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An easy way to think about the entropy of black holes is to consider that entropy represents the loss of free energy – that is, energy that is available to do work – from a system. Needless to say, anything you throw into a black hole is no longer available to do any work in the wider universe.

An easy way to think about the second law of thermodynamics (which is the one about entropy) is to consider that heat can’t flow from a colder location to a hotter location – it only flows the other way. As a result, any isolated system should eventually achieve a state of thermal equilibrium. Or if you like, the entropy of an isolated system will tend to increase over time – achieving a maximum value when that system achieves thermal equilibrium.

If you express entropy mathematically – it is a calculable value and one that tends to increase over time. In the seventies, Jacob Bekenstein expressed black hole entropy as a problem for physics. No doubt he could explain it much better than I could, but I think the idea is that if you suddenly transfer a system with a known entropy value past the event horizon of a black hole, it becomes immeasurable – as though its entropy vanishes. This represents a violation of the second law of thermodynamics – since the entropy of a system should at best stay constant – or more often increase – it can’t suddenly plummet like that.

So the best way to handle that is to acknowledge that whatever entropy a system possesses is transferred to the black hole when the system goes into it. This is another reason why black holes can be considered to have a very high entropy.

Then we come to the issue of information. The sentence *The quick brown fox jumped over the lazy dog* is a highly engineered system with a low level of entropy – while drawing out 26 tiles from a scrabble set and laying them down however they come delivers an randomly ordered object with a high level of entropy and uncertainty (to the extent that it could be any of a billion possible variations).

Throw your scrabble tiles into a black hole – they will carry with them whatever entropy value they began with – which is likely to increase further within the black hole. Indeed it’s likely that the tiles will not only become more disorganized but actually crushed to bits within the black hole.

Now there is fundamental principle in quantum mechanics which requires that information cannot be destroyed or lost. It’s more about wave functions than about scrabble tiles – but let’s stick with the analogy.

You won’t violate the conservation of information principle by filling a black hole with scrabble tiles. Their information is just transfered to the black hole rather than being lost – and even if the tiles are crushed to bits, the information is still there in some form. This is OK.

But, there is a problem if in a googol or so years, the black hole evaporates via Hawking radiation, which arises from quantum fluctuations at the event horizon and has no apparent causal connection with the contents of the black hole.

A currently favored solution to this problem is the holographic principle – which suggests that whatever enters the black hole leaves an imprint on its event horizon – such that information about the entire contents of the black hole can be derived from just the event horizon ‘surface’ – and any subsequent Hawking radiation is influenced at a quantum level by that information – such that Hawking radiation does succeed in carrying information out of the black hole as the black hole evaporates.

Zhang et al offer another approach of suggesting that Hawking radiation, via quantum tunneling, carries entropy out of the black hole – and since reduced entropy means reduced uncertainty – this represents a nett gain of information drawn out from the black hole. So Hawking radiation carries not only entropy, but also information, out of the black hole.

But is this more or less convincing than the hologram idea? Well, that’s uncertain…

**Further reading:** Zhang et al. An interpretation for the entropy of a black hole.

Black hole entropy is a form of entanglement entropy. In fact I am doing work which involves an isomorphism between black hole types, such as BPS and extremal black holes, and quantum entanglements. These entanglements can be bipartite, tripartite, W states and the GHZ state. An entangled state across the event horizon has some certain entropy, which is a measure of the inability to access states in the entanglement beyond the event horizon. These states as seen from the exterior are holographically tied to the horizon of a black hole, but vastly redshifted so they are not directly accessible.

For two systems A and B in an entanglement the entropy of the system A, say what the exterior observer sees, is S(A) which defines a total entropy

S(A+B) = S(A) + S(B) + S(A|B).

For a bipartite state S(A) = S(B) and for the net system a pure state S(A+B) = 0. Hence the joint entropy S(A|B) is negative. So the observer who find S(A) does so largely because the black hole conceals information.

The quantum evaporation of a black hole maintains S(A+B) = 0. The exterior observer then find their A part of the bipartite entanglement, or EPR pair, has a vanishing entropy, while the joint entropy of A and B becomes larger. This means the exterior observer has an uncertainty up to the end of the black hole evaporation as to exactly what any event associated with A means. The states accessible on the horizon are then quantum destroyed by Hawking radiation (they are cancelled out and converted into this radiation), which is indistinguishable for saying the states were absorbed by the black hole interior. The two sets of events are equivalent, even though they occur in apparently very different epochs in the evolution of the black hole. The notion of an event as a unique or invariant point in space is no longer a general truth about nature.

LC

I thought I had a handle on the article, but, after reading your comment several times, I now have a headache. I am just glad there are people who can get their heads around it all and I will continue to try. Thanks!

I thought I had a handle on it too.

Just delete your article and paste LC’s post. 😀 And don’t forget to give him some money. :d

I’m not an expert, but just by reading the article I could detect some problems, philosophically. For example, if the entropy is immeasurable, then how can it plummet or vanish as a violation of the law? Apparently, it can vanish. A violation would be a decrease of entropy. Then, there is a problem of systems which LC explains nicely. I hope it helps somehow…

Also, I’m not sure if I understand the first paragraph which is funny.

However, Astronomy without a telescope is a pretty great franchise. It pushes my limits. I bet it explodes many brains. 😀

Thanks – the first paragraph offers a way to think of BH’s as possessing high entropy without appealing to quantum mechanics. Loss of free energy is a classical definition of entropy.

LC’s post is too technical for the average reader. this site would not have many readers if the articles were such.

that’s not to say that they are not helpful and appreciated if you’re reading this LC…

@ Postman,

Do not worry, the brane-ache you are experiencing is related to the time invariant form expressed most often by the class of zombie particles, you have heard them often I am sure, “Branes… I want Branes.”

I’ll leave now.

Nerlich’s article is fine, for it covers the basic issue. I extended it some, and I could have mentioned how BPS black hole types connect up with supersymmetry.

In what I wrote the total entropy S(A+B) is constant or zero. What this tells us is that black holes do not destroy information. Black holes conceal information in certain ways, and the quantum evaporation of a black hole recovers that information in a transformed manner. This transformation is a quantum evolution, we might call it unitary or unital, I think it is modular, but the states which emerge by quantum tunneling from a black hole ultimately have all the information of the states which went in.

This of course largely involves quantum black holes, and black holes which are near the string length, or Planck length. The Planck length is a wave length for a black hole when it equals the Schwarzschild radius of the black hole. This is L_p = sqrt {G-hbar/c^3} ~ 10^{-33}cm, which is very small. The Bekenstein entropy is then

S = k*A/(4L_p^2)

Where k = Boltzmann’s constant and A = 4pi r^2 is the area of a black hole horizon. This area is then some integer number of Planck units of area A = NL_p^4. The integer N is then the number of units of area which comprise the black hole and the number of microstates which make it up.

It is also interesting to note that a black hole is never in equilibrium. Consider the thought experiment. Suppose there was a black hole with mass of the moon and about 1mm in radius would have the same thermal horizon temperature as the CMB at 2.7K. This black hole sits in open space and gets radiation from the CMB, and if the BH has the same temperature it emits radiation to the CMB. If the black hole emits a quanta of energy &E = &mc^2 (& = delta) its horizon area and thus entropy decreases and its temperature increases. It then preferentially will now likely radiation energy to the CMB and decay away. Conversely suppose the black hole absorbs a quanta of energy &E = &mc^2. Under those conditions the black hole horizon increases its area and entropy and the temperature decreases. The black hole is now preferentially or statistically going to absorb mass-energy from the CMB and grow. Equal temperature does not mean equilibrium, and in fact the equal temperature point is unstable. The effective heat capacity of spacetime (or event horizons) is negative, which gives this funny reversed relationship between temperature and entropy.

This leads to the question of how does one “bottle” a black hole so it does not escape or quantum decay or grow endlessly. It turns out the bottle is an anti de Sitter spacetime. This has a negative Gaussian curvature which counter acts the negative heat capacity. The AdS spacetime is a mathematical gadget in a sense, but it does tell us things about the relationship between gravitation and elementary particles,. This correlates events on the horizon with those on the boundary of the AdS, where that boundary is equivalent to a conformal quantum field.

For very large astrophysical black holes A >> L_p^2 and the thermodynamic and quantum mechanical aspects of the black hole become negligible. A solar mass black hole has a temperature of around 10^{-7}K and will take about 10^{67} years to quantum evaporate. Super massive black holes will take 10^{100} years to quantum evaporate. So of course all we see is a tiny time slice in these processes with large black hole. Quantum black holes might in certain forms be produced in accelerator experiments, where the AdS correspondence above can connects certain quark-gluon processes with a graviton or even a small amplitude for a black hole.

LC

Thanks Crowell.

So then it sounds like if we can dial into the black hole some how, we can observe all the light that has gone through them and learn all about the past information that has already traveled through it. And maybe even link to other black holes and learn all about the info. that is traveled through them. So we could see the whole universe from all different angles of life in general.

I can see where you are going with that line of thinking, but I think the concept of ‘information’ in quantum theory has a much narrower definition. It is largely about wave functions. I don’t think we are ready to consider black holes as cosmic data servers (though it’s a nice idea).

Can anyone tell me why the black hole loses weight when it has the same amount of particle dropping in it as evaporate off (I thought I understood Hawking Radiation till I was asked this)

Cautiouslythrowing my hat into the ring . I suggest a simpler view point.

Consider :

That a black hole singularity is total neg-entropy where all the forces are unified.

That our Universe is only one of an infinite quantity of universes.

That our Universe is an electro-magnetic globule expanding into a region beyond our event horizon that I like to call ‘The Big Nothing’ That is total entropy.

That Singularities syphon energy out of our system into total entropy.

Our Universe was spawned from a previous univers’s singularity.

That the cycle is singularity to singularity

It is just a matter of infinite scaling

Maybe someone out there who is intrigued by the idea and has a better maths background than me would like to comment. I would like to have a reply

Sorry, comment on what?

It looks like a free association chain, incorporating some non-physics (such as the idea that a universe expands into “something” when it is self-contained spacetime), and have little or no relation with something we can put the quantifications of math on.

Oops. “zero energy (over time) particles” – zero energy (over time) fluctuations.

I’m not sure I follow. Add up the particle trajectories of zero energy (over time) particles that Steve’s figure shows. Some particles will escape from the vicinity of the BH to infinity, taking spacetime mass-energy with them: mass loss.

The main problem with that figure is that Hawking radiation is not from vacuum fluctuations but from thermal fluctuations by way of the Unruh effect, something you just reminded me of and I didn’t nitpick earlier:

“Hawking radiation is required by the Unruh effect and the equivalence principle applied to black hole horizons. Close to the event horizon of a black hole, a local observer must accelerate to keep from falling in. An accelerating observer sees a thermal bath of particles that pop out of the local acceleration horizon, turn around, and free-fall back in. The condition of local thermal equilibrium implies that the consistent extension of this local thermal bath has a finite temperature at infinity, which implies that some of these particles emitted by the horizon are not reabsorbed and become outgoing Hawking radiation.”

Here the mass loss is made explicit.

I think the “vacuum fluctuation” picture is some old folk physics. Somebody must have once reached for an explanation, without checking with the theoretical physics guys. And since “vacuum fluctuations” are sexier than thermal fluctuations (but by the Unruh effect they are not!), it stuck.

Fair nitpick – I am a bit old folk.

ROFL! That *is* one way of reading it. Sorry if my english isn’t up to snuff, if nothing else the “too straight, no nuances” of 2nd languages phenomena is always there for us all.

This particular piece of physics knowledge (well…) tend to be an on-off thing for me, since I have never studied GR but SR sufficed. I believe I heard of the pair production model first, and the Unruh effect much later, and still flips between images. Probably why I didn’t nitpick at once, I bought the whole package hook, line and sinker.

I like the subject, I like the article, I don’t like the popular science entropy theme in general (you can as well call information entropy “information qwerty” for all its relation to TD information), and this was a minor physics nitpick. Really the problem comes if you try to derive the Hawking radiation distribution, it is bound to differ. (Or the models would be equivalent.)

And who does that for breakfast? &_&

Misplaced comment, 2nd try:

Oops. “zero energy (over time) particles” – zero energy (over time) fluctuations.

Pity that much of this cannot be proven by experimentation and that it remains basically a thought experiment.

One point that bugs me some what is the narrow concept of the name black hole. The event horizon is not only defined by gravitation and mass, but also time. At the event horizon is basically a

frozen star — frozen in the dimension of time. Whilst the concepts of entropy, information and Hawking radiation are truly fascinating (and are so-callednear-horizon limits), IMO again the limitation are tied to the knowledge of how time is ‘physically’ created in the quantum mechanical world (string theory). Concepts (that I have read or implied here) and there like time being like tiny looped strings suggest that the vibrations of these strings are fundamentally changed at the black hole’s horizon; whose behaviour is limited at the size of the so-called quantum foam or whether these forces / particles / spacetime do cancel out under some manifested and theoreticalsupersymmetry. (It also might be something to do with the number of ‘spacetime’ dimensions.)I reallly still think perhaps we are missing something important piece of the puzzle. How does quantum mechanics / quantum field theory work at the event horizon and how does it structurally change from the near-horizon limit to the event horizon?

If asked, I’m the first to acknowledge that maybe BHs are extremely large quantum objects. But I also think that there is a dynamic. Maybe both have to be accommodated in a larger model.

But I don’t get your claim that a BH is frozen beyond the event horizon specifically. The classical picture is that you can’t notice the event horizon as you fall in, it is the singularity that is the end of worldlines then, right?

“Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. Because of this property, the collapsed stars were called “frozen stars,”[13] because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius.” [Wp]

But that is the same as if we would say that a photon is “frozen in time” and therefore would never interact with a receiver (say). The photon beg to differ, the infalling observer beg to differ. We must sum over all observers in relativity to understand the physics.

So if we fall in we would not see a star surface come at us, it isn’t actually “there”.

“We must sum over all observers in relativity to understand the physics.” That didn’t come out right.

Better to say that we must be able to transform between observers (and that is really the whole idea anyway). Hence no observer is privileged, hence “frozen star” is not quite right.

“Pity that much of this cannot be proven by experimentation and that it remains basically a thought experiment…”

salacious, i just gained some respect for you. i’ve been itching to get in a word while reading these comments and now you’ve calmed me down somewhat.

Err.. “(and are so-called near-horizon limits)”

I should have say “(and are applicable at the so-called near-horizon limits)” and not at the event horizon itself.

“But, there is a problem if in a googol or so years, the black hole evaporates via Hawking radiation, which arises from quantum fluctuations at the event horizon and has no apparent causal connection with the contents of the black hole”

There is one more problem, the black hole will evaporate before anything gets to pass the eventhorizon, atleast for black holes that evaporate in finite time.

I dont know if all black holes _do_ evaporate in finite time,

Lawrence & Excalibur are both on the right path here (L_p = sqrt {G-hbar/c^3} ~ 10^{-33}cm is getting warm). I’ll try to place it all in simplier terms, like I have done here once before.

Time is not constant at an event horizon like a black hole. The time we actually witness an event occur (Matter crushed, etc…) & the time it actually happened is 2 totally different places in time. So, the release of matter does happen as figured but at a completely different place in time.

As an example before in my speed of light parable, the actually event of going at the speed of light is only the first step in a highly succinct group of events that can propel you to many more times the speed of light. I actually wrote the formula out in extended terms there but in the essence of time now, let’s just say that matter can be transported to different places based on when the energy source decided to release them.

Goodluck to all.

For the infalling matter, that will later participate in any evaporation, that doesn’t apply. There is no line saying “event horizon” that an infalling observer can note.

The notion of an event is radically changed when you consider black holes in the context of quantum mechanics. If you watch a quantum oscillator, say some system with a definite quantum frequency, fall into a black hole that frequency becomes less and less as it approaches the event horizon. As the system approaches the event horizon that frequency approaches zero, so that on a membrane just a string length (about 10 Planck lengths) that frequency goes to near zero (about 10^{-30} times smaller). The quantum system appears frozen to a near dead stop just above the event horizon, and it remains there for a vast period of time. There are some odd things which happen. An observer who witnesses the quantum system along its fall will see something radically different, where within a very short period the quantum system is absorbed by the singularity within the black hole. Of course the infalling observer gets absorbed as well.

If the exterior observer can wait out an enormous period of time something funny is then observed. The quantum modes (degrees of freedom) of the quantum system watched to reach near the horizon are annihilated and replaced by radiation or quanta which are transformed by the gravitational interaction (actually quantum super-gravity). So in this enormous time into the future the exterior observer watches the quantum states of the system annihilated, and this is the same annihilation or transformation which occurred in the interior of the black hole when the quantum system was absorbed by the singularity. So the spatial and temporal uniqueness or invariance of an event is not a general principle of quantum gravity and cosmology.

This is something which happens with new developments in physics. Previous ideas about the nature of processes or of space or space and time are abandoned. They prove to be obstructions to deeper understanding of nature that are in effect “excess baggage.” We are at an age where various ideas canonized in physics are likely to shown as excess baggage. The holographic principle has removed one of these obstructions; the uniqueness of events in spacetime.

LC

Thank you for your eloquent response here. You put your words into far better context than I ever could. Looks like I’ll have to catch up on some cosmology articles to make up the short fall in current knowledge!

Cheers

Good, it seems to me the use of HP as you do forces one to make explicit the realism of states, that they can’t be interpreted to have an existence before they are observed.

I.e. the old “counterfactual definiteness” that so many does not accept and that the whole issue of a “non-locality” notion grows out of. YMMV and those who rather see systems with instantaneous action-at-a-distance instead of simple correlations may continue to do so of course.

Also the generalization from observation of states to observation of spacetime events is sweet.

@LBC

I have to agree completely with your first and last paragraph, but the middle paragraph seems a bit muddled. Can you expand a little on what you’re saying there please?

If you have the time, can you also elaborate on my conclusion/conundrum above that “if a black hole evaporate in finite time (Quantum Physics), then nothing will actually reach the event horizon (General Relativity)” I would appreciate it. I accept that I can be wrong, but then I would like to be corrected. I am certain to be wrong in a grander sense, because QP and GR do not mix, better theories are under construction (String Theory), and my conundrum’ might have a more mundane explanation within one or more of these theories.

@ Excalibur, That middle paragraph which you find muddled is actually the crux of the matter. It is what requires a bit of brain wrapping in order to understand. The point is that the event of the destruction of quantum modes of a system which became entangled with the black hole is not something which is invariant. The destruction of those modes by the black hole singularity and the far future witnessing of those modes being demolished or transformed by black hole quantum mechanics are the same event. This is even though this event appears as two events identified at entirely different regions of spacetime. This is related to how string interactions do not have point vertices, but merge at a continuous space, a 2-sphere with 4 holes for the strings, that is covariant.

This gets one into the deep issue of quantum gravity and the equivalency between quantum gravity states and states of elementary particles. The observable physics only becomes apparent when the black hole is very small and the physics merges into high energy particle physics. For astrophysical black holes, say how stars collapse into black holes or supermassive black holes blasting galactic structures to bits with jets these matters of quantum black holes can be safely ignored.

LC

Much appreciated and overall well written article. But I can’t agree with LBC on the article as fine when it covers basic issue. (I did enjoy his technical comments, if only because I have seen some of it before. :-o)

There are several types of entropy and their different representations that are equivocated on to the extent that it forms a particular form of popular modern folk science. The science, I believe, is much simpler much as LBC discussed.

If you look at the microstates of entropy, unitarity of quantum mechanics means that wavefunction information (such as charge conservation) is preserved. It is this conservation of QM information, that is the BH information concern.

As for information entropy of Shannon, it has no relation to thermodynamical entropy aside from the similar choice of measure and an analogy between message information and state occupancy vs channel capacity and availability of states (TD microstate entropy). The measure for each availability looks the same because they measure analogous characteristics with the same statistical properties.

There is for example no physical unit, no QM conservation law and no TD increase law for Shannon information. This is because information is a relative, not absolute, property of a system. As for complexity, which it relates to by way of coding, it can be expressed in many ways.

Addendum: “entropy represents the loss of free energy”

True, for isothermal systems. Since dQ = TdS the differential of entropy tells of the differential of energy by ratio.

Classical thermodynamics of black holes is dQ = dM = (g/8pi)dA, where the area of the horizon stands in for entropy and g is the surface gravity. There are additional terms for rotation and charge. The gravity g is the surface gravity defined by the Killing vector on the horizon. This all works fine from a classical perspective. However, if there is entropy there is then a temperature and g ~ T. Then if there is a temperature this means there is some radiation emitted. This lead to Hawking radiation, but this also violated unitarity. The rest is a fairly long history of trying to understand this on deeper levels.

Information is classically, or according to classical thermodynamics, subjective. However, the game is different with quantum mechanics. Here information is identified with quantum states, and the unit of information is a quantum bit. For quantum mechanics to hold quantum bits are conserved, for the reason that quantum states, or the volume identified with the quantum states of a system, is conserved. It is for this reason the problem has gotten into such deep and subtle territory.

LC

string theory is certainly a work in progress: mathmatically equisite, but difficult to test.

i like it, but i’m still not sure if i’m comfortable seeing it used so “lawfully”.

Actually you can derive all of this AFAIK, including the holographic principle, without string theory.

ST makes math easier or even possible which is why it will continue to earn its keep I’m sure, whether or not it is actual physics.

ST may have more intuitive interpretations IMHO, and it is the first physics that makes some sense towards unifying GR and QM (making particle interactions smooth over time, allowing for background scaffolds instead of demanding a lot of hard-to-get invariance on them).

But ST isn’t something that BH phenomena lives and dies on.

Unfortunately perhaps, because then we *would* have an easier test for ST.

“which is why it will continue to earn its keep I’m sure, whether or not it is actual physics”

Note that since math uses “theory” as well, it would even keep its name. Why do I get the feeling someone though about that at the outset? (¬_¬)

Holographic results with standard quantum field theory results in amplitude functions which are “stringy.” Once the degrees of freedom are restricted entirely to the horizon the BH in effect “derives” or recovers aspects of string theory.

It appears that string theory, or its general formulation as M theory is universal. It turns out this emerges with the physics of Dirac fields on graphene and is at the foundations of quantum critical physics or phase transitions with superconductivity.

LC

In my considered opinion: Black Holes do not exist, as Nature will not allow them to form. Black Holes are truly ‘thought experiments’ only. The Natural Laws of Physics will prevent their formation, and I interpret the ‘jets’ that we observe emanating from highly-massive stellar and galactic objects to be the confirmation that black holes are not being allowed to form there, regardless of our calculations about the mass suspected to be present in those locations. The other half of my argument is: The reason that black holes are postulated to exist in the first place, is that normal gravity alone is not able to account for the motions of the bodies we observe orbiting the central locations in question, due to the fact that we do not observe sufficient mass in that central location to account for the orbital velocities of the satellite bodies we observe orbiting that central location (galactic rotational properties included, as Dark Matter substitutes for Black Holes in that context). Therefore: a super-gravity object; a ‘super-dense unobservable central object’ aka ‘a black hole’, or ‘a singularity’ surrounded by an observationally impenetrable event horizon, must exist, and which exhibits an enormous gravity that is then sufficient to make our observations consistent with our gravitational physics.

[Black Holes and Dark Matter are fictions, like pink elephants and unicorns, they do not exist in the real world.

As for my explanation of what does exist, and supplies the ‘missing mass’ that black holes and dark matter are invented to account for; well that’s ‘not allowed’ in the religious views of Mainstream Physics at present, so I won’t mention it, and be not blasphemous.]

And now; for some input/comments on the ‘thought experiment’ of Black Holes, and to your possible surprise, I am not averse to conversing about BH’s in the form of an hypothetical argument ! I’m not that ‘confined in perspective’ an agent provocateur that I can’t talk about “of cabbages and kings, and why the sea is boiling hot, and whether pigs have wings”.

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Regarding the above three quotes from the UT article: Could it be that evaporating black holes (in the distant past) are what gave the Universe its ‘virtual entropic floor’, and for that floor to have a level ‘above zero’ at present. This ‘virtual entropic floor’ would create a ‘reservoir’, in a sense, from which virtual particles are now allowed to spontaneously appear/disappear, from/into. This idea is predicated on the assumption that the Universe has always been here. And as such that the Universe has always been here, a near infinite amount of black holes have already ‘evaporated’ in the past, and this is how the ‘virtual entropic floor’ for the Universe has arisen, and also risen above zero, in terms of the ‘level of nature’ that virtual particles are spawned from/disappear into.

[Hawking Radiation being the vector that raised the level of the entropic floor above zero, so that Hawking Radiation could then have a place of origin from which to exist ! A real ‘chicken or the egg’ conundrum. (The inscrutable answer to which is: the rooster !)]

In terms of the ‘level of nature’ that ‘regular everyday’ Energy and Matter inhabit, their entropic floor would be spoken of in a different context than the ‘virtual world’s entropic floor’. (Not trying to complexify the issue, but to denote a difference between the ‘virtual world’ and the ‘normal everyday world’ of physics. Not that the two worlds don’t mix or correspond or commute on some level, they do, it’s just less confusing to separate the two at this level of the presentation.)

And as the ‘voice of the Universe’ said, “The entropic floor must always be greater than zero.”

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I didn’t realize that a double <> will erase its insides !

Here are the quotes that are missing.

1. “So the best way to handle that is to acknowledge that whatever entropy a system possesses is transferred to the black hole when the system goes into it. This is another reason why black holes can be considered to have a very high entropy.”

2. “There is a fundamental principle in quantum mechanics which requires that information cannot be destroyed or lost. It’s more about wave functions.”

3. “But, there is a problem if in a googol or so years, the black hole evaporates via Hawking radiation, which arises from quantum fluctuations at the event horizon and has no apparent causal connection with the contents of the black hole.”

and then

4. Holographic: “Hawking radiation does succeed in carrying information out of the black hole as the black hole evaporates.”

5. Zhang: “Hawking radiation, via quantum tunneling carries entropy out of the black hole – and since reduced entropy means reduced uncertainty – this represents a net gain of information drawn out from the black hole. So Hawking radiation carries not only entropy, but also information, out of the black hole.”

I didn’t realize that a double will erase its insides !

Yes I did, so why didn’t you do so from the beginning and the end of all this text, eh? is what I think of your absolute nonsense here!

is what I think of your absolute nonsense here!

“In my considered opinion: Black Holes do not exist, as Nature will not allow them to form.”

And as the ‘voice of the Universe’ said, you are absolute fool, sir.

In my considered opinion: Black Holes do not exist, as Nature will not allow them to form.

The interesting thing is that the universe does not care what your opinion is.

HAHAHA!!

The universe is so sober, it makes me laugh

Just to clarify the filthy ignorant falsehood made by lars here; I dis say; “

Pity that much of this cannot be proven by experimentation and that it remains basically a thought experiment.”When I was speaking of this I was talking about entropy and information; and not black holes. Black holes can be easily ascertained to be true by the motion under gravitation of two stars acting as a binary. There is direct evidence that support that black hole are not fiction but are observational fact.

If you want to deliberately misquote me, as this nitwit seems to think is perfectly OK, I promise you I will not be nice!!

The basic 101-black hole has been demonstrated astronomically beyond a reasonable doubt. One might not want to get into the quantum mechanics and entropy-information theory of black holes. However, the basic black hole has been found to exist.

LC