Hawking's preprint: Information loss in Black holes

[Hans de Vries]

Found this on Woit's:


http://www.arxiv.org/abs/hep-th/0507171

Authors: S. W. Hawking
Report-no: DAMTP-2005-66

"The question of whether information is lost in black holes is investigated using Euclidean path integrals. The formation and evaporation of black holes is regarded as a scattering problem with all measurements being made at infinity. This seems to be well formulated only in asymptotically AdS spacetimes. The path integral over metrics with trivial topology is unitary and information preserving. On the other hand, the path integral over metrics with non-trivial topologies leads to correlation functions that decay to zero. Thus at late times only the unitary information preserving path integrals over trivial topologies will contribute. Elementary quantum gravity interactions do not lose information or quantum coherence.


Regards, Hans

 

[marcus]

Hi Hans, I posted notice of the hawking paper when it appeared on arxiv yesterday, in this thread
https://www.physicsforums.com/showthread.php?p=682928#post682928

and also in the "new Hawking paper" thread
https://www.physicsforums.com/showthread.php?t=82580

there has been a bit of comment in those places so far, not much though

In the new Hawking paper thread, I put a link to the text of the talk hawking gave in Dublin last year, at GR17 conference, that is rather similar to this paper he just posted
and also link to John Baez comments.

regards back

 

[Hans de Vries]

Hi Hans, I posted notice of the hawking paper when it appeared on arxiv yesterday, in this thread
https://www.physicsforums.com/showthread.php?p=682928#post682928

and also in the "new Hawking paper" thread
https://www.physicsforums.com/showthread.php?t=82580

there has been a bit of comment in those places so far, not much though

In the new Hawking paper thread, I put a link to the text of the talk hawking gave in Dublin last year, at GR17 conference, that is rather similar to this paper he just posted
and also link to John Baez comments.

regards back

Oops, missed that, There's quite a lot of posting here these days so I didn't look far enough back. It already appeared strange to me that you hadn't noticed it given your usual reaction speed.

Regards, Hans.

 

[EnumaElish]

Hi, this is from a non-physicist who hopes to follow the glitz, so to speak. My uneducated impression is that "preservation of information" is being treated similar to the postulate of "conservation of matter and energy." I am arriving at this from an understanding that seems to be part of the background to Hawking's speech: if information is not being preserved in this universe, then it must be leaking to another universe, hence the possibility of time travel etc. My question is, how is this commensurate with the 2nd law of thermodynamics (increasing disorder)? Doesn't one rather expect the information content of the universe to be decreasing over time, because of the 2nd law? Isn't a black hole gobbling up information and spewing out thermal energy the perfect mechanism for the "enforcement" of the 2nd law? Why was there a need for the information to go to "someplace else," in the first place?

If this sounds elementary, or even worse, confused, and just possibly, inconsistent, it is because this is the equivalent of me drumming fingers in an attempt to produce a Deep Purple concert, and yet hoping to be in sync with the musical giants at some level.

 

[Hans de Vries]

Hi, this is from a non-physicist who hopes to follow the glitz, so to speak. My uneducated impression is that "preservation of information" is being treated similar to the postulate of "conservation of matter and energy." I am arriving at this from an understanding that seems to be part of the background to Hawking's speech: if information is not being preserved in this universe, then it must be leaking to another universe, hence the possibility of time travel etc. My question is, how is this commensurate with the 2nd law of thermodynamics (increasing disorder)? Doesn't one rather expect the information content of the universe to be decreasing over time, because of the 2nd law? Isn't a black hole gobbling up information and spewing out thermal energy the perfect mechanism for the "enforcement" of the 2nd law? Why was there a need for the information to go to "someplace else," in the first place?

If this sounds elementary, or even worse, confused, and just possibly, inconsistent, it is because this is the equivalent of me drumming fingers in an attempt to produce a Deep Purple concert, and yet hoping to be in sync with the musical giants at some level.

The paper looks more like an extended abstract plus conclusion to me. Partly one should see this in light of the "media pressure" which is on Stephan and requires him to perform such amazing feats as solving this rather abstract puzzle. Many may envy such media attention, however often the person in question raises his or her expectations about what he or she has to achieve in a way too high to be healthy, for instance losing the feeling of self fulfillment in finding out more modest, but otherwise very useful, things.

I presume, that those who are specialists in the field would, rather than being told some end-conclusion, prefer to get some insight ideas coming out of all the time spend thinking and working on the math. For instance, why the Euclidian geometry instead of the Lorentzian geometry. He’s says a little bit more now but still in the form of a conclusion, rather than explaining how he reached that conclusion.

Off course, to solve this puzzle in one way or another one has to first proclaim a number of presumptions which are not testable or falsifiable. Like “information leaking to other universes”. It is these kind of presumptions that make the end-conclusion actually less interesting in my eyes than the experience gained by developing the math needed along the way, and it’s the latter which the specialist were hoping to see more from.


Regards, Hans

 

[Haelfix]

I love how there is an addendum at the end of the paper

'My grad student is working on a proof that nontrivial topologies decay away'

Ouch, basically one of the harder parts =)

Other than that, this is an example of a physics paper that makes claims and shows nothing concrete. The same problems as the speech more or less.

The usual complaints apply, ads/cft is already established and understood, he introduces a negative but small CC to regulate the infrared divergences, which basically trivializes the problem and begs the question.

Also its not entirely satisfying dynamically, as this is the usual Smatrix approach, and there is a bit of a disparity in what we understand at infinity and with regular time evolution (eg a usual problem with QG)

 

[nightcleaner]

Hi, this is from a non-physicist who hopes to follow the glitz, so to speak. My uneducated impression is that "preservation of information" is being treated similar to the postulate of "conservation of matter and energy." I am arriving at this from an understanding that seems to be part of the background to Hawking's speech: if information is not being preserved in this universe, then it must be leaking to another universe, hence the possibility of time travel etc. My question is, how is this commensurate with the 2nd law of thermodynamics (increasing disorder)? Doesn't one rather expect the information content of the universe to be decreasing over time, because of the 2nd law? Isn't a black hole gobbling up information and spewing out thermal energy the perfect mechanism for the "enforcement" of the 2nd law? Why was there a need for the information to go to "someplace else," in the first place?

If this sounds elementary, or even worse, confused, and just possibly, inconsistent, it is because this is the equivalent of me drumming fingers in an attempt to produce a Deep Purple concert, and yet hoping to be in sync with the musical giants at some level.

This looks like a good question to me, but of course I am at best self-educated on these topics, or perhaps semi-educated, or really, to be honest, only just barely house-broken with occassional infantile lapses. However, for what it is worth...

Seems to me that disorder is not the opposite of information, but a kind of information in itself. How do we know the entropy of a universal system? Certainly it must require information to be able to say a system is disordered...

I recall reading about the heat-death theory of the end of the universe...sometimes called the big freeze, which depends on the idea that the total mass of the universe may not be enough to overcome the forces of expansion, so that in the end, each bit of dust in the universe becomes widely separate from every other bit of dust. Eventually no information about location or temperature or anything else can be exchanged between bits. This condition is thought to lead to another big bang...total disorder becoming a new kind of order. The extreme vacuum pressure of such an empty system pulls a new universe out of the hat, so to speak.

I guess if I were to pursue this question I should have to go back to review the field known as Information Theory.

However, Hawking in this paper seems to be talking about something else. In scattering experiments, we shoot xrays or other small probes at a target and get information about the target based on where the xrays come back out. Some of the xrays are absorbed, some are bent or reflected, and some are unaffected. Think of a medical xray photograph, I am sure you must have seen one. Bones and things show up as shadows because the atoms in the bones scatter or absorb the rays.

Only Hawking is taking the case to the extreme. He considers an otherwise empty universe, with a very small radiative input from infinity. You see even the smallest amount of radiation, coming into a center point from infinity in every direction, has to produce a black hole at the center. No matter how small the radiation input at infinity, it all has to add up to an infinitely intense radiation at the center. Infinity times almost nothing is still infinite. Of course you do not need to obtain infinitely intense radiation to produce a black hole, but I hope you get the idea.

But the uncertainty principle throws a ringer. We cannot know, from infinity, exactly where the center is, so, we cannot say that all the radiation from infinity meets up in the exact center to produce a black hole. We have to use a sum over path integral method, which means that each ray has to be thought of not as having a single path, but as being a sum of every possible path. In short, a black hole does not have to form, since the energy from infinity cannot be said to meet up at a commonly determined center. Since the radiation from infinity cannot be said to meet up at the center, it doesn't all just simply add together, so a black hole does not have to be produced.

You see we can only know the three things about the black hole, that is, charge, mass, and entropy. Location is not included. In this simplified case, the information we want is one of location...is there a place where a black hole forms, or is there no such place, hence no such black hole? So you see information (in the form of a very small contribution of energy from infinity in every direction) goes in, but nothing comes back out except a question mark.

So Hawking concludes that information going into a black hole may come back out again, but if it does, it is in a form we cannot use. Hence the analogy of the burning book. Presumably the information in the text is still there in the cloud of smoke, but no one will ever have enough time or energy to get it back out again.

Now I should like to add a personal thought or two, if I have not exhausted your patience already. We have this idea of a universal set, one which contains, well, everything. Then we ask, is there anything which is not part of the universal set? That is, if there is a universe, can it have a baby, connected to itself, but not part of itself? If you say yes it can have a baby, then you are saying it is not really universal.

What is outside of the universe? Nothing. Is nothing something? You will have to decide for yourself, or, as I have done, conclude that the question is meaningless.

Now about black holes. We have ample astronomical evidence that they exist. Are they part of our universe, or do they lead to another universe? Well, what do you mean, another universe?

Here is a potential solution, but you probably won't like it.

Consider two people, let's say, George W. Bush, and Marcus the Honorable Librarian. George gets on Airforce One and proceeds to fly toward Marcus, who is sitting next to his fish pond cursing the racoons. George is in his universe, which includes everything he could ever possibly know about anything. His universe, defined this way, is limited by the speed of light. Even if George is immortal and will live forever, there are definable places from which George will never receive information. This is not due to the fact that he has a pointy little intellect, but more simply because he is moving. His motion toward Marcus (don't be afraid, Marcus, I swear I am just making this up as I go along) results in the irretrievable loss of information about the universe behind him.

Marcus, on the other hand, is sitting quite still, waiting for the little masked bandits to make their approach. He is not moving away from the end of the universe which George is fleeing, so, may he live forever, Marcus could get information about places which George can never know anything about. This is not due to the great scope and depth of Marcus' perception, but due to the fact that he is sitting quite still. As compared to George, anyway.

Marcus and George live in different universes, by this definition. There are things in the Marcus universe that will never be found in the universe George gets to inhabit, and to be fair, George has things in his universe that Marcus cannot ever know. To be sure, there is an overlap. In fact the overlap is nearly identical, but there is still this small difference.

So, The Universe does include everything, but, everything to Marcus is not identical to everything for George.

In fact, we have to give each location and each motion a universe of its own, distinct and separate, to some degree, from every other universe. There is no Universe which contains all universes. To some of the posters on PF, this will no doubt be tantamount to saying that there is no God, but I will leave that argument for another universe.

Thanks for being here,

Richard

 

[Hans de Vries]

So, is this the whole point then?

So in the end everyone was right in a way. Information is lost in topologically non-trivial metrics like black holes. This corresponds to dissipation in which one loses sight of the exact state. On the other hand, information about the exact state is preserved in topologically trivial metrics. The confusion and paradox arose because people thought classically in terms of a single topology for spacetime. It was either R4 or a black hole. But the Feynman sum over histories allows it to be both at once. One can not tell which topology contributed to the observation, any more than one can tell which slit the electron went through in the two slits experiment. All that observation at infinity can determine is that there is a unitary mapping from initial states to final and that information is not lost.

He uses an idea like 't Hooft's Holographic principle to look at the black hole
from an (infinite) distance since say "the surface enclosing the universe
should hold all information" (The ADS/CFT, Anti deSitter Space / Conformal
Field Theory stuff)

Then, although a black hole doesn't preserve information, a black hole isn't
always a black hole because of uncertainty. Result: some information should
escape when it fluctuates into a non-black hole state.

This (~infinitely?) small amount of information then grows back to unity
because unitarity must hold and the contribution of the real black hole
decays to zero (the latter is to be proved by his student Christophe Galfard )

?

For me this begs the question then how exact physics must be (to how many
digits) to reliable achieve this


Regards, Hans

 

[alias25]

hi this is prob a little off topic, but someone mentioned entropy up there and I am not sure what it is. is it a measure of disorder? of spacetime? i can't understand how you can measure disorder. i saw the equation for it somewhere with area of event horizon and c^3 and boltzman constant and planks, planks constant that's energy over frequency? but i still don't understand sorry if I am being dumb can some one explain?

 

[EnumaElish]

hi this is prob a little off topic, but someone mentioned entropy up there and I am not sure what it is. is it a measure of disorder? of spacetime? i can't understand how you can measure disorder. i saw the equation for it somewhere with area of event horizon and c^3 and boltzman constant and planks, planks constant that's energy over frequency? but i still don't understand sorry if I am being dumb can some one explain?

http://www.entropysite.com/students_approach.html has a nice summary of the second law of thermodynamics.

 

[alias25]

thanks that was a gd site i think i might be doing that in chemistry. ill get ahead of everyone.