Hawkings Theory

OK & thanks. I would (and did) assume that the emission rate would increase, just on he crude popular idea about vacuum polarization and more time for one member to get sucked inside EH by the gradient, but I do not see the connection to temperature, except by "working backward" from this increase in emission. (If radiating more, must be hotter logic.)

You appear to be working /using the "forward logic": (Bigger H-bar, => hotter so radiation increases.) can you suggest why it is hotter, without my "backwards logic." i.e. justify the "forward logic" you seem to be using.

 

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Sure. BH temperature is defined this way: T = h-bar.c^3/8Pi.k.G.M. If h-bar increases, then T increases.

 

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Thanks again. Surely "k" is Boltzman's as if pulled to left side we have kT, an energy. I assume G is Universal gravity constant and M is BH mass. Thus, doubling the mass cuts temp in half. I forget how EH radius goes with mass (Perhaps linear in mass? So to illustrate, I will assume linear and then EH surface it proportional to M^2). Now making use of the T^4 law, I then get the total radiation is proportional to M^2/M^4 or M^-2, which is at least in the correct direction as I know that big BH radiate less. (they also live longer because they have greater mass to lose, but one must integrate the changing radiative loss down to zero M to get how long they live as function of initial mass.)

If you care to, using the total initial mass energy of Mc^2 and either the above (or correct verion if EH radius is not linear in the math) please educate us. (I you do, I will try to remember how this goes for at least a month.)

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PS if you do, it might be nice to stop integration at M/2 remaining also I am courious if the time to lose half the mass is always N times longer than to lose the last half or is N(Mi) where Mi is the inital M at t=0.

 

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"Physicists at Penn State have provided a mechanism by which information can be recovered from black holes, those regions of space where gravity is so strong that, according to Einstein's theory of general relativity, not even light can escape. The team's findings pave the way toward ending a decades-long debate sparked by renowned physicist Steven Hawking."

Read more

 

What a crock. They used a 2-dimensional mathematical model, and assume it will apply to 4-dimensional space-time. They are now seeking additional funding for their 'research'.

A simpler explanation to the paradox, of course, is that black holes don't evaporate, and information that falls into them remains trapped forever.

 

Yes, that would solve the problem,
except that Hawking radiation appears as a natural consequence of quantum mechanics.
(An even bigger problem would be to show how it couldn't work).

So, if we accept that hawking radiation is real, and does happen, then we are left with the problem (which has already been solved) of the destruction of `information`.
ie BH evaporates, but where has the information gone?

(Answer - It has been scrambled in the `featureless radiation`)

 

I thought it came from the complex math of General Relativity, not QM, but I could be wrong as do not understand GR at all. Why do you say it comes from QM? Links preferred, but if you have none, your reasons. Thanks.

 

Blobrana:

Not everyone would agree that "Hawking Radiation" naturally follows from the established laws of physics:

"Yet this prediction [of "Hawking Radiation"] rests on two dubious assumptions ... [there is] no compelling theoretical case for or against radiation by black holes" 2003 Adam Helfer
http://www.arxiv.org/abs/gr-qc/0304042

and

"However, we have also demonstrated counterexamples, which do not appear to be unphysical or artificial, displaying deviations from Hawking’s result. Therefore, whether real black holes emit Hawking radiation or not remains an open question and gives non-trivial information about Planckian physics."
http://arxiv.org/PS_cache/gr-qc/pdf/0408/0408009v2.pdf Ralph Schutzhold.

BillyT:

Hope this answers your question, too.

Regards,


Walter

 

Here's one more:

Prof. V. A. Belinski: Physics Letters A 209 (1995) 13-20, National Institute for Nuclear Physics (INFN) and International Center for Relatiuisric Astrophysics (ICRA), Rome University “La Sapienza”, Rome 00185, Iraly; Received 1 September 1995; accepted for publication:

On the existence of quantum evaporation of a black hole.


"A conjecture is made that the standard derivation of the black hole evaporation effect which uses infinite frequency wave modes is inadequate to describe black hole physics. The proposed resolution is that the problem is not due to the absence of the as yet unknown 'correct' derivation but rather that the effect does not exist."
...

"no permanent evaporation process can exist."

 

Hum,
it can be regarded as being both,
but, the process is essentially a quantum particle-antiparticle process that occurs at an event horizon.

http://en.wikipedia.org/wiki/Hawking_radiation

 

Hum,
yes i would partly agree; which is why the hawking calculations cannot be taken as a proof of BH radiation.
Yes, it could supposed that the laws of physics do not hold at high energy scales at the event horizon, or you could simply introduce some new particle or quantum process - but as i mentioned earlier, it is very difficult to formulate a convincing tweak of the laws to stop such radiation.
Given what we know, Hawkings calculations appear to work. Future observations or LHC experiments may confirm them.

 

In your Wiki link you find:
"... thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. ..."
Thus I understand why you made your statement, but as is often the case, Wiki, IMHO, does not have things quite correct.

Probably, because it is not really possible to be correct in words (instead of the GR math). This is quite obvious in that there are two, mutually contradictory, ways to explain in words Hawking Radiation. (Wiki manages to contradict itself in the single phrase I quoted above. I.e. "thermal radiation" is a classical, not "quantum effect")*

Some word descriptions imagine that photons ("thermal radiation”) remove mass for the BH.
Others imagine that the vacuum polarization (usually electron/position appearing from nothing but for such short time that this is allowed by the QM uncertainty product of Delta E times Delta T). Then if these oppositely charged particles happen to be very close to the EH, one may be captured by the intense gravity gradient near the EH and the other not so it is new energy of long duration in our universe, and that energy must (not well explained in words how) come from the mass of the BH. This is definitely a QM POV.
(Note that as gravity gradients are inverse cube but the field is only inverse square, the gradient at the EH of a small BH is much greater than a large BH's gradient at its EH. - Why the small BHs evaporate more rapidly in this "vacuum polarization POV." - I.e. the stronger gradient is more likely to pull one of the pair inside the EH if BH is small.)

If I were to try to summarize in words, I would say that the prediction of Hawking's radiation is "permitted" by the QM uncertainty but not caused by QM. It is caused by the (math as done by Hawking - hope he is correct, given that the LHC may make one, which is not moving fast wrt Earth as all those made by cosmic rays are**) the nature of space time as described by GR.

----------------
*The "QM part" of thermal radiation is the distribution of it vs. wavelength, not the existence of it. I.e. Planck was the first to explain that distribution with the then "crazy" idea that not all wavelengths were possible as energy levels only exist in quantized levels. The classical "equal partition of energy" distribution suggested that the short wavelengths (for example the UV) should have the same energy as the long wavelengths, but in fact from thermal material sources there is no UV. This was in an era when Physic was getting boring as there was nothing more to do or discover - everything was known, except for this "UV catastrophe" of the classical theory, as it was called back then. (No I am old, but this was before my time too.)

**For some time, I dismissed the danger of a BH made by the LHC based on the fact that much more energetic collisions occur high in the atmosphere many times each hour and Earth is still here; however, now I think there may be danger of an LHC's BH eating Earth, and doing so in much shorter time than others have suggested because they IMHO falsely focus on the BH's tiny size and gravitation. - In contrast, I note that even if it had no gravity, only the power to make matter that entered inside a small sphere cease to exist (by magic) then the huge pressure deep in the Earth would constantly deliver by "plastic flow" matter to and thru that small sphere's surface. So in about the time it takes for matter to fall into the center of Earth's mass point, or wherever that small "matter vanishing sphere" is, the Earth might disappear, even under the quite optimistic assumption that the small BH has NO gravitational attraction power even when it has grown to have the mass of the Earth!

 

BillyT:

There are two ways I've seen of explaining "Hawking Radiation" by verbal description alone, which I will repeat at the risk of appearing overly simplistic, since I believe they both point up the fact that "Hawking Radiation" does not necessarily flow from established physics.

In the first, most usually given explanation, 'virtual particle pairs' along the lines of PAM Dirac's "Dirac Sea" can pop into existence very near to the 'event horizon', existing for a fleeting moment of time following the standard uncertainty principle [as you referenced; (deltaE)X(deltaT)<h/pi].

Thereafter, one of the two particles [either the particle, or its anti-particle opposite; e.g. electron or positron] would 'fall in' to the blackhole, allowing the other particle to wander away. The particle that wandered away [either particle or antiparticle] would be seen by an outside observer as "Hawking Radiation", making it appear as if the blackhole were emitting radiation. Thus, in order to conserve mass [which conservation law Hawking seeks to follow], the particle that falls into the blackhole is required to have a "negative mass" [described by Frank Wilczek in an article he wrote describing Hawking's idea as "freely propagating negative energy states"], thereby reducing the mass of the blackhole, preserving the law of conservation of mass/energy.

The problem I have with this explanation is that the concept of "negative mass" is as foreign to physics as "negative speed" or "north of the north pole". While it works on paper as a nice mathematical crutch to preserve the law of conservation of mass/energy, I don't believe there is any actual basis to allow such; only in abstract theory which therefore might be wrong [as shown by Helfer, et al. discussed above].

The other explanation given is that mass from the interior of the black-hole is able to "quantum tunnel" outside of the event horizon. As we know, quantum tunneling is a real phenomena that has been well detailed. IBM even invented a "quantum tunneling microscope" that can detect distances well less than an Angstrom, using electrons that "tunnel" across a gap. It generally is described by the wave-function of a particle that is bound within a 'well' as having standing waves inside the well [the 'particle'], with the waves 'leaking' beyond the boundary to infinity, though with rapidly diminishing amplitude the greater the distance from the boundary.

Under this alternative explanation, the mass of the blackhole would continue to have particles in the interior with their wave-functions extending beyond the 'event horizon', and occasionally one of the particles would 'teleport' outside the event horizon [its standing wave appearing on the real-world side of the event-horizon, again following uncertainty principles] and wander away, which we would then see as "Hawking Radiation".

Again, I have a problem with this explanation, as it directly contradicts the definition of the 'event horizon' under classical relativity. It could well be that once the 'boundary' of the particle falls within the event horizon [and its mass added to the blackhole mass] then the wave function that otherwise extends to infinity can now only extend to the interior edge of the event horizon, and not beyond, as would be implied by the definition of the event horizon.

That is, of course, the intriguing nature of Hawking's idea. How do we compute quantum effects in conjunction with relativity.

In any event, for safety reasons, I would have to take the position that unless "Hawking Radiation" were proven to be a real phenomena by direct observation, that it is at least as unlikely to be true as to be false. I believe the authors cited above all reached the same conclusion by varying methods.

I hope I've not given too short of an explanation of these two verbal descriptions of "Hawking Radiation", and how it appears to contradict known physics.

Regards,


Walter

 

Yes,
This is a problematic point.
It is worth outlining that we are dealing with virtual particle - and more importantly virtual photons. And our current understanding is that photons are their own antiparticle. And in an Einstein universe it is permissible (or even require) for negative mass energy to be created during the creation of photon-antiphoton pair production.
But perhaps we should just regard virtual particles as a mathematical trick to get the sums to balance; similar to the particle/wave duality model of photons - which is a meaningless concept in our macro world.
Either way, the physics on paper works out.

 

Hi Walter. A few comments on your post:

I prefer what I said about how the mass escapes from the BH. Namely is not well explained in words.

I definitely do not like the idea that the electrons (or positrons) have "negative mass" because if that were true Then there should be two types of electrons now (the + and the _ mass ones).

Thus, one of your arguments for the possibility that Hawking Radiation is not real is built on an obviously false base.

The idea that mass can materialize outside of the EH because the mass-less wave function may extend outside of the EH is more reasonable to me. In fact I made this same argument when I suggested that as the tiny (compared to atom size) LHC made HB traveled thru atoms it would find that there was some of the bound electron's wave function inside of the EH as it passed thru the space in which (in words) the electron is "everywhere and no where" along its QM permitted "orbital."

You say you do not like this mechanism for explaining the mass loss because (and I quote you):
"... contradicts the definition of the 'event horizon' under classical relativity ..."

I can agree with that, but with a different "twist" than you have on it. I.e. I do not think that "classical relativity" is a valid idea, so I do not mind contradicting it if that is the case here. I take this POV not because I can do the GR math well enough to show that "classical relativity" is inconsistent with correctly (by current standard of Hawking et. al. who can do the math) done GR. I take this POV because Hawking et.al. have done the GR math (correctly I assume) and they have come to the conclusion that BHs, especially the small ones, do radiate. I.e. in my POV what is wrong, is what you are calling "classical relativity," not the contradiction of it. Contradicting it is instead the correct thing to do.

SUMMARY 1:
IMVHO (the extra "V" is for "very") neither of the foundations for you stated doubt of Hawking Radiation is valid. - They are more like “false straw men” set up (unintentionally) to be knocked down. HOWEVER, this does not mean I firmly believe that Hawking Radiation is real.

I do believe that it follows from the current math of GR, but I am not firmly convinced that description, especially with no way to "correct" the classical conclusion that very dense objects must form point singularities. I.e. I suspect that someday a better understanding will emerge that brings in some currently unknown physics that blocks the formation of point singularities with infinite density. This does not necessarily (in fact probably does not IMHO) mean that Black holes with EHs do not exist. It simply means that the current understanding of these BHs and their EHs is not exactly correct. (Sort of like Newtonian gravity physics was not exactly correct) Thus, I believe, that Hawking Radiation is real consequence of the current GR, but that GR may not be a perfect description of reality. If an improved GR is developed, it may or may not predict Hawking Radiation.

SUMMARY 2:
On the important "bottom line" we agree that it is possible that Hawking Radiation does not exist, and that this possibility does give cause for concern about the LHC if the LHC can produce a tiny BH that is not moving at near the speed of light in the Earth's frame.

Where we differ is I think this frightening possibility is opened up by the possibility that the current GR is not exactly correct. You seem, by your posted statements at least, to think that this “frightening possibility is opened up“ because both the "negative mass" and the "tunneling" ideas (in words) are wrong so there is no valid explanation of how the mass could evaporate away. Hence, in your POV, Hawking radiation probably does not exist and consequently your are more scared than me of the LHC.

PS I am old and falling into the “Earth eating BH” seems like a relatively quick, interesting way to die, with little (or at least brief, compared to weeks with cancer etc.) pain. As they say: ”Bring it on!”

My generation has “f - - - ed the youth economically, used up all the cheap energy, etc. so this is really a kindness on our part to keep them from a long life of suffering etc.

 

“A virtual particle is one that does not precisely obey the m2c4 = E2 − p2c2 relationship for a short time. In other words, their kinetic energy may not have the usual relationship to velocity, indeed, it can be negative.”

http://en.wikipedia.org/wiki/Virtual_particle

 

Nothing wrong with this post but do not confuse the "virtual particles" that modern physics imagines are the solution to the "action at a distance" problem - I.e. the particles that are exchanged between the sources of various forces with the real, but briefly existing particle of the vacuum polarization. Those polarization pair particles normally mutually annihilate within the time allowed by the uncertainty principle for them to exist. 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 - perhaps even one that Milliken watched when measuring the charge of the electron and found it was not a variable amount or now one that is in you orbiting around a carbon nucleus, etc.

Another difference is that "virtual particles" do not of necessity come only in pairs as do the vacuum polarization particles. I think you are not clear on this difference. The one of the verbal explanations of how a BH loses mass is that it is carried away when one, and only one, of the vacuum polarization pair escapes to “live forever” in our universe. This has nothing to do with “virtual particles.”

 

You mean something like Quantum entanglement?

http://en.wikipedia.org/wiki/Action_at_a_distance_(physics)

This is wrong.
The process is not a electron / positron etc type process.
Hawkings radiation is essentially from a photon-antiphoton nonannihilate effect.

http://en.wikipedia.org/wiki/Vacuum_polarization

Could be. i`m not too clear about the difference.

Hum,
point taken,
But the term "virtual particles" is correct.

 

No. "action at a distance" is an old mystery, much older than quantum entanglement, or even quantum mechanics. Newton worried about it and he was far from the first.

Humans understand how the wind make tha sail boat go - they can feel the wind. How the horse pulls the wagon by pushing on the colar around its neck etc. - every thing that has a direct link is compatible with human direct experience, but not well when no direct link exists.

I.e. how one magnet moves a piece of iron with no connection between them or static electricity picks up pieces of papar, etc. - that is the fundamental mystery that the invention of "fields" swept under the rung but did not really explain. Modern physics does a little better with the idea that there is actually something going back and forth between the objects but still it is not very satisfying to say they are "exchanging virtual particles."

Quantum entanglement is a recent mystery. Two particles (photons included) can be very distant, but in some way humans can not understand are really one system that has some things with total fixed value. If you force one to be 3 the other will be 7 immediately even is light years distant if the total of the system is 10. etc. to make an annology.

Physics has explored regions that man has no direct experience with and it turns out in many cases that extrapolation from his limited experience gives non real results. I.e. Nature ain't like it "ought to be" from human POV.

You will need to tell me what you think I stated incorrectly instead of just "This is wrong." Your wiki link does not contradict any of my statement. It only tells some as to why Vacuum polarization exist and I DID NOT COMMENT ON THAT.

 

tnx for the clarification.

Here is a quote/link for others.

“Most physicists today believe that quantum mechanics is correct, and that the EPR paradox is only a "paradox" because classical intuitions do not correspond to physical reality.”

http://en.wikipedia.org/wiki/EPR_Paradox

No worries,
as i said,
The process is not a electron / positron etc type process.
Hawkings radiation is essentially from a photon-antiphoton nonannihilate effect.

The Hawking radiation is basically a statistical result; So while one pair of virtual electron/positrons, in which one is emitted and one swallowed by the BH may work:
in reality there are many such events; and the total amount emitted is exactly in a 50/50 ratio so there is no overall mass loss.
Ie, we will see no Hawking radiation if we were to just use virtual electron/positrons. We have to use virtual photons.
(mentioned in post 3)

http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/011125b.html
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html