Saturday, January 24, 2009

Conservative solutions to the black hole information problem

Exclusively for the readers of this blog, an executive summary of my recent paper:
    Conservative solutions to the black hole information problem
    By Sabine Hossenfelder and Lee Smolin
    arXiv: 0901.3156,

which provides a classification of solution attempts to the black hole information loss problem. As a warm-up, I recommend you read my post on the Black Hole Information Loss Paradox. You will notice that in this earlier post the basic argument of the paper is already outlined. The paper just makes the definitions more precise, and discusses the options one has to solve the problem based on how radical departures from semi-classical gravity they require. Not to mention that the paper has a lot of nice figures. We have made some effort to make the paper understandable for a broad audience, so don't be shy and download the full thing.

The Core of the Problem: The Singularity

The essence of the argument is the following: A singularity is something you don't want to cross your path. Why? Because infinities are dangerous. They crunch and destroy things, they literally set an end to existence, and in doing so they are indifferent as to what exactly crossed their way. A singularity is always singular. Infinity is always infinity. As such, crossing a singularity is an irreversible process. The problem is that once an initial state ended up being singular, you can't figure out what it looked like originally.

The problem with black hole information is that evolution is not unitary if you believe that the initial state of the black hole gets converted mostly into thermal radiation to excellent precision. Non-unitarity is generally considered an unappealing property because it is in conflict with quantum mechanics and can cause all kinds of nasty side-effects you don't want. But an evolution that is not reversible cannot be unitary. Reversibility is not a sufficient, but a necessary condition for unitarity. However, since irreversibility is a characteristic of the presence of singularities, first thing you want to allow for a unitary evolution is to remove the singularity. Classically, this singularity is unavoidable. But we know that close to the singularity the curvature gets very strong (into the Planckian regime) and classical General Relativity (GR) is no longer valid. It should be replaced by a more fundamental theory that can be expected to remove the singularity, though the details are not well understood today.

The paper offers a generalization of the classical singularities in GR that can be used for spacetimes that might have quantum gravitational regions. Throughout the paper we have tried not to make any specific assumptions about the unknown fundamental theory. The problem with the classical definition of geodesic completeness is that the notion of a geodesic, which relies on the presence of a metric, might not make sense any longer in the presence of strong quantum gravitational effects. The definition we are suggesting is motivated by the classical definition, and is then what I outlined above: a space-time is non-singular if evolution is time-reversible. It then follows trivially that a singular space-time generically suffers from information loss. Thus, a black hole space-time without information loss can not be singular in the so defined sense. If you want to understand what happens to the black hole information, first thing you should do is thus to get rid of the singularity.

It is honestly a mystery to me why some people are so obsessed with the black hole horizon, believing that the horizon is the problem. The horizon is not where information gets destroyed. It is merely some surface where the information becomes irretrievable from the outside. Not to mention that the horizon can be at arbitrarily small background curvature. One thus shouldn't expect any quantum gravitational effects to be relevant at the horizon, and no reason to seek a solution there.

Radical and Conservative Solutions

Removing the singularity removes an obstacle to unitary evolution, but it doesn't explain how information survives. In the paper we discuss the possibilities one has if one just accepts that quantum gravitational effects are negligible until the very endstate of the evaporation. These solutions we have dubbed “conservative” . Everything else that requires non-locality on horizon scales or quantum gravitational effects in the weak curvature regime and so on, we have called “radical”.

The conservative solutions can be classified into three cases. In all of them it is assumed the singularity is removed by quantum gravitational effects:

  1. The information is released in the final Planck phase, in which case there never is a real event horizon (in the paper, that's option 3).

  2. The information survives in a baby universe that disconnects from our universe ( option 4A).

  3. The information survives in a permanent, massive remnant (option 4B).

Most importantly, conservative solutions imply that the endstate of black hole evaporation - when the black hole has about Planck mass and Planck size - carries a (potentially arbitrarily large) amount of information. The reason is simply that, if one accepts that the semi-classical approximation holds, Hawking radiation does not carry any information (except its temperature). Thus, the information has to remain inside. We thus have an endstate that must be able to store a large amount of information, even though it has a small surface area. This speaks in particular for the surface-interpretation of the black hole entropy. Objects with these properties are known to be possible in General Relativity, we have discussed such “bags of gold” and “monsters” in a recent post.

The three above mentioned possible cases have been discussed for some while in the literature until some time in the mid 90s. There are some objections to all of them that we address in the paper. All in all, though valid objections, they are not terribly convincing. It is thus puzzling to some extend why there hasn't been more effort invested in what seem to be the most straightforward outcomes of black hole evaporation. Unfortunately, I have had many times the impression these conservative solutions were abandoned prematurely for the sake of creating more fanciful radical solutions, for not say, absurd speculations.

A note on the definition of singularities we are using: If one had a fundamental theory to describe spacetime in the regions with strong quantum graviational effects, one could consider other notions of singular spacetimes, for example by using divergence of operators describing the background curvature or likewise. Then there arises the question how this definition would coincide with the one we have been using. One could imagine cases where they do not. Eg, the information of fields propagating in the background might not be sensitive to a curvature singularity, or the singularity itself could encode information.

Bottomline

The sane thing to do is to stick with conservative options until we are sure it's a no-go. That requires in particular understanding the properties of Planck-sized quantum graviational objects with high entropy.

210 comments:

  1. The key word is MEASUREMENT.

    Think of Feynman 2 slits experiment with and without measurement in between.

    Yes, you use classical timespace of GR, but that means you can't have radiation in between measurement, since that modifies background;

    And if you keep radiation, you are using thermodynamic equations where background is constantly modified which is consequence of measurement - you include measurement- and time ireversibility is natural.
    A.

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  2. Hi Bee,

    “If you want to generally avoid black hole formation you need to have significant modifications of the theory in regimes that we have well tested.”

    Well the last thing this physics novice would do is try to explain such a theory to a theoretical physicist. To be honest with you I don’t think the book serves well in doing it either, at least not to the level that would be required. Like I said it was a little scant on the details even for someone like me.

    As far as a significant modification that it is, with the main component being adding a vector field attributed to a particle he calls a phion that is the carrier of this new phion field which adds another (fifth force). This acts both as means to strengthen gravity to vary with an increase in distance and in combination with other aspects of the theory explain the repulsive nature (dark energy), It also is responsible for altering gravity in collapse scenarios which doesn’t allow matter to ever reach, let alone fall below what is known as the Schwarzschild radius in the GR solution. Dark Matter is also eliminated in the theory and dark energy explained with an expected not and unexpected repulsive force.

    Rather then read the book you would be probably better served by visiting his Web site and down load the main paper describing his theory and a second more recent one that discusses the cosmological consequences that it holds. To be truthful this is well beyond my understanding yet I feel probably the best way for you to assess it.

    In the end what I find as interesting is the same thing Moffat cites as the main reason he feels it’s largely ignored, that being if it were true then all the concern about the implications of black holes along with the ongoing inquiry to discover what is dark matter would all vanish simply resultant of them never having existed. He equates it with the long held notion of the ether which when all this commotion in regards to dark matter and dark energy I had at first though the same. Then when the bullet galaxy stuff came in I was convinced my initial suspicions were unfounded. Interestingly this also is one of the things he deals with and find alternative explanation for in his theory. Then again of course it’s easy for me to be so nonchalant about it, as unlike Stephen Hawkings I don’t have a entire lifetime's career tied up in such notions.

    As for being conservative, I would say that as most of Moffat’s thinking about black holes is consistent with Einstein’s, who thought in someway it would be demonstated to not be able to physically exist, I think if asked Moffat would say he was being the most conservative ;-)

    Best,

    Phil

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  3. This comment has been removed by the author.

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  4. Hi Anonymous,

    “My point then is that every semiclassical model includes measurement in it, meaning irreversibility is expected and it would be strange if there were not time-ireversibility.”

    “And any such speak about quantum nonunitarity based on semicl. calculus is non sequitur.”

    I have been trying to understand the gist of your argument along with that of Bee’s and what it seems to boil down to is that you in essence are saying any semi-classical approach by in itself is contradictory; while Bee admits as much yet says currently it’s the only way it can be approached and essentially lends a good approximation in the analysis of the situation. The way I look at is that you in essence are saying that any act of measurement is non admissible when one is talking about the quantum domain, which is what’s accepted in any semi-classical treatment. There are other notions however that also should be excluded which J.S. Bell qualified as being the following when he said:

    “Words that should be forbidden in serious discussion; system, apparatus, microscopic, macroscopic, reversible, irreversible, observable, measurement, for all practical purposes. “

    However, as you know these concepts (words) for years have been considered in the discussion of QM and continue to be, so until you come up with a quantum gravity theory (or a replacement) they will continue to be used. In the strictest sense it could be said that QM and all extensions of it since in there nature of treatment and consideration are in some ways in and of themselves semi-classical.


    Best,

    Phil

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  5. Just a note to point out that the extension and length of the comment section while it has been reduce on first appearance, can be seen in it's full entirety in two ways.

    One is by posting a comment of course. The other is to click on the time of the original posting by Bee located at the bottom of her original post.

    I am suspecting that this was the original problem( the number of comments) with the comment widget?

    Best,

    ReplyDelete
  6. hi Phil,

    there is much to be discussed about this, yes.
    Bad thing is that we always fall in semantic black hole.

    So, Bee's paper is indeed an excellent overview of conservative solutions of black hole information problem.

    ReplyDelete
  7. hmm,

    but let me try to describe it this way.

    QED is purely quantum extension of QM in a strict sense.

    Semiclassical gravity is semiclassical gravity in a strict sense - it treates matter fields as being quantum and the gravitational field as being classical.

    Newton theory is a classical theory in a strict sense.

    So - when you take even one part of your theory to be classical you enter classical regime, and therefore ireversibility etc. is natural.

    No semantic ambiguity there.
    A.

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  8. And Hawking calculation is in the context of semiclassical gravity . strictly(matter field quantum, gravity field classical)
    A.

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  9. Yes, Phil,

    all extensions of QM are classic mechanical.
    A.

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  10. Hi Anonymous,

    “all extensions of QM are classic mechanical”

    Yes just as in most circumstances QM itself is often so considered. That being that QM tells us what are the limits and probabilities of what we see in terms of outcome without actually describing a mechanism that mitigates it and thus we’ve invented a few. So truly when things like quantum gravity theories are considered they will be restricted to the same limitations. It then comes down to what you consider as most important and relevant; answers related to specific situations and circumstances or the reason behind the answers. What non-classical theory gives us more clearly is the former while classical the latter. What I’ve felt for so long as the only thing that will lead to a more true understanding is that both to be reconciled as having them becoming one in the same.

    Best,

    Phil

    ReplyDelete

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