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A frequently asked question on this talk page is:

Is it really true that in Physics is it presumed that "information cannot be destroyed" ?

Please first read the thread #Completely false premise. below, before asking this question. Then, if you still want to start a new thread on this question, please start it at the end of this talk page. Jheald (talk) 13:51, 8 February 2010 (UTC)

## homogeneity and BHIP

I removed the following paragraph which was recently added;

The homogeneity of space and the space-time position independence of the laws of physics is a fundamental assumption of all physics science since Newton. Recenlty, because of the dead end of the Scientific method, scientists like Hawking concluded that the laws of physics are not actually space-time position independant but space-time position bounded, thats why they created the black holes concept and claimed that space or time is absent inside them. The information paradox of black holes is, for some anti-scientists philosophers, the proof that space is not homogeneous and/or that the laws of physics are actually space-time position dependant and not space-time position bounded, as long as, according to the paradox, information seems to vanish or (alternatively) stored to unconventional material (or non-material) objects. Apart from the black hole information paradox, some experiments came also close to the philosophy of the position dependancy of the laws of physics. Some universal constants used in well known equations have been found to change their values (increase or decrease) when measured in small fragments of time or when time passing [1]. A group of pioneer "scientists", lead by John K. Webb [2], continues the experiments in this revolutionary field.

This mostly reads like pseudoscience. The invariance of fundamental physical constants with space and/or time is open to question, and John K. Webb and other's cited may well work on this. However I can't see any connection or relevance to the Black Hole Information Paradox. -- Solipsist 09:16, 10 Apr 2005 (UTC)

## The Equation

This page ought to have the equation which started it all off. —Preceding unsigned comment added by Pydos (talkcontribs) 16:02, 16 September 2005

S = c^3xA/4ħG

S=thermodynamics (Entropy), G = gravity, c is einsteinian theory (speed of light). ħ ("h-bar") = reduced Planck Constant (or Dirac's constant). A is the area. —Preceding unsigned comment added by Karl Leibrecht (talkcontribs) 13:54, 3 April 2006

Hey, what’s up. I wandered over here after seeing a thing on YouTube about “Stephen Hawking’s paradox,” and in it, they included his formula as above, i.e. without the k (Boltzmann's constant) that’s currently in the article. Is that a mistake? Also, at one point, a guy writes $S_{BH} = \frac{c^{3}A}{4 \hbar G}$ on a chalkboard, with a subscript BH after the thermodynamics S. Is it still the same formula? Wouldn’t that make S equal something else? Some webpage has it as in the article $S = \frac{\pi Akc^{3}}{4hG}$ (with the k), but also with a π symbol. Where’d that come from?? Post-junior high math isn’t my strong suit, but I’m curious; if someone could break down whether any of this matters, that’d be great. —Wiki Wikardo 21:27, 23 April 2009 (UTC)

The only real way to destroy information, is to destroy the human race. A black hole cannot destroy information because of the fact that if we observe a star, and a black hole consumes it, we still know the star was there....

Now if we destroy the human race, there is no-one to reproduce with or to share data with, thus destroying the facts and information that we have learned... —Preceding unsigned comment added by 207.63.186.15 (talkcontribs) 18:14, 19 September 2005

...That's not quite what's meant by "information" in this context. You refer to information in terms of human knowledge, which is only the interpretation of sensory input, which will vary from individual to individual. The Great Attractor 00:52, 25 May 2007 (UTC)

it is impossible to know, trying to answer this paradox is purely futile. the reason for this is that if the information were destroyed we would have no recelection and it is possible that things are disappearing, however we are uncertain because the information which is the memory no longer remains. A more plausible theory is that information is neither stored or destroyed but recycled, for if it were stored there would inevitably be answers to "the beginning" and if it were destroyed then one would see or wonder about a black hole the black hole would itself cease to exist. thoughts of K. Alonzo Valentine II —Preceding unsigned comment added by 70.105.1.37 (talkcontribs) 02:18, 28 January 2007

## assumed tenet of science?

I read with astonishment -in several media in connection with this paradox- that a commonly assumed tenet of science is that information cannot be destroyed. I am a physics graduate, never heard of it and it seems to be in contradiction with the second principle of thermodynamics and the foreseen cold and hot deaths of the universe. Worse I cannot find in the whole web anything about this "assumed tenet of science". I think someone should explain it.

Manuel Navarro —Preceding unsigned comment added by 84.120.154.136 (talkcontribs) 21:36, 8 February 2007

## surface area of the event horizon

I stopped by this page but I have no astronomic background nor any dedicated skills to the matter but how can you calculate or even define the surface area of the event horizon? I'm quoting the article here: To an external observer the event horizon would appear to take an infinite amount of time to form due to gravitational redshift, and the black hole would dissipate via pre-Hawking radiation before an event horizon would ever form. so how do we define a surface we can never see formed? Does an event horizon even has a surface? I know it is the edge where light remains "trapped" forever but can we even have a clear appreciation of it? I mean can we put or even imagine an observing element (of the ideal size, like the smallest possible) exactly on the edge of the event horizon (where going at the speed of light the opposite way it would remain exactly at the same place, the aspiration of the hole and the movement speed of the observer being in a perfect balance) or can't we?

PS: please answer me directly on my user page if you do :). PSS: I'm a noob, don't forget it plz :)). Matthieu (talk) 13:04, 17 November 2007 (UTC)

If the information survives in parallel universes with no black holes then no information can exist in the first place. AnaxMcShane (talk) 12:25, 30 January 2008 (UTC)

• Well, I'm not sure how Mr. Hawking is coming to the conclusion that black holes couldn't or wouldn't exist in a parallel universe, but information could, would & does exist in this universe. Hawking is just figuring that any information sent through a black hole in our universe would survive a travel into another universe. His new theory seems awfully rushed... I'm not sure how he's proposing information would be "injected/ejected" into the other universe after being blown/pulled through a black hole. Would it be a white hole on the other side? -Rayne 14:30, 7 February 2008 (UTC) —Preceding unsigned comment added by 206.208.93.60 (talk)

The term 'Black Hole' is a rip off of the term 'Implosive Gravity' and 'Black Holes' should not be thought of as they are currently...

If "Black Holes' function the way some say they do, then why doesn't a 'Black Hole' implode in on itself for infinity until acted upon by some external force?

There is an infinite amount of dimensions for each surface anyway, just as there are an infinite amount of universes with in/on/around each surface.

If we went through a 'Black Hole' and the 'Black Hole' functions as a mover of sorts then it's possible that every thing that goes / went through it will be reconfigured / re-calibrated randomly...

Like a big puzzle cut into smaller pieces and then each piece reshaped and resized to fit into a partial whole or whole again or not at all. AnaxMcShane (talk) 13:57, 16 February 2008 (UTC)

## Who deleted it?

Someone deleted the part I put in where cause and effect become unrelated and nothing science knows can be trusted. Why did they do that? I gave citation and everything. Besides, I'd say it's pretty relevant, considering it undermines the whole of physics. —Preceding unsigned comment added by Dstebbins (talkcontribs) 02:26, 2 March 2008 (UTC)

## Completely false premise.

It is most certainly NOT "a commonly assumed tenet of science that information cannot be destroyed.". Who came up with that nonsense? Information is thermalized all around us all the time -- scratch a message into an ice cube and then melt the ice cube and the message is irretrievably lost forever. The information contained in it has been destroyed - it is not contained in the universe anywhere any more. If this absurd contention of a "conservation of information" is dropped, then what is "paradox" about a certain particular process in which information is lost? Where's the "conflict" here? What is "paradoxical" about this?Iron Condor (talk) 04:09, 4 July 2008 (UTC)

▲▲ You don't understand what is meant by "information" here. Everything in the universe is made up of matter or energy, (which are actually the same thing) but where does that come from? The current term for base existence of matter and energy is "information". Information cannot be destroyed in that, a part of the universe can never cease to exist without something of equivalent exchange being returned. It's like the hash code on a piece of software, change even the slightest thing and you will get a totally different number. ▲▲

You are using the wrong connotation of information; what is being said here is that a certain kind of information, as explained by quantum physics, is encoded into every subatomic particle in existence;
This is absurd gibberish. There is absolutely no such thing as "a certain kind of information, as explained by quantum physics" that is somehow magically "encoded into every subatomic particle in existence". To the contrary: quantum mechanics shows (through Bell's inequality, experimentally tested in the Aspect experiments) that there is NO information contained in any particles that is not retrievable through all the known means of physics. There is NO "hidden information" or any such nonsense.
The problem here is not that you are ignorant -- there is no requirement for you to know what you are talking about. There is something VERY wrong with an ignoramus like you presuming to tell someone knowledgable like myself about science. If you don't know what you're talking about, THEN DON'T. Do not go and confuse things more than they are by posting blatantly FALSE and UNINFORMED bits of opinion.
in essence, if you destroy something or morph it, the information encoded onto individual atoms would allow you, technically, to reconstruct an object into the condition that it was in before it was destroyed.
This is the direct diametrical opposite of what Quantum Mechanics actually says. —Preceding unsigned comment added by Iron Condor (talkcontribs)
What is being said here is that if this "information" is destroyed, then this lost information, which has accounted for so many things in the past, can no longer account for much else; therefore, cause no longer meets effect.
I just wanted to clarify that. --Starstriker7(Dime algoor see my works) 02:00, 28 October 2008 (UTC)
Everybody, please be civil and please sign your posts. Iron Condor, I wish to point out that this whole article is about the supposed black hole information loss paradox, so if you think information loss isn't paradoxical you ought to be seeking to delete the whole article, not one little part of it. That's unlikely to happen, though, because you have powerful enemies, like Stephen Hawking.
I think the problem is indeed conflicting meanings of the word "information". When the people who talk about this kind of thing say that information is not lost, what they mean is that different initial states evolve into different final states. That's a property of Lagrangian/Hamiltonian evolution both classically and quantum mechanically. If you melt an ice cube in a universe governed by a Lagrangian, the final state differs depending on what message was written on the ice cube, and in that sense the message is not lost. It's diffused into the environment to such an extent that you (a creature in that universe) could never hope to recover it, but it's still there, at least as far as the mathematical model is concerned. Black hole evaporation, in the sort of semiclassical model that Hawking like to work with, violates that principle. You squeeze an ice cube until it becomes a black hole, then wait for it to evaporate. You've converted the ice cube into thermal noise, but, in contrast to ordinary melting, the fluctuations in the noise do not encode the initial state of the ice cube. The particles that make up the ice cube literally cease to exist at the singularity, and after that you can't run the evolution operator backwards to find out what they were.
That's the idea. Don't ask me to defend it, because I don't understand this subject nearly well enough for that, but it isn't patently ridiculous, once you understand the specific technical sense in which "information loss" is used. -- BenRG (talk) 12:34, 1 February 2009 (UTC)

I have no quarrels with the existence of "something" that happens to be called a "black hole information paradox". That sounds intriguimng enough for me to want to know more about it, to be precise. So I go to Wikipedia and I find that there's a bunch of ignoramuses who *freely invented* some supposed law of physics that supposedly states that information cannot be destroyed.
Which is absurd gibberish, of course, since information is destroyed all around us all the time every day in a billion processes. Every time an atom absorbs a photon, the information that the photon existed, where it came from and what energy it had are all destroyed. No examination of the atom in question can ever reveal it, because it is not contained in the universe any more. Complete knowledge of the full wavefunction of everything will not tell you that this atom was hit by a photon of that energy from such a direction this long ago. Because information has been destroyed -- as it is destroyed routinely all the time.
In science, it is not acceptable to make up things because they seem plausible to you and then proclaim that they're true. If QM teaches us anything about information, then it is that the universe is substantially *noise* at the bottom. This may seem counter-intuitive to people like yourself who have never actually thought about reality, but that's what you find if you are willing to sit down and study the actual, real, honest physics of the universe in which we live.
In science it is *also* unacceptable to try to resolve a dispute by invoking an assumed authority. That may fly in your church, but in science it doesn't matter who said something; if something disagrees with experiment, then it's wrong. And observing a process in which information is lost is trivially easy. But of course Mr. Hawking never claimed such absurd nonsense as "information cannot be destroyed" -- that's just you making stuff up and putting it into his mouth. You're perfectly happy to post vile insulting lies about Mr Hawking -- yet you imagine you get to admonish people to "be civil". You're happy to insult *me* with your lies and yet you find iot objectionable when I call you a liar.
Here's a hint for when you grow up: As long as you find it acceptable to lie (*to* other people, *about* other people) you should better be comfortable being called a liar. If you resent being called a liar, then don't lie. It's that easy, really.
Iron Condor (talk) 15:25, 2 February 2009 (UTC)
Well it isn't a bunch of "ignoramuses" on Wikipedia that thought of the idea of the Black Hole Information Paradox, it was actually Stephen Hawking. Although he has since admitted he was wrong, it was him who coined the idea over 30 years ago, and btw Stephen Hawking isn't an "ignoramus on Wikipedia". SaiferPhoenix (talk) 04:06, 28 March 2011 (UTC)
Let me see if I can try to give my understanding, and maybe calm things down a little.
Yes, entropy tends to increase in physics, and that can be seen as equivalent to information being lost. But there is actually some subtlety here, even in purely classical models, which is worth looking into in rather more detail. (See also for example discussion of topics like the H theorem and/or Loschmidt's paradox in standard books on statistical mechanics - eg the classic work by Tolman - or standard works on the philosophy of thermal physics).
The issue - even with conventional entropy increase - is that we correctly predict entropy increase, even though at a microscopic level we tend to assume the dynamics are deterministic, reversible, and (in the classical case) Liouvillian, or equivalently (in the quantum case) unitary. In loose terms this means information is not lost -- at least not by the dynamics. Unitarity of this kind is one of the basic assumptions made in constructing quantum mechanics.
But if information isn't being destroyed by the dynamics, how is the entropy increasing, in situations like eg two gases being allowed to mix? The answer, put forward at least as far back as Gibbs is coarse graining. It is us, as analysts, who throw the information away, not the dynamics. So for example, in thermodynamics, by insisting on a description of the system only in terms of its current macroscopic thermdynamic variables -- with no room for taking account of detailed microscopic correlations -- we have chosen a description where there is no way to keep track of some of the information which the detailed dynamics themselves actually still preserve.
Similarly in the example of the atom and the photon, if you had the full knowledge of the full wavefunction of everything, the assumption of unitary evolution means that you should be able to run that forwards or backwards to get to the state of the universe at any other time. Given the state, not just of the atom and the photon but of the rest of the universe as well, under unitarity no information is destroyed, and in principle an entity with the capabilities of Laplace's demon could retrodict where that photon had come from. On the other hand, if we ignore that (in quantum mechanics) both are unavoidably connected to the rest of the universe, again that is a simplifying approximation made by us, but one which has the effect that our description no longer reflects the full underlying dynamics, and from then on some information coded in the relationship of the atom and the photon to the rest of the universe is being ignored. This looks like coarse-graining again.
The black hole information paradox arises from the same assumed world-view once more: that in a full quantum description, the dynamics should be deterministic, reversible, and information preserving (unitary). The assumption is that the dynamics aren't throwing information away, we are. The challenge is to (a) confirm this, and (b) to try to work out where. Hawking's recent work has been on (a) - to try to produce a picture in which it is clear that information has been conserved, and has not been destroyed and then re-created out of nowhere. As for (b) - where might coarse-graining by us have lost track of the information, I am no expert in this area, but as I understand it a strong candidate would be in Hawking's semi-classical treatment of the black hole - in a fully quantum treatment, one would expect, in moving to a black hole description with a finite (non-zero) temperature, and a finite (non-infinite) entropy, a full description would identify a finite (non-infinite) collection of states for the black hole, each with amplitudes and phases with respect to the rest of the universe, therein containing information. My understanding is that Hawking's semi-classical work manages to get answers for the total BH entropy, but without identifying any finite collection of corresponding distinguishable quantum states for the BH, and this could well be the kind of coarse graining done by us as analysts that messes up the information preservation of underlying unitarity. Jheald (talk) 23:29, 2 February 2009 (UTC)
Your attempt to misrepresent thermodynamical misconceptions from the 1800s as actual, current tenets of science makes it clear that your intent is not communication of reality, but obsuration of truth. You, Jheald, are a liar. Physics did away with determinism about a hundred years ago now. Your desperate attempt to deny this make you a liar. You desperate attempts to proclaim that Mr. Hawking supports your pathetic lies makes you an insulting, subhuman lying swine.Iron Condor (talk) 00:13, 4 February 2009 (UTC)
Are you trying to imply that evolution of quantum mechanical wave functions is NOT unitary? That would kinda go against pretty much everything that has been written on quantum mechanics in the last century. Evolution of a wavefunction in a completely quantum mechanical system is unitary, this is a basic fact that you will find in any QM textbook (although may be worded differently). This in particular means one thing, if you would know the wavefunction at some particular time (slice) you can, in principle, calculate the wavefunction at any other time. (This, of course, is a pretty big "if" as it is not physically possible to actual know the wavefunction of the universe since you yourself are part of that same universe.
Now, modern physics is actually plaqued by two major (non)unitarity problems. It seems that your misunderstandig of the first is causing your inability to understand the second. The first non(unitarity) problem is the so called measurement problem, in which a "magic" act of measurement cause the instantanuous collapse of the wavefunction. This instantanuous collapse of the wavefunction is non-unitary, and information is lost in the process. (If the wavefunction truly collapses, it is impossible to reconstruct the state before the collapse from it.)
The second, is black hole unitarity problem (sometimes referred to as the information paradox, but it is unclear that there actual is a paradox). If during the evoltuion of a wavefunction a black hole is formed, and that black hole completely evaporates through the process first described by Hawking. Then the calculations show that this evolution is not unitary, the end state contains no more information about the begin state then a few quantum numbers.
In the last few decades understanding of problems has been converging on the notion that both are caused by the inherently semiclassical nature in which they have been treated. In the case, of the measurement problem the culprit seems to be that while the measured system is treated quantum mechanically, the observer is not. If the observer is replaced by a quantum mechanical system it can be shown that while the interactions between the observer and the measured system cause the wavefunction of the measured system to collapse to a classical mixed state, the evolution of the combined wavefunction of both systems is in fact unitary. The information about the original state of the measured system is not lost but smeared out over the (considering the percieved classical nature of the observer) very large number of degrees of freedom of the observer. This process is called decoherence, that it is real can be attested to be the people working on quantum computing because it is a major pain in their ass. Now, decoherence is not (yet?) been completely succesful in explain how a final classical pure state is picked, this might require the adoptation of a many-worlds type of interpretation, but it has in fact the unitarity problem in measurements.
The black hole unitarity problem is expected to have a similar cause and resolution. The percieved non-unitarity is expected to result from the classical treatment of the black hole geometry, which effectively gives the black hole (horizon) infinitely many states. A proper quantum mechanical treatment is expected to restore the finite number of states in the black hole, and the unitary evolution of the complete system. (TimothyRias (talk) 10:00, 4 February 2009 (UTC))
The problem for wikipedians is to formulate the supposed paradox in a way that is both technically correct and accessible to lay readers. Personally I think the bit in the introduction about "commonly assumed tenet of science" should be dropped, as it is too imprecise and sounds a bit Ptolemaic. Maybe part of what TimothyRias writes above should be included in the article. Maybe one should write the introduction as "this violates an assumed tenet of quantum mechanics, that the evolution should be unitary", then explain what this means in layman's terms (this is the difficult part) and then, later in the article, add TimothyRias's point about wavefunction collapse as an example of a situation that is non-unitary in some interpretations of quantum mechanics, for clarification.
The situation is complicated. I don't think all professional scientists in this research area agree on what the physical problem is. For example, one can read in this well-known paper [3] Ashtekar and Bojowald pointing out that information loss has nothing to do with uniqueness theorems, despite what Hawking has been saying since 1976.--Eujin16 (talk) 06:50, 18 February 2009 (UTC)
Use the s-matrix and the info is restoredAbc9100 (talk) 14:10, 3 May 2011 (UTC)

## Information cannot be destroyed?

I know that relativity and black holes and quantum mechanics predict things that are completely counter-intuitive. But let's take this statement in its simplest way. Let's say I make a major discovery. But then I die immediately afterwards, having had no chance to share my discovery, my information. Or, alternatively, let's say I discovered something and wrote it down but then burnt my notes and NEVER mentioned anything I discovered to anyone else. So, exactly, how can information NOT be destroyed? Sure, in a philosophical sense, the information was there "always". But I don't think the statement here meant that interpretation. 68.200.239.84 (talk) 00:21, 19 July 2008 (UTC)

Read the excellent explanation by Jheald above. Dauto (talk) 02:05, 3 February 2009 (UTC)
If you discover something, it means it existed before your discovery. It was there, but you just didn't know about it. So if you never mention your discovery and you die, no information is lost: what you discovered is still out there, waiting to be discovered by someone else. But what does this has to do with the article? Cogiati (talk) 08:16, 27 July 2011 (UTC)

## Must it be local?

I have some trouble understanding the paradox as a paradox. The light speed is limited, and so, travelling farther and farther away from the hole, the information on what fell into the hole is still there. If everything is to be run backwards, the light is to be run backwards too, and after a time coming back to the hole. Is there a further requirement that the "lost" information is to be localized in any way? ... said: Rursus (bork²) 09:09, 3 February 2009 (UTC)

It is a paradox insofar that it leads to contradictions if you start from the premise that the laws of physics are reversible (as encoded in QM as unitary evolution). A black hole fundamentally changes the spacetime direction of what is future into a radially-inward directed convergence into a singularity. Once you accept that, there is no longer a causal path radially outward back to the outer universe. So, Hawking radiation can not 'carry any memory' and the starting assumption of reversibility is lost.
Bottom line is that in a certain deep sense quantum mechanical uncertainty is incompatible with classical causality. Problem is to word that in an accessible yet technically accurate way. JocK (talk) 23:32, 26 February 2009 (UTC)
OK, I see! I have suspected that quantum mechanics for being fishy, a long time now. ... said: Rursus (mbork³) 22:33, 5 December 2009 (UTC)

## An outdated concept?

Isn't the idea "that in principle complete information about a physical system at one point in time should determine its state at any other time" based on the "clockwork universe" idea from classic Newtonian Physics? It's Laplace's Demon all over again, isn't it? Didn't this idea go out when the Uncertainty principle came around (or the 2nd law of thermodynamics?) If this is true, why are people bothering with this? --71.99.31.143 (talk) 03:57, 15 August 2009 (UTC)

I'd like to add to the disapproval of the first paragraph as it it pretty misleading "It suggests that physical information could "disappear" in a black hole, allowing many physical states to evolve into precisely the same state. This is a contentious subject since it violates a commonly assumed tenet of science—that in principle complete information about a physical system at one point in time should determine its state at any other time.[1]" My reasoning is that you cannot have complete information about a physical system from Heisenberg's uncertainty principle, and even if we could know the complete system state this tells us nothing about the elements of the system so the fact that many physical elements can combine into the same physical state doesn't matter because the elements of the state do not exist. —Preceding unsigned comment added by 86.134.234.6 (talk) 03:49, 2 January 2010 (UTC)

## Point of View check

I have marked this article for a Point of View review in response to all the statements of concern listed below. --Tediouspedant (talk) 14:38, 7 February 2010 (UTC)

Agree that it's far from neutral. There is no paradox! Please change the title or atleast reference whoever said it's a paradox. Or ditch the article altogether. —Preceding unsigned comment added by Dhatsavan (talkcontribs) 15:54, 2 September 2010 (UTC)
• I removed the tag. The article does need clarification and probably expansion, and certainly better references, but bias is not evident. This is called a paradox, and the sense that information is conserved by quantum systems is expressed by unitary evolution of the wave function. The problem is language: determinism and information have different meanings with respect to quantum and classical logic. When people say that the quantum world is non-deterministic, they mean it's not classically deterministic. I broadly agree with the comments of Jheald, TimothyRias, and BenRG on this talk page. Tim Shuba (talk) 01:02, 15 November 2010 (UTC)

## A Law of Conservation of Information?

Is there any accepted - or even proposed - 'Law of Conservation of Information' corresponding to the accepted laws of conservation of mass and energy? The information in the world's libraries has not been 'extracted' from the natural world; it is the cumulative product of human observation and reflection. If you burn a library the information is not dissipated into the atmosphere; it is destroyed. The metaphysical concept of the 'Conservation of Information' appears to have been invented by the Christian Creationist William Dembski [see his book "Intelligent Design: The Bridge Between Science & Theology"] in order to "prove" that evolution of complex organisms from simple organisms is "impossible" and violates some imaginary law of conservation of genetic information. It is based upon unsubstantiated dogma rather than being deduced from scientific observation. --Tediouspedant (talk) 13:56, 7 February 2010 (UTC)

You are completely correct, of course. Unfortunately this article and it's talk page are overrun by Christian Fundamentalists.Iron Condor (talk) 02:31, 25 August 2010 (UTC)
Yes, it is called unitarity. TimothyRias (talk) 12:47, 8 February 2010 (UTC)
You have no idea what you are babbeling about. Unitarity is the property of some mathematical operators. It has nothing whatsoever to do with an imagined "conservation of information" (which flies in the face of every observation of every quantum system ever performed).Iron Condor (talk) 02:31, 25 August 2010 (UTC)
Appaarently, I have a lot more idea what I'm talking about than you. Quantum evolution of a system is unitairy, meaning that the evolution operator is unitairy. In particular, this means that the time evolution of the system can be inverted (at least mathematically). This means that if you have the complete (quantum) information of the state of the universe at any one time, you should in principle have all information about the state of the universe at all other times. TimothyRias (talk) 05:49, 25 August 2010 (UTC)

## Uncertainty Principle

"This is a contentious subject since it violates a commonly assumed tenet of science—that in principle complete information about a physical system at one point in time should determine its state at any other time."

Since by the Heisenberg uncertainty principle, it is not possible to know complete information about a physical system (and in fact, the system does not HAVE an exact value for a given property when other properties are forced toward values with higher degrees of accuracy), wouldn't this render the whole paradox a non-paradox since the 'commonly assumed tenet of science' is actually the opposite of one of the tenets of quantum theory? 184.10.255.198 (talk) 05:17, 24 June 2010 (UTC)

No, it isn't. Even in quantum mechanics all information about the future and the past of a system is contained in the wave function. The wave function itself is not an observable, which makes it impossible to exactly know the wavefunction at a given time. The problem with black holes is that their presence seemingly causes the wave function to forget about its past, which is not possible in a completely quantum mechanical system.TimothyRias (talk) 07:58, 24 June 2010 (UTC)

## Expanding Main approaches to the solution of the paradox

The section "Main approaches to the solution of the paradox" should mention the Holographic principle, however, I am not able to provide deep enough inside to write about (dis)advantages... TF —Preceding unsigned comment added by TinyFirstman (talkcontribs) 22:17, 3 September 2010 (UTC)

I don't think it should be mentioned in that section. The holographic principle as used in a resolution of this paradox implies that the information is encoded at the event horizon of a black hole, and is released as part of the Hawking radiation. Therefore it's part of the approach given, Information gradually leaks out during the black-hole evaporation. However, it might be worth expanding on the holographic principle and black hole complementarity in another section of this article. Tim Shuba (talk) 01:02, 15 November 2010 (UTC)

## Information Theory

I don't know what is meant by information in the context of black holes, but suppose it means the same thing it means in Information Theory. In IT, the more unexpected a signal is, the greater the information it carries. If you come to me every day at noon and report that the sun is still working, you have conveyed very little information since that report was expected. On the other hand if you report that the sun is no longer working, you have conveyed a lot of information. It is so unexpected that I would suspect I was getting information about a failure of the sensor or the reporter.

The English language has structure. The letter u usually follows q. A u after a q conveys very little information. If I have a book that has the same number of characters as does the Encyclopedia Britannica, but all the letters in it were selected at random, the book of random characters has more information. But that book is composed of characters in straight lines. I can get even more information by letting each page be random black and white dots.

So, you have a black hole and you drop Encyclopedia Britannica into it. A long time later the black hole eventually evaporates and the Encyclopedia Britannica comes out as random thermal radiation. Not only was no information lost but the process actually increased information.

Increasing entropy is equivalent to generating information. But information is not the same as meaning or knowledge. Constant314 (talk) 04:33, 13 April 2011 (UTC)

Entropy is the opposite of information, so more entropy means less information. But what does this has to do with the article? Discussion over articles is about what we should put in them and structure them. Cogiati (talk) 08:07, 27 July 2011 (UTC)
In quantum mechanics information is conserved so increasing entropy doesn't create or destroy information. It simply scrambles it increasing the amount of fine grain information at the expense of the coarse grain information. A page with random dots has more fine grain information than a page of text but it has less coarse grain information. That explains how the two statements above that seem contradictory are actually both correct, if interpreted correctly. Constant314 is talking about fine grain information which is indeed increased by entropy. Cogiati is talking about coarse grain information which is indeed decreased by entropy. And the article is talking about total entropy which is preserved by quantum mechanics evolution operators. The increase in fine grain information achieved by dropping the encyclopedia in a black hole and then collecting the thermal radiation as described by Constant314 makes sense but you don't need a black hole to do that. Burning the encyclopedia would have a similar effect. But that's not what the article is talking about. The article is about the far more subtle question of whether black holes actually do preserve total (fine plus coarse) information as required by quantum mechanics. Stephen Hawking pointed out some strong theoretical reasons to believe that black holes may violate that tenet of quantum mechanics. But without information conservation quantum mechanics doesn't work, hence the theoretical paradox. Dauto (talk) 15:01, 3 September 2011 (UTC)

## And no-one thought of it...

If an object enters a blaack hole, it remains permanently visible. 203.129.51.101 (talk) 06:16, 15 October 2012 (UTC)

No, it does not. The light it radiates as it approaches the horizon quickly redshifts to zero. In any case, this is a wikipedia talk page. Do you have a comment on the content of this article? Waleswatcher (talk) 12:23, 17 October 2012 (UTC)

## complementarity & firewalls

i) this page is lacking a description of susskind's complemnentarity solution, which has its own page Black hole complementarity

ii) it is lacking the (recent) rebutall of this arguemnt, see eg. http://arxiv.org/abs/1207.3123 - Black Holes: Complementarity or Firewalls?

iii) is doesn't describe a remaining solution, discussed above - a violation of "no drama" at event horizon (and equivalence principle) by a firewall at the event horizon.

maybe an expert can add these things nicely? i guess iii) needs also to be added to Black hole complementarity?

Lioinnisfree (talk) 01:37, 19 December 2012 (UTC)

## multiverse

This sentence should be replaced:

"In 2004 Hawking himself conceded a bet he had made, agreeing that black hole evaporation does in fact preserve information." Michael H 34 (talk) 12:52, 11 January 2013 (UTC) Michael H 34

## Formatting

Putting URLs or references in section headings makes linking to those headings difficult, and seems to be disapproved in WP:MOS. For instances, one of the sections is now: [[Black hole information paradox#Information is irretrievably lost[9][10] ]], which would change if any sources were added above those sections. — Arthur Rubin (talk) 02:26, 9 March 2013 (UTC)

Actually, that doesn't work, either. It has to be written Black hole information paradox#Information is irretrievably lost.5B9.5D.5B10.5D. I don't know if all the [] have to be "quoted", but.... — Arthur Rubin (talk) 02:29, 9 March 2013 (UTC)

## Heat Death

Is information about the past still conserved after the heat death of the universe? Once the perfectly uniform state of maximum entropy has been reached, how can you retrieve information about the past when you know every possible history leads to the same uniform final state? In other words, shouldn't the post-heat death wavefunction of a universe where Hitler won WWII be equal to the post-heat death wavefunction of a universe where Hitler lost WWII and doesn't that imply loss of information? Or is this not what is meant by "conservation of information", is it enouh that after the heat death you could still know how much information the universe could ahve contained in the past, even though you cannot know which information existed at a certain point in time? But if that is the case then why is/was the "black hole information paradox" a paradox; a bigger black hole should produce more raditation when it vaporizes, so you would be able to infer how much matter fell into it and therefore how much information the universe could have contained before the stuff fell into the black hole? In any case the relation between increasing entropy (the loss of information as information is normally understood) and this "conservation of information" law isn't clearly stated in the article.89.99.122.33 (talk) 13:06, 5 May 2013 (UTC)