, while the other miraculously manages to escape the enormous gravitational field extant near a BH, when it cannot [possibly have enough momentum to do so.

i know all this must just be just so far beyond my poor little brain, but it just makes no rational sense to me whatsoever that hawking radiation can be a real thing.
According to physicist John Baez the whole pair creation explanation doesn't really correspond to the actual mathematical derivation of Hawking radiation:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html
 
  • #22
Haelfix
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Yea, the pair creation analogy isn't perfect, simply b/c its not something that is localized. It is wrong to think of a tiny little pair of electron/positron moving a few feet and one getting sucked in and the other escaping away.

A human being in a rocket ship close to the horizon of a blackhole is really *inside* the entire 'quanta' that becomes Hawking radiation to an observer at infinity.

Its really an analogy about the entire blackhole, and a set of Bogoliubov transformations done to the field equations of semiclassical gravity that you have to solve. It is in this sense, that you have negative energy modes that the gravitational field 'absorbs'. It is also intimitely tied to the difficulty in defining a vacuum in quantum field theory in curved space.

The calculations for Hawking radiation are very technical and nontrivial, and it really requires a set of lectures (with background material) before you can even attempt to explain it without handwaving.
 
  • #23
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One of the pieces of this puzzle that has not been discussed in this thread is the view of the infinitely distant stationary observer. While a free falling observer plunges into a black hole and eneters inside the black hole, never even being aware of an event horizon, and while a hovering stationary observer just outside the event horizen is vaporized by thermal radiation, a distant observer sees the free falling event as a never ending plunge...time stops at the horizon and the free falling seems to last infinitely long at the horizon....

So three observers in different frames see entirely different events.

i'm sorry, but i still have no idea what you mean when you say a particle has negative energy relative to infinity. when a spontaneous particle pair is created from the quantum foam, you have a particle and an antiparticle - not a positive energy particle and a negative energy particle.
From the above quote, a distant observer sees (in theory) a positive energy particle...one of a pair of formerely virtual particles, is now real. If the particle pair started from "zero energy", then the particle that disappeared must have negative energy....hence the black hole "shrinks" a tiny quantum.

These ideas are described in great detail in Leonard Susskind's THE BLACK HOLE WAR,2008 which is a fascinating read for a conceptual [non mathematical] treatment of Susskind vs Hawking's views on black holes....
 
  • #24
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inre:
"The calculations for Hawking radiation are very technical and nontrivial, and it really requires a set of lectures (with background material) before you can even attempt to explain it without handwaving. "

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

i am reminded of my attempts to read "the nature of space and time" by hawking and penrose. while i did not have any particular trouble reading the penrose portions of that book, i simply could not follow ANYTHING hawking wrote - it all sounded like gibberish to my "unedumacated" mind.
 
  • #25
JesseM
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feynman once said that if you cannot explain something to a layperson in terms they can understand, then you really do not understand it yourself...
Are you sure he said something like that? Don't see any quote like that on his wikiquote page. The page does mention that he said "If I could explain it to the average person, I wouldn't have been worth the Nobel Prize", though, which seems to have something of the opposite meaning. And I'd definitely recommend taking a look at this video where he talks about how difficult it is to explain "why" some physical fact is true to a layperson without knowing exactly what they want explained and what assumptions they take for granted, saying at 3:56 "when you ask, for example, why two magnets repel, there are many different levels, it depends on whether you're a student of physics, or an ordinary person who doesn't know anything or not, if you're someone who doesn't know anything at all about it, all I can say is that there's a magnetic force that makes them repel, and that you're feeling that force." And at 5:55 he says "at an early level I have just got to have to tell you that's gonna be one of the things you'll just have to take as an element in the world, the existence of magnetic repulsion, or electrical attraction and magnetic attraction. I can't explain that attraction in terms of anything else that's familiar to you. For example, if we said 'the magnets attract like as if they were connected by rubber bands', I would be cheating you, because they're not connected by rubber bands--I'd soon be in trouble, you'd soon ask me about the nature of the bands--and secondly, if we were curious enough you'd ask me why rubber bands tend to pull back together again and I would end up explaining that in terms of electrical forces, which are the very things I'm trying to use the rubber bands to explain, so I have cheated very badly you see. So I'm not going to be able to give you an answer to why magnets attract each other, except to tell you that they do, and to tell you that that's one of the elements in the world of the different kinds of forces, there are electrical forces, magnetic forces, gravitational forces, and others, and those are some of the parts. If you were a student I could go further, I could tell you that the magnetic forces are related to the electrical forces very intimately, that our relationship between the gravity forces and the electrical forces remains unknown, and so on. But I really can't do a good job--any job--of explaining the magnetic force in terms of something else that you're more familiar with, because I don't understand it in terms of anything else that you're more familiar with."

He also said (another quote from wikiquote) "I think I can safely say that nobody understands quantum mechanics"...obviously that didn't stop him from basing his career around work in QM, and it didn't cause him to doubt the predictions of QM!

The closest I can think of to a quote from him about the need for simple explanations is this one from 4-3 of Volume III of the Feynman Lectures on Physics where he talks about particle statistics:
This brings up an interesting question: Why is it that particles with half-integral spin are Fermi particles whose amplitudes add with the minus sign, whereas particles with integral spin are Bose particles whose amplitudes add with the positive sign? We apologize for the fact that we cannot give you an elementary explanation. An explanation has been worked out by Pauli from complicated arguments of quantum field theory and relativity. He has shown that the two must necessarily go together, but we have not been able to find a way of reproducing his arguments on an elementary level. It appears to be one of the few places in physics where there is a rule which can be stated very simply, but for which no one has found a simple and easy explanation. The explanation is deep down in relativistic quantum mechanics. This probably means that we do not have a complete understanding of the fundamental principle involved. For the moment, you will just have to take it as one of the rules of the world.
Still, here he is not talking about a "simple and easy explanation" in layman's terms using some kind of analogy to everyday life, but just an explanation in terms of physical axioms that could be understood by an undergraduate physics student.
 

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