According to Stephen Hawking himself, an inspiration came to him before going to bed one evening in 1970 (getting into bed is a rather slow process with his disability). He suddenly realized that since nothing can escape from a black hole, the area of the event horizon might stay the same or increase with time but it could never decrease. In fact, the area would increase whenever matter or radiation fell into the black hole. This non-decreasing behavior of a black hole's area was very reminiscent to that of entropy, which measures the degree of disorder in a system. One can create order out of disorder, but that requires expenditure of effort or energy such that there is an overall increase in disorder.
In simple mathematical terms these statements can be expressed in differential forms as:
m dm = k dA ---------- (16a) for the black hole (since A rs2 m2 from the Schwarzschild's solution),where m is the mass of the black hole, A is the area of the event horizon, and k is a proportional constant;
dE = T dS ---------- (16b) for the entropy,
where E is the energy, T is the temperature, and S is the entropy.
Since mass and energy are equivalent, we can equate Eqs.(16a) and (16b) to obtain:
dS = K dA / ( m T ) ---------- (16c) where K is a new proportional constant. This equation implies that the area of the event horizon A is a measure of the entropy S of the black hole. Furthermore, the black hole is associated with a temperature T, and should emits radiation as any hot body. Thus, the black hole is not completely closed to the universe outside. It turns out that vacuum fluctuations at the edge of the event horizon may allow one member of the virtual particle / anti-particle pair to fall inside with negative energy; while the other escapes as a real particle with a positive energy according to the law of energy conservation.
This is known as Hawking radiation (see Figure 09u); it is the first successful attempt to combine general relativity and quantum theory. The flow of negative energy (or mass) into the black hole would reduce its mass. As the black hole loses mass, the area of its event horizon gets smaller, but this decrease in the entropy of the black hole is more than compensated for by the entropy of the emitted radiation, so that the second law of thermodynamics is never violated. If we demand that in Eq.(16c) dS dA as stated originally (actually, it can be shown that S = (kBc3/4G) x A), then T 1 / m, and the rate of radiation L can be expressed as L rs2T4 1 / m2. Therefore, as the black hole loses mass, its temperature and rate of emission increase, then it lose mass even more quickly
(Figure 09v). What happens when the mass of the black hole eventually becomes extremely small is not quite clear, but the most reasonable guess is that it would disappear completely in a tremendous final burst of emission.
It can be shown that the temperature T associated with the thermal radiation for a black hole is:
T = 0.6 x 10-7 msun / m (in degrees Kelvin)
where msun is the mass of the Sun. If the Sun is reduced to a black hole, its temperature would be just about 10-7 oK. On the other hand, there might be primordial black holes with a very much smaller mass that were made by the collapse of irregularities in the very early stages of the universe. Those with masses greater 1015 gm could have survived to the present day. They would have the size of a proton (~ 10-13cm) and a temperature of 1011 oK. At this temperature they would emit photons, neutrinos, and gravitons in profusion; they would radiate thermally at an ever increasing rate, and sending out X rays and gamma rays to be discovered. The lifetime of a black hole is roughly equal to = m / L = 10-35 m3 year, where m is in gm. This makes an ordinary mass black hole (m ~ 2x1033 gm for the Sun) live for a long time and its radiation unobservable.
This phenomenon of Hawking radiation also occurs in the event horizon created by an accelerating observer. Figure 09w shows that light ray emitted at certain distance can never catch up with the observer and thus an event horizon exists beyond which the observer cannot communicate. Theoretical arguement suggests that even in empty space, the observer will be able to detect radiation from the event horizon. A simple formula is derived to express the relationship between the acceleration a and the temperature T: T = a (/2kBc). It is suggested that members of the correlated virtual photon pairs are separated by the event horizon. As a result part of the information is missing, the observer detects random motion associated with the temperature. In this case the energy is extracted from the acceleration, which according to general relativity, is equivalent to gravitation.
Black hole and information:
According to general relativity anything that crosses the event horizon is trapped inside forever lost to the outside world.
In spite of his own discovery of Hawking radiation, which can return matter-energy back to the outside world, Hawking himself insists that information would be destroyed by the black hole.
Since entropy is related to information, the loss of information would violate the second law of thermodynamics, which holds that entropy would neither decrease nor disappear. Thus, the critics argue that nature may scramble information but never destroys it.
To resolve the dispute,
't Hooft and Susskind proposed the "Principle of Black Hole Complementarity" in which both sides are correct. For the outside observer, matter
(the elephant in Figure 09x) would be reduced to thermal radiation at the event horizon (as it takes an infinite time for the elephant to cross such boundary according to observer a) and returns as scrambled information. For an observer crosses the event horizon into the black hole, nothing untoward happens until the tidal force takes over ... information is forever lost.
Such duality is further likened to a hologram located on some surface. There are two possible ways to interpret the hologram: one view corresponds to that for the outside observer a in Figure 09x; while the other represents the perception from observer b falling into the black hole. Meanwhile, other research in superstring theory finds the black hole to be a "fuzzball"
(Figure 09y). The modified black hole does not possess a sharp event horizon; information can be stored in the strings and imprinted on outgoing Hawking radiation. Models of black holes from superstring theory also cast doubt on the idea of the singularity (at the center of the black hole). Yet another scheme suggests that information might leak out by means of quantum teleportation between the entangled pair of virtual particles (one of which has escaped while the other is trapped inside the black hole). However in the theory of loop quantum gravity, it has been shown that the information trapped in a black hole will be unable to escape via Hawking radiation. But it will survive, eventually rejoining the rest of the universe when the black hole evaporates.
I've "highlighted" certain parts from the post quoted to make things a bit easier.
Equations? Ok, I see them.
Figures? I don't see any "fuzz-balls" or "elephants." I don't even see any pink tutus.
Could HawkingBrain truly be this good of a writer?--
No! Well Mr. Brain, it seems you've plagiarized once again.
...check this link out:
http://universe-review.ca/R15-17-relativity.htmPS:
AN, as a San Diego (which is a nice 30~45min drive from Tijuana, Mexico) native,
I'd like to give you a kind reminder to not drink the water down there-- that is, unless it's bottled.
Trippy
21st December 2007 - 02:29 PM
QUOTE (AlphaNumeric+Dec 21 2007, 09:41 PM)
Your failure to understand things you claim to know is no fault of mine. Quantum mechanical processes are non-classical. Relativity is classical. The combination of the two (as Hawking radiation is) is semi-classical.
Let's see if I (a none physicist) have grasped this correctly (no, I'm not afraid of ambarresing myself by getting it wrong in public).
Relativity is classical because it regards space-time as being continuous, and fields as being continuous, whereas QM is non-classical because it regards space-time as being discrete and quantized, and fields as being discrete and quantized. And this is the basic source of all the problems of trying to unify them (well, general relativity and QM at least).
ubavontuba
21st December 2007 - 06:19 PM
QUOTE (AlphaNumeric+Dec 21 2007, 08:41 AM)
Your failure to understand things you claim to know is no fault of mine. Quantum mechanical processes are non-classical. Relativity is classical. The combination of the two (as Hawking radiation is) is semi-classical.
Grasp that?
Trying to dodge and weave, are we? You described it both in the classical
Newtonian sense and QFT,
without regards to General Relativity. You even compared it to electromagnetism!
Grasp
that?
QUOTE
You mentioned me talking over his head. I pointed out that all topics I'd mentioned were brought up by him. If he doesn't want to talk about quantum mechanics and relativity, he shouldn't bring them up.
Instead of trying to dazzle him with your stupendousness, have you thought to answer as simply and earnestly as you can, and then move on? Does it really matter whether he gets it? Are you forgetting the other readers?
QUOTE (->
| QUOTE |
| You mentioned me talking over his head. I pointed out that all topics I'd mentioned were brought up by him. If he doesn't want to talk about quantum mechanics and relativity, he shouldn't bring them up. |
Instead of trying to dazzle him with your stupendousness, have you thought to answer as simply and earnestly as you can, and then move on? Does it really matter whether he gets it? Are you forgetting the other readers?
Besides, I'm not talking about very complex things, on the scale of it. I'm talking on a level which any graduate student should understand. Anyone who has got far enough through a physics course to have been lectured Hawking radiation will follow me.
What makes you think he's gone that far?
QUOTE
Just because you don't doesn't mean I'm talking over people's heads deliberately. It's just your head is so low it's easy to talk over yours.
Watch it with the short jokes! (sarcasm)
QUOTE (->
| QUOTE |
| Just because you don't doesn't mean I'm talking over people's heads deliberately. It's just your head is so low it's easy to talk over yours. |
Watch it with the short jokes! (sarcasm)
That the best you've got? Your usual fallback onto "OMG, u r a ch@tbot!!"
It's no worse than your stupid smilies and deflection. Argue the relevant points, or don't argue at all.
QUOTE
I pointed to a speciic case in that very post. I didn't even have to leave the thread!
You mean the one where you were blatantly wrong? The one where you insisted gravity is both properly described in the Newtonian and QFT sense in General Relativity? Give me a break!
QUOTE (->
| QUOTE |
| I pointed to a speciic case in that very post. I didn't even have to leave the thread! |
You mean the one where you were blatantly wrong? The one where you insisted gravity is both properly described in the Newtonian and QFT sense in General Relativity? Give me a break!
And your list of my 'errors' is nothing more than a list of things students understand about relativity and quantum mechanics...
So your point is that you didn't understand them when you should have?
QUOTE
...that you don't.
Remember, it was you that was wrong, not me. Seems kind of silly to say the one that was right didn't understand, while the one that was wrong did... doesn't it?
QUOTE (->
Remember, it was you that was wrong, not me. Seems kind of silly to say the one that was right didn't understand, while the one that was wrong did... doesn't it?
The fact you don't believe the personal webpage of one of the best known theoretical physicists in the world is no fault of mine. You consider them 'questionable' because you don't understand them. You offered no reason other than "I don't believe that". What am I supposed to refute about that? I don't refute the fact you don't believe them, I don't consider you intelligent enough to gasp them.
A blatant lie. I offered a list of specific reasons that reference was questionable. Have you forgotten already? I even asked you to explain the apparent discrepencies I noted. You then tried to back it up with that stupid blog reference about QFT gravity, ignoring all the other discrepencies I noted!
QUOTE
The one which you then argued against because you considered the equivalence principle not something physicists should be resting on?
Where'd you get that? I never said any such thing. I argued for the paper I mentioned. Trying to spread false information, are we?
QUOTE (->
| QUOTE |
| The one which you then argued against because you considered the equivalence principle not something physicists should be resting on? |
Where'd you get that? I never said any such thing. I argued for the paper I mentioned. Trying to spread false information, are we?
No, a real physist uses logic, evidence and rationality. That's why you're not a physicist.
Then apparently you're not either. How could you be appling "logic, evidence and rationality," when you've been wrong so often?
QUOTE
Do you think you take the 'high ground' be constantly having to fall back on "You're a chat bot".
No more than you turning every argument into a personality debate, rather than keeping the discussion relevant to the topic.
QUOTE (->
| QUOTE |
| Do you think you take the 'high ground' be constantly having to fall back on "You're a chat bot". |
No more than you turning every argument into a personality debate, rather than keeping the discussion relevant to the topic.
My feedback demonstrates people consider my comments and posts interesting and useful.
Or, their gullibility. Or, manipulation.
QUOTE
The discussions I have with people demonstrate my ability to converse. Threads like [url=http://forum.physorg.com/index.php?showtopic=19278
this one[/url] show the level of mathematics I actually work at. Notice the lack of cranks in that thread. You're all scared away by real science discussion. What's the matter, a 'chat bot' having a discussion too scary for you?
Ooh. More irrelevance. What's the matter, too embarrassed to keep to the discussion at hand? Can't handle being wrong? Feel the need to retreat to a place you feel safe?
If you can't describe physics by simply stating what happens given certain conditions, you can't describe physics!
QUOTE (->
| QUOTE |
The discussions I have with people demonstrate my ability to converse. Threads like [url=http://forum.physorg.com/index.php?showtopic=19278 this one[/url] show the level of mathematics I actually work at. Notice the lack of cranks in that thread. You're all scared away by real science discussion. What's the matter, a 'chat bot' having a discussion too scary for you? |
Ooh. More irrelevance. What's the matter, too embarrassed to keep to the discussion at hand? Can't handle being wrong? Feel the need to retreat to a place you feel safe?
If you can't describe physics by simply stating what happens given certain conditions, you can't describe physics!
What does 'x' represent in the geodesic equation? Here's a clue to help you Google, 'test mass'.
More irrelevance. Why, after I've been right so often (and you not), would you continue to try and test me?
Do you now know that gravity is curved spacetime in GR?
ubavontuba
22nd December 2007 - 04:31 AM
QUOTE (Trippy+Dec 21 2007, 07:10 AM)
I've often thought something similar.
Okay, you guys got me. I am a fat guy, and I do like polka. Don't forget the beer!
Sapo
22nd December 2007 - 04:40 AM
Or the nuts, either.
BigDumbWeirdo
22nd December 2007 - 07:54 AM
QUOTE (ubavontuba+Dec 21 2007, 12:06 AM)
Self importance (a.k.a. puffery) is wholly unattractive.
Well, first AN would have to display some puffery. Instead, he seems to often display a lack of patience with people who claim to understand physics but really don't, and you seem to interpret that as "puffery."
QUOTE
Don't hero worship this weasel. He knows a lot less than he pretends.
My hero worship is reserved for people of heroic deeds, not people of shocking intelligence and incredible knowledge. He knows a lot more than he talks about here, I can promise you that. Hell, even I know a lot more than I talk about here, AN damn sure has more knowledge in reserve than I do.
QUOTE (->
| QUOTE |
| Don't hero worship this weasel. He knows a lot less than he pretends. |
My hero worship is reserved for people of heroic deeds, not people of shocking intelligence and incredible knowledge. He knows a lot more than he talks about here, I can promise you that. Hell, even I know a lot more than I talk about here, AN damn sure has more knowledge in reserve than I do.
Which matters because...?
He knows what he's talking about.
QUOTE
AlphaNumeric was contending it was a force properly described in QFT. It isn't.
Well, for starters, I don't see him making that claim anywhere in this thread. Second, why don't you provide some evidence to support your claim that it's not?
QUOTE (->
| QUOTE |
| AlphaNumeric was contending it was a force properly described in QFT. It isn't. |
Well, for starters, I don't see him making that claim anywhere in this thread. Second, why don't you provide some evidence to support your claim that it's not?
All valid questions.
Illogical, tautological questions are somehow valid in your little world? Wow, it must be easy to win a debate: Just ask a few meaningless questions and let your opponent's inability to answer them speak for itself, as long as your opponent doesn't get wise to you and give meaningless answers. Such as those I detailed before. (Actually, the last one has a meaning. I wonder if you can figure it out?)
QUOTE
Why not? Why answer at all then?
You can figure out what my point is, but not see it... How bizarre....
QUOTE (->
| QUOTE |
| Why not? Why answer at all then? |
You can figure out what my point is, but not see it... How bizarre....
He doesn't seem to be objecting to my answer.
Yes, when I get annoyed I ignore the annoying people, too.
QUOTE
I didn't condemn him. I certainly didn't berate him in the crude and derogatory fashion that you so often use. I was merely expressing my personal disappointment.
Aww, you've hurt my feelings

Well, not really. I don't really give a crap. To be honest, I'm a little amused, if anything.

QUOTE (->
| QUOTE |
| I didn't condemn him. I certainly didn't berate him in the crude and derogatory fashion that you so often use. I was merely expressing my personal disappointment. |
Aww, you've hurt my feelings

Well, not really. I don't really give a crap. To be honest, I'm a little amused, if anything.

Or the nuts, either.
Oh, I think we'll do just fine without any more nuts that we already have.
ubavontuba
22nd December 2007 - 08:12 AM
QUOTE (BigDumbWeirdo+Dec 22 2007, 07:54 AM)
Well, first AN would have to display some puffery. Instead, he seems to often display a lack of patience with people who claim to understand physics but really don't, and you seem to interpret that as "puffery."
My hero worship is reserved for people of heroic deeds, not people of shocking intelligence and incredible knowledge. He knows a lot more than he talks about here, I can promise you that. Hell, even I know a lot more than I talk about here, AN damn sure has more knowledge in reserve than I do.
He knows what he's talking about.
Well, for starters, I don't see him making that claim anywhere in this thread. Second, why don't you provide some evidence to support your claim that it's not?
Illogical, tautological questions are somehow valid in your little world? Wow, it must be easy to win a debate: Just ask a few meaningless questions and let your opponent's inability to answer them speak for itself, as long as your opponent doesn't get wise to you and give meaningless answers. Such as those I detailed before. (Actually, the last one has a meaning. I wonder if you can figure it out?)
You can figure out what my point is, but not see it... How bizarre....
Yes, when I get annoyed I ignore the annoying people, too.
Aww, you've hurt my feelings Well, not really. I don't really give a crap. To be honest, I'm a little amused, if anything.
QUOTE (Sapo+)
Or the nuts, either.
Oh, I think we'll do just fine without any more nuts that we already have.
Blah-de-blah-de-blah.
Do you have anything relevant to add to the discussion?
More importantly, can you add anything relevant to the discussion?
I doubt it.
AlphaNumeric
24th December 2007 - 09:41 AM
QUOTE (ubavontuba+Dec 21 2007, 07:19 PM)
Trying to dodge and weave, are we? You described it both in the classical
Newtonian sense and QFT,
without regards to General Relativity. You even compared it to electromagnetism!
Grasp
that?
Newtonian gravity : Classical
Maxwell's Electromagnetism : Classical
General and Special Relativity : Classical
Electrodynamics : Classical
Quantum mechanics : Non-classical
Quantum Field theory : Non-classical
Hawking radiation : Semi-classical
QFT is a combination of two classical theories, SR and EM and then
fully quantised in it's dynamical fields. Space-time in QFT is not dynamical.
GR has dynamical space-time but makes no attempt to quantise it.
Putting QFT into a GR background results in some dynamical fields being quantised and some not. Hence, semi-classical.
My previous comments about Newton's and Maxwell's work was entirely consistent. Your ability to understand is not.
QUOTE (ubavontuba+Dec 21 2007, 07:19 PM)
Instead of trying to dazzle him with your stupendousness, have you thought to answer as simply and earnestly as you can, and then move on? Does it really matter whether he gets it? Are you forgetting the other readers?
Previous attempts to engage the original poster in discussion, in numerous threads and via PMs have failed. He has been caught plagerising on more than one occasion and he sees no problem with telling flat out lies. Subtley has been tried. As with you, it failed. Hence I didn't bother in this thread. If I'm blunt in one thread and he stops posting this crap, then it's worth it.
QUOTE (ubavontuba+Dec 21 2007, 07:19 PM)
What makes you think he's gone that far?
If this is his own work, he should have. He has told me, via PM, that he's an Oxford graduate in physics. I know several such people and they are intelligent to know what they know. He's claiming detailed knowledge about Hawking radiation and to be an Oxford physics graduate. If he wasn't lying about the latter, he'd not be lying about the former. However, he is lying about both.
QUOTE (ubavontuba+Dec 21 2007, 07:19 PM)
You mean the one where you were blatantly wrong? The one where you insisted gravity is both properly described in the Newtonian and QFT sense in General Relativity? Give me a break!
Give me a link to a post of mine where I said relativity describes a quantised gravity. I never had. Neither have I said relativity describes gravity in a Newtonian fashion. 'Classical' doesn't mean "In the way Newton did it". Plenty of classical physics came after 1680.
GR is classical. QFT is non-classical. QFT in a GR background is semi-classical.
http://en.wikipedia.org/wiki/Semiclassical"Third, semiclassical gravity is the approximation to the yet unknown theory of quantum gravity in
which one treats matter fields as being quantum and the gravitational field as being classical. The classical Einstein equations are computed with the expectation value of the quantum matter fields in the classical background. Semiclassical gravity has applications in black hole physics and physical cosmology."
http://en.wikipedia.org/wiki/Semiclassical_gravity"The most important applications of semiclassical gravity are to understand the Hawking radiation of black holes "
Your lack of knowledge on a subject doesn't mean your claims built on that ignorance are correct.
QUOTE (ubavontuba+Dec 21 2007, 07:19 PM)
So your point is that you didn't understand them when you should have?
My progress through education has demonstrated I have understood them. Perhaps not as well as I should have, but I've certainly proven a set level of knowledge and understanding.
For instance, I sat
this exam and attained a Distinction in it. Care to have a shot at a few of the questions?
QUOTE (ubavontuba+Dec 21 2007, 07:19 PM)
A blatant lie. I offered a list of specific reasons that reference was questionable. Have you forgotten already? I even asked you to explain the apparent discrepencies I noted. You then tried to back it up with that stupid blog reference about QFT gravity, ignoring all the other discrepencies I noted!
Your reasons amounted to "I don't understand relativity, therefore your link is wrong". The 'blog' was the webpage of the theoretical physicist I mentioned. You do realise that some very clever people have personal websites? Just because it doesn't have a company sticker on it or you haven't heard of their name doesn't mean they aren't right.
http://arxiv.org/find/math/1/au:+Baez_J/0/1/0/all/0/1There's
some of his work. He's well known for this blog precisely because he presents such high level material and understanding in a way which is so accessible.
You offered no actual evidence against the list of experiments and effects my link provided. You just said "I don't agree" but padded it out.
QUOTE (ubavontuba+Dec 21 2007, 07:19 PM)
Where'd you get that? I never said any such thing. I argued for the paper I mentioned. Trying to spread false information, are we?
You questioned how much physicists should use the equivalence principle to link gravity-less systems to gravitational ones. Your evidence also relies on scalar QED, quite different from fermionic QED.
Here is a more indepth roundup of Unruh work in physics. No controversy at all. It is a shown to be a reformulation of free QFT in different coordinate. There's plenty more on ArXiv.
QUOTE (ubavontuba+Dec 21 2007, 07:19 PM)
Then apparently you're not either. How could you be appling "logic, evidence and rationality," when you've been wrong so often?
If your example is because you didn't understand what 'classical' mean