# PF member solves black hole info paradox

1. Jun 29, 2004

### marcus

Jorge Pullin co-authored a recent paper aimed at
resolving the BH information paradox. This just out

http://arxiv.org/abs/hep-th/0406260

It seems to make sense, they say look at an actual clock and
you have to admit that evolution aint unitary and states eventually decohere and before the BH evaporates the information would have
all been lost anyway!

Jorge Pullin is a PF member---he comes here occasionally and reads a thread---I've seen him at Quantum Gravity forum at least once. He and Gambini have written some intesting QG papers and he also puts up the highly informative "Matters of Gravity" newsletter. So it behooves us to notice when they have done a possibly
cool thing like resolve a paradox

Last edited: Jul 1, 2004
2. Jun 29, 2004

### jeff

Why did you feel it necessary to lie by claiming in the title of this thread that the BH information paradox has been solved?

Anyway, the most dramatic bit of evidence we have that there needn't be information loss is the string calculation in which there's an explicit accounting for all black hole microstates. No other approach has been able to do that.

Last edited: Jun 29, 2004
3. Jun 29, 2004

### marcus

"Realistic clocks, universal decoherence and the black hole information paradox"

Rodolfo Gambini, Rafael Porto, Jorge Pullin

http://arxiv.org/abs/hep-th/0406260

It looks like they did it. Probably not everyone is familiar with the BH information paradox. Here is a simple statement taken from GPP paper:

"We now turn our attention to the black hole information paradox. Simply stated (for a review see [9]) the paradox goes as follows: take a pure quantum state and collapse it into a black hole. Let the black hole evaporate. The end state is the outgoing thermal radiation, that is, a mixed state. In ordinary quantum mechanics, since evolution has to be unitary, a pure state cannot evolve into a mixed state, hence the puzzle. As we argued above, if one uses realistic clocks in ordinary quantum mechanics, pure states can evolve into mixed states. There is therefore the possibility that the collapse into a black hole and subsequent evaporation of a pure quantum state may not constitute a puzzle. The requirement is that the fundamental decoherence, that would turn the pure state into a mixed one anyway, operate fast enough to occur before the black hole evaporates entirely.

We will now show that this is the case. In a previous paper we analyzed this problem using a sub-optimal clock [10]. The current calculation yield a better picture in the sense that it implies that all information is lost by the time the black hole evaporates, ..."

[10] is the earlier paper by GPP this year in which they tackled the problem and came close but not all the way.

[10] R. Gambini, R. Porto, J. Pullin “No black hole information puzzle in a relational universe,” arXiv:hep-th/0405183.

The BH information problem is well-known, for references GPP give several sources including the review article [9] and as footnotes in
http://arxiv.org/hep-th/0405183

[9] S. Giddings, L. Thorlacius, in “Particle and nuclear astrophysics and cosmology in the next millennium”, E. Kolb (editor), World Scientific, Singapore (1996) [arXiv:astro-ph/9412046].

for more recent references, see S. B. Giddings and M. Lippert, [arXiv:hep-th/0402073] and D. Gottesman and J. Preskill, JHEP 0403, 026 (2004) [arXiv:hep-th/0311269].

Last edited: Jul 1, 2004
4. Jun 30, 2004

### marcus

From Gambini, Porto, Pullin conclusions in the paper they posted today:

"... Summarizing, we have shown that unitarity in quantum mechanics only holds when describing the theory in terms of a perfect idealized clocks.

If one uses realistic clocks loss of unitarity is introduced. We have estimated a minimum level of loss of unitarity based on constructing the most accurate clocks possible. The loss of unitarity is universal, affecting all physical phenomena.

We have shown that although the effect is very small, it may be important enough to avoid the black hole information puzzle..."

5. Jun 30, 2004

### marcus

Apparently several different attempts have been made to solve the BH info puzzle within stringy contexts:

"Several alternatives have been proposed as solutions of the black hole information problem. A good brief summary can be found in the paper by Giddings and Thorlacius [6]. Hawking [7] had proposed that unitarity is lost in quantum mechanics due to interactions with virtual black holes forming the “space-time foam”. This approach has been criticized on the grounds that it leads to the loss of the conservation of energy [8]. It should be noted that our proposal, although it has in common with Hawking’s that it leads to pure states evolving into mixed states, does conserve energy due to the particular form of decoherence (it is a Lindblad [9] type of evolution, but it is governed by the Hamiltonian and automatically guarantees its conservation, see [4].) It should be noted that other effects, like the production of virtual pairs of black holes [8] or the entanglement of the clock and the system upon evolution could lead to lack of conservation of energy, but to a first approximation energy is conserved in our approach. A second alternative that was proposed as a solution to the paradox is that the black hole does not evaporate completely, and a “remnant” containing all the information is left. A challenge for proponents of this approach is to find a satisfactory description of the remnants and to avoid infinite production rates [10]. Finally, a third avenue is to attempt to find a way to send the information out with the outgoing radiation in a process similar to quantum teleportation. A main concern is to find dynamics that is non-local enough to achieve the teleportation. Susskind has argued that string theory is non-local enough in this sense [11]. A very recent and attractive proposal along these lines is due to Horowitz and Maldacena [12] in which they propose giving a boundary condition at the singularity that transfers information to the outgoing radiation in a process similar to quantum teleportation. Recently Gottesman and Preskill have shown that one may still face non unitarities within this scheme [13]."

however all this "teleportation" stuff is a bit speculative
and the Gambini Porto Pullin treatment does away with the need for it

the hawking thermal radiation can be just that, thermal random radiation---it doesnt have to carry encoded information about what went into forming the hole---the hole can simply evaporate because the info would have gone away naturally anyway

the teleportation stuff sounds like jumping through hoops. however i will copy down the references for it in case anyone wants to research it:

[11] L. Susskind, Phys. Rev. Lett. 71 (1993) 2367; Phys. Rev. D49 (1994) 6606.
[12] G. T. Horowitz and J. Maldacena, JHEP 0402 008 (2004).
[13] D. Gottesman and J. Preskill, JHEP 0403 026 (2004).

6. Jun 30, 2004

### marcus

Congratulations to Labguy who will be 100 years old next april and who
has finally made the move out to Arizona where the air is clearer than in Florida

for some months i was seeing labguy's sig say he was about to move out to AZ where the seeing was better---better place for amateur astronomy.
now that move is accomplished
good viewing!

7. Jun 30, 2004

### Gokul43201

Staff Emeritus
8. Jun 30, 2004

### marcus

Gokul thanks for the input!

Actually that article won honorable mention in an essay prize contest in year 2000 and was by Mathur alone, not by several co-authors.
I dont think it actually resolved the paradox
but it explored changing the rules some in a particular context
(putting a technical limit on a foliation----something without clear physical meaning: the "stretching" of the leaves of the foliation)
and Mathur explored what consequence that mathematical restriction might have on the paradox.

Personally I would not say he resolved it, tho his essay did get honorable mention in the annual contest that year.

----from the abstract-----

RESOLVING THE BLACK HOLE INFORMATION PARADOX

SAMIR D. MATHUR

Department of Physics, The Ohio State University, Columbus, OH 43210, USA

The recent progress in string theory strongly suggests that formation and evaporation of black holes is a unitary process. This fact makes it imperative that we find a flaw in the semiclassical reasoning that implies a loss of information. We propose a new criterion that limits the domain of classical gravity: the hypersurfaces of a foliation cannot be stretched too much. This conjectured criterion may have important consequences for the early universe.

Last edited: Jul 1, 2004
9. Jun 30, 2004

### marcus

Gokul, your link seems to have a pay per view feature!
they only show you the abstract and then to access PDF you must
be a subscriber.

Fortunately however the same article is available free
at arxiv.

Also I see that Mathur is still trying to resolve the paradox!
he has yet again an essay on this in 2002

Here is the arxiv links to the one you cited:

http://arxiv.org/gr-qc/0007011
Resolving the black hole information paradox
Samir D. Mathur
(This essay received an "honorable mention'' in the Annual Essay Competition of the Gravity Research Foundation for the year 2000.)

Here is the more recent Mathur article

http://arxiv.org/hep-th/0205192
A proposal to resolve the black hole information paradox
Samir D. Mathur
(Essay given an `honorable mention' in the Gravity Research Foundation essay competition 2002)

Last edited: Jul 1, 2004
10. Jun 30, 2004

### jeff

You must keep in mind gokul that marcus understands little about the subjects he posts. His choice of title for this thread is a good example of this in that there are all sorts of proposals about how to deal with the idea of pure states transforming into mixed ones as black holes evaporate. (the alternative is of course that marcus knew this, but chose to lie about it as part of his lqg misinformation campaign)

The concensus is that this is a problem that will be solved only by finding the correct quantum theory of gravity since this should give us the correct microscopic picture of what's actually going on. Everything that's been published up to this point is highly speculative.

As I mentioned above, string theory does in fact provide us with a microscopic picture of all of a black hole's degrees of freedom, and is the only picture that correctly reproduces the hawking-bekenstein black hole entropy formula in the macroscopic limit, and needs no supplementary arguments.

11. Jul 1, 2004

### marcus

The way the authors handle time is interesting they go back to
a paper by Salecker and Wigner(!) showing how quantum mechanics limits the accuracy (and useful lifespan) of any real clock

here is the GPP paper
http://arxiv.org/abs/hep-th/0406260
"Realistic clocks, universal decoherence and the black hole information paradox"

their argument is pretty transparent and easy to follow (though clever)

then from Wigners clock (the light bouncing back and forth and quantum uncertainty as to the distance between the mirrors) they go to a paper of
Amelino-Camelia, Ng, Van Dam, which says that the accuracy of such a clock (or any real clock) is limited by gravity!!! because to make it more accurate you need heavy mirrors close together and eventually making the clock more accurate will cause it to collapse into a black hole!!!

In fact, a black hole is the most accurate clock available for a given mass

this is great. this is the way physics ought to look and feel.
I will quote GPP it is just too good

12. Jul 1, 2004

### marcus

---exerpt from GPP's hep-th/0406260---

...the clock collapses into a black hole (the size of the clock cannot be increased to prevent the collapse, since it would imply losing accuracy).

Infact, a black hole is the most accurate clock available for a given mass. A simple way of viewing the blackhole as a clock is to recall that when excited, black holes behave like a (damped) oscillator.

The fundamental frequency is inversely proportional to the mass of the hole, and therefore the resolution of the black hole as a clock is proportional to its mass.

Moreover, since Hawking [3] showed that black holes evaporate due to particle production, one has a maximum possible time that can be measured by a black hole clock.

If we take this time to be the black hole evaporation time, the inequality listed above is satisfied as an equality. Therefore if one wishes to measure time intervals smaller than a certain value Tmax, the optimal clock is a blackhole with lifetime (atleast) Tmax, a bigger black hole will be less accurate, a smaller one will evaporate too fast to operate as a clock.

------end quote----

Last edited: Jul 1, 2004
13. Jul 1, 2004

### marcus

so by means of a rather ingenious thought experiment they learn that the best possible clock is a black hole

and the frequency of a BH is inversely proportional to its mass

so if you make it too massive the resolution goes down because the frequency gets too low to use as a time signal

but if you make it not massive enough it will evaporate before the job is done.

so they derive an equation for delta T the time increment to be measured

$$(\delta T)^2 =\frac{\hbar T_{max}}{E}$$

where E is the rest energy of the clock, its mc2
and Tmax is the lifespan of the clock
and delta T is the resolution it has to measure

and then they solve that

$$\delta T = t_P ( \frac{ T_{max}}{t_P})^{1/3}$$

this is a beautiful formula that says you find what the lifespan is in PLANCK UNITS and you take the cube root of the lifespan and that is the resolution again expressed in natural units of time.

if you work in natural time units then, GPP say, the best resolution you can expect from any clock is the cube root of the lifespan of the clock. whoah.

14. Jul 1, 2004

### holly

Pardon, am I the only one unhappy to see PF members call other PF members names and cast aspersions on them?

I want to read about interesting things, such as these black holes, not read mean remarks that are unwarranted.

Where are the Thread Police when you need them?

15. Jul 1, 2004

### marcus

---another exerpt from Gambini Porto Pullin---

Since we have argued what an optimal clock is, we can now estimate what is the minimum rate of non-unitarity that one can expect from quantum mechanics in the real world by providing a concrete model for the spread &sigma;(T ). Notice that this effect is fundamental, it affects all physical systems and cannot be eliminated. In particular, it does not depend on any interaction of the clock with the system. Quantum systems can decohere due to other effects, and in many practical applications these will operate much faster than the fundamental effect we discuss here [7]. The latter is nevertheless ever present. The formula we get starting from (1) for &sigma;(T ) for an optimal clock is given by,

$$\sigma (T) = (\frac{t_P}{T_{max}-T})^{1/3}$$

----end quote---

you can follow it just by looking at their paper

this sigma spread function shows the rate of non-unitarity or the decoherence---intuitively they can show that the information is all gone (at this rate) by the time the BH evaporates

they really do resolve the paradox (which a lot of other people tried and failed to do with string theory and teleportation and suchlike paraphernalia)
and they do it with simple general-purpose arguments
thought experiments with the bare minimum of formulas

I think its brilliant. bravo Gambini et al

Last edited: Jul 1, 2004
16. Jul 1, 2004

### jeff

Respectfully holly,

Marcus shamelessly and regularly employs tactics to mislead naive members about physics (marcus has a kind of personal political agenda) while remaining under the radar of site administrators. What would you have me do?

As I alluded to earlier, few believe that the information paradox can be resolved by these sorts of semi-classical arguments. In fact there are many such arguments, none of which are particularly convincing. There is only one argument put forward thus far that is uniformly regarded as the strongest piece of evidence we have that there is no information paradox. And that's the string theoretic one in which black holes are constructed from d-branes so that all of their quantum states can be explicitly accounted for.

This is what I've been wondering ever since I joined PF. My conclusion is that they're not serious about looking out for the best interests of the site and will only do something if someone despite warnings repeatedly does something extreme, obvious, and completely unprovoked. Again, what would you have me do?

I have a question for you holly. Do you believe that this black hole problem has been soved as marcus claims?

My apologies to you holly for anything that I've said that has cut down your enjoyment of this site.

17. Jul 2, 2004

### holly

I can't vouch for the legitimacy of anyone's physics. I have seen a number of long-running feuds, much serious misbehavior, and two physical fights (forgive the pun) between physicists with a difference of opinion. Rather than a simple difference, I think it is the refusal of peers to "play fair" and refute things properly that leads to these brawls. I saw you come out swinging when this thread was initiated. To me, that was unwarranted, but I don't know the history of these boards. And I don't know have enough knowledge to say, "Great Scot! Those are 'fighting equations' where I come from! I'm going in..."

For all I know, marcus is a crank and this infuriates others. Or, perhaps you are a crank and this infuriates others. We know I'm a crank, but I don't have enough knowledge to infuriate others. One of my ex-husbands has a PhD in physics, and he assures me everyone on the boards is a crank.

Rest assured, if various PF members truly are sufficiently errant in their reasoning, all of the more astute people will soon be aware of that. Then remains a moral question of what to do with the knowledge...with no offense to any non-Believers, I suggest following a path of tolerance and forgiveness. This is the idea by Him they call a "Wonderful Counselor," and it's hard to follow (because naturally we enjoy tearing lesser intellects to shreds), but I've never met anyone who regretted following this path. This path does not preclude deconstructing erroneous reasoning, however. I like a fair fight.

And now, back to physics...

18. Jul 2, 2004

### selfAdjoint

Staff Emeritus
Marcus is not a crank but he is an enthusiast. He likes to bring new papers to our attention, and he has enough physics and math background to read them, but perhaps not enough to be completely at home in the broader context.

Jeff believes that Loop Quantum Gravity is a phony field, which it is not, and has a hater response when that comes up. This latest thread comes up because Marcus made a rash claim in an area where Jeff is knowledgeable and Jeff used it as a club to beat him with. I agree with you about the tone of all this, and wonder why Jeff hasn't been warned by the mentors.

19. Jul 2, 2004

### jeff

Everything marcus has ever posted here indicates quite clearly that he is in no way a crank and I've never said or thought he was. In fact I don't know how many people have pm'ed me to say they think he's a crank and in each case I've pm'ed them not just that I "disagree" with them but that they're just plain wrong. That's really never been the problem.

This is the majority view.

I think that's a bit strong. I don't "hate" lqg or any other wrong theory. I've spent just as much time on lqg as anyone here and much (much much) more than most stringy people.

I'm puzzled by alot of things about the mentors. It's as if one can get away with anything as long as it doesn't involve cursing three times in a row or something.

20. Jul 2, 2004

### marcus

Hi sA and holly,
so far no one has pointed out any flaw in the GPP paper

a reference has been made to Vafa's paper in 1996 which
"counts microstates" of an extremal BH and gets the right
entropy formula. This is old news and suggestive
that a stringy approach might succeed in elucidating more
about black holes in the future: so it holds out hope.

But getting the right entropy formula (in certain restricted
cases) does not resolve the paradox of lost information that
arises when the black hole evaporates.

Some notable stringy people, susskind, maldacena and others,
have made heroic attempts to resolve the paradox. but still
all one can say is that the impressive not-quite-pertinent 1996 result holds out hope.

By contrast, the GPP paper gives a remarkably clear straightforward
argument that goes to the heart of the paradox and may in fact
resolve it!

It would be very valuable to have people try to find some flaw or catch
in the GPP handling of the paradox.
the papers here are short----like 3 pages----and the arguments are
in a sense fundamental. they do not depend on particular paraphernalia
like the loop formalism.
they depend on work of Wigner, and general arguments

so far, AFAIK, no one has administered a beating to anyone

I find that Gambini Porto and Pullin have resolved the paradox

(One could say "But that's impossible! they aren't string theorists! Nothing but string theory, which has excellent hopes, could resolve such an
important paradox!" but that wouldnt speak to the substance.)

I have stated that it appears to me they have resolved it
and there has been some clamor.

But no flaw has been found in the paper.

I would be pleased if some objective-minded people around here would have a look at it

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