Black hole information paradox

[Passionflower]

At the singularity, worldlines *end*--anything hitting the singularity simply ceases to exist.

At the singularity proper time no longer extends but isn't it a stretch to call that ceasing to exist? Perhaps things are simply 'frozen' there?

 

[PeterDonis]

At the singularity proper time no longer extends but isn't it a stretch to call that ceasing to exist? Perhaps things are simply 'frozen' there?

This would require changing how the math corresponds to the physics. Mathematically, the singularity is a spacelike surface that is a boundary of the spacetime, and worldlines end when they reach it. Physically, a worldline ending is normally interpreted as an object ceasing to exist; similarly, the manifold having a boundary is normally interpreted as spacetime itself ceasing to exist. (Or starting to exist, in the time-reversed case; compare, for example, the classical FRW model of the Big Bang, in which spacetime itself, and the worldlines of all objects, start existing at the intial singularity; there is nothing "before" it.)

That's not to say that it would be impossible to come up with an interpretation that changed the rules at singularities; but nobody to my knowledge has ever done so. Perhaps this is because everybody expects quantum gravity to change the actual physics anyway, so there are no actual singularities in the real universe.

 

[Naty1]

Quote by Naty1

or ala ADS/CFT style,' nothing makes it to the center'...its all captured on the horizon.

ADS/CFT doesn't imply that "nothing makes it to the center"; it just says that there is no additional information inside the horizon, over and above what is captured at the horizon.

Well, Mitchell Porter's comment [my post #19] appears to reflect two alternative viewpoints that I have also seen elsewhere...Susskind for sure, maybe Smolin and/or Greene,... obviously I do not personally know which if either is correct...

In the GR approach, it appears particles/mass 'disappear' at the singularity...are 'destroyed'...where in QM approaches, like that of Susskind, seems like the degrees of freedom are 'smeared' at the horizon...I don't know if a QM 'particle' can exist after it's degrees of freedom are 'removed'...seems unlikely...

[In fact after I posted previously, I noticed Kip Thorne in BLACK HOLES AND TIME WARPS even mentions the possibility of particles transiting to another universe via the singularity! ]

I have also read of views, and I can't recall the term, of 'dual existence'...a kind of holographic copy...since we can't can't see what's inside an event horizon, duplicate copies may exist...one inside and one residing on the horizon...no violation since we can never compare nor see both...ultimately that's 'above my paygrade'...but as you already implied, 'fun' to consider...Cheers!

edit: From whence did this fancy new physicforums format emanate?? I can hardly tell which is the 'Quotes' button!

 

[bobc2]

At the singularity proper time no longer extends but isn't it a stretch to call that ceasing to exist? Perhaps things are simply 'frozen' there?

I think you are closer to the point here. I think PeterDonis is being a little presumptuous with such concepts as time and existence.

 

[PeterDonis]

In the GR approach, it appears particles/mass 'disappear' at the singularity...are 'destroyed'...

Yes, that's the standard classical GR prediction.

in QM approaches, like that of Susskind, seems like the degrees of freedom are 'smeared' at the horizon...

It's actually more like they are copied and then "smeared". See further comments below.

I don't know if a QM 'particle' can exist after it's degrees of freedom are 'removed'...seems unlikely...

In the Susskind model (he's by no means the only one advocating it or working on it, but he seems to be the current popular figurehead...), the quantum state of an infalling object is "copied" into the quantum states contained in the stretched horizon. Technically this violates a theorem called the Quantum No-Cloning Theorem, which says that you can't make an exact copy of an arbitrary quantum state.

Susskind's model gets around that by saying that since experimental results from inside the horizon can never be communicated back outside, nobody will ever actually observe a violation of the No Cloning Theorem, so it's OK. However, I don't think everybody is comfortable with that answer.

[In fact after I posted previously, I noticed Kip Thorne in BLACK HOLES AND TIME WARPS even mentions the possibility of particles transiting to another universe via the singularity! ]

This is speculative, but it seems to be a popular speculation; Hawking talks about "baby universes" (it's in the title of one of his popular books), and Lee Smolin talks about black holes spawning new universes with slightly changed physical laws as a way of explaining why the laws of our universe favor black hole formation--basically our universe is the result of an evolutionary process that favors laws that make black holes easy to form.

I have also read of views, and I can't recall the term, of 'dual existence'...a kind of holographic copy...since we can't can't see what's inside an event horizon, duplicate copies may exist...one inside and one residing on the horizon...no violation since we can never compare nor see both...ultimately that's 'above my paygrade'...but as you already implied, 'fun' to consider...

I think the Susskind view I described above falls into this category, yes.

From whence did this fancy new physicforums format emanate?? I can hardly tell which is the 'Quotes' button!

Greg Bernhardt has been working on the new format for some time, I believe; it just went live today. Overall I think it's an improvement, but I think there is an open thread somewhere for giving feedback if there's something you don't like.

 

[PeterDonis]

I think PeterDonis is being a little presumptuous with such concepts as time and existence.

I don't think it's presumptuous to describe the standard way of matching the math of a particular theory to the physics it's supposed to describe. That's quite different from claiming that a particular theory is giving us direct information about how things "really" are. Did you read my post #32?

 

[Passionflower]

In the GR approach, it appears particles/mass 'disappear' at the singularity

I do not believe GR shows that at all.

Mass certainly would not disappear, actually it would increase even more than the hole plus the mass of the particle.

Suppose a mass M_small enters a black hole, it would increase the mass of the hole:

M_total = M_hole + M_small + a little extra

Certainly non elementary particles will be 'cracked' due to increasing tidal forces however what can we say about elementary particles? How do you 'crack' an elementary particle?

Interesting thing to ponder on: where does the extra mass/energy go to as there is no pressure in a black hole?

 

[Passionflower]

This would require changing how the math corresponds to the physics. Mathematically, the singularity is a spacelike surface that is a boundary of the spacetime, and worldlines end when they reach it.

For a non-rotating black hole that is. Would it be reasonable to assume that all black holes in our universe rotate? Perhaps a completely non-rotating black hole is a physical impossibility?

Unfortunately the discussion at large (I am not particularly referring here to physicsforums but in general) limits itself to the Schwarzschild solution, I think we should really have a discussion about rotating black holes with respect to the information 'paradox'.

 

[PeterDonis]

Suppose a mass M_small enters a black hole, it would increase the mass of the hole:

M_total = M_hole + M_small + a little extra

Sure, but this has already happened as soon as the small mass crosses the horizon (the *new* horizon, corresponding to the larger final mass). The hole's mass is not "stored" at the singularity; it's a property of the spacetime as a whole.

Certainly non elementary particles will be 'cracked' due to increasing tidal forces however what can we say about elementary particles? How do you 'crack' an elementary particle?

I don't know. I don't know that anyone has come up with a specific model for how tidal forces increasing without bound as the singularity is approached will affect elementary particles. But that's a much a function of our ignorance of what "elementary particles" really are as anything else. The smallest length scale we can probe experimentally is something like 15 to 20 orders of magnitude larger than the Planck length, so even something that looks like a structureless "elementary particle" to us might have plenty of internal structure that could be "torn apart" by spacetime curvatures at the Planck scale.

Interesting thing to ponder on: where does the extra mass/energy go to as there is no pressure in a black hole?

It doesn't have to "go" anywhere; it's "stored" in the spacetime around the hole. Remember that the singularity is to the future of anything outside the horizon; all of the external effects that we attribute to the hole's mass come from the past, from whatever has fallen into the hole.

 

[PeterDonis]

For a non-rotating black hole that is. Would it be reasonable to assume that all black holes in our universe rotate? Perhaps a completely non-rotating black hole is a physical impossibility?

This is a good question, and I don't know if anyone has ever really tried to answer it rigorously. Most of the current black hole candidates that I'm aware of appear to be rotating, so in practical terms the assumption is probably reasonable.

However, a rotating black hole interior doesn't exactly "solve" the problem; it gets rid of the spacelike singularity, yes, but in its place we have an inner horizon inside which there can be closed timelike curves. Of course this is also a highly idealized solution, just like the perfectly non-rotating one is; but that just means we don't really know what goes on in the interior of a rotating black hole. (In the non-rotating case we at least have the BKL model as a more realistic interior; AFAIK there is no corresponding model for a rotating interior.)

Unfortunately the discussion at large (I am not particularly referring here to physicsforums but in general) limits itself to the Schwarzschild solution, I think we should really have a discussion about rotating black holes with respect to the information 'paradox'.

Good point, I've never seen a discussion of whether dropping a quantum object into a rotating black hole would violate unitarity. That may be because we know less about the interior (see above), so it's harder to say anything definite at all.

 

[Crazymechanic]

No offense to anyone intended but I think we are spitting out assumptions and speculation even with our standard peer reviewed accepted theories not because they would be wrong but because they are just theories and are mostly usable for one process but when there comes another one we are usually lazy and try to talk about that other too with the one theory we have.
Now the math of GR breaks at singularities and we know that yet PeterDonis you keep saying that matter and time and etc ceases to exist at singularity , well I can understand your point but honestly I don't think that we should say that firstly because the math leads us nowhere when used about singularities secondly because when we say that something ceases to exist there should be an explanation because matter can't just disappear in 'thin air" and we all know that.
Thirdly elementary particles probably get very compressed at the singularity and something happens to them but what exactly we don't know.
I guess the debate about the Event horizon and the question what's behind the doors is really a dead end for now on atleast because physics itself forbids us from exploring such places so all we are left is guessing and maths based on what we think would be logic.But our logic is just our logic not natures and as R.Feynman said "nature is going to come out the way she is" the only problem is that in the case if BH nature is not coming out instead she is going in and running away from us.

It is easy even for such known physicists like Hawking , Susskind and others to put forward theories of baby universes and etc.Because nobody can know what's really going on there , and even a quantum gravity theory no matter how good would not be the total answer because how do we know a theory is correct? Just because we see and love the way it works or we try to get empirical evidence.Now even with a QG theory just as good as Einsteins GR the problem would arise how do we measure the correctness of the theory.I can see how we do that with GR but tell me how do we probe a Singularity? Are we or will be forever left with a doubt about it just because the laws that govern both us and the universe like so? That's an open question.

Passionflower basically said it right in my opinion that proper time no longer stands and the states of matter as we know them do not stand but is that enough to suspect that matter disappears now that is what I would call a speculation.

 

[Naty1]

It is easy even for such known physicists like Hawking , Susskind and others to put forward theories of baby universes...

Perhaps, but we should remain at least open to such ideas from such experts...Peter too included...we need to work with what we have and additional clues...we need also new ideas and different perspectives even if we had a workable theory of quantum gravity we thought was complete.

Thirdly elementary particles probably get very compressed at the singularity and something happens to them but what exactly we don't know.

Don't know about the first part, I agree with the second...just what IS quantum foam??
or space...or time...an electron?? not easy issues...

 

[PeterDonis]

Now the math of GR breaks at singularities and we know that yet PeterDonis you keep saying that matter and time and etc ceases to exist at singularity

Just to be clear, I am saying that that is the classical GR prediction. I am not saying I believe that the classical GR prediction is necessarily correct. I personally think it isn't because I don't think infinite spacetime curvature is physically reasonable; I think once you get to the Planck scale (roughly, when the radius of curvature of spacetime is of the same order as the Planck length), some kind of new quantum gravity physics will take over. But that's just my opinion; it seems to be a fairly common opinion among physicists, but it's still just an opinion.

the math leads us nowhere when used about singularities

That's not really true. The math (meaning the math of classical GR as it stands) says that tidal gravity (spacetime curvature) increases without bound as the singularity is approached, just as the value of the function f(x) = 1/x increases without bound as x approaches zero. (Technically, the singularity itself, r = 0, is not part of spacetime, so we can't actually say what happens "at" it; we can only say what happens as it is approached.) There is nothing ill-defined or mathematically suspect about it at all. Whether it is physically reasonable is a separate question, but mathematically, it's perfectly valid.

when we say that something ceases to exist there should be an explanation because matter can't just disappear in 'thin air" and we all know that.

This is one of the reasons why many physicists think singularities are not physically reasonable. But it's not as simple as "matter can't disappear into thin air". The mathematical expression of that statement is that the Einstein tensor and the stress-energy tensor are covariantly conserved (their covariant derivatives are identically zero), and that's true all the way down to the singularity. The real issue is that a timelike worldline reaches the singularity in finite proper time (to be technically correct, since the singularity itself is not part of the spacetime--see above--we should say that the limit of the proper time to fall to a radius r, as r goes to zero, is finite); but some people think that's OK because spacetime curvature increases without bound as r goes to zero, which could mean that any object, even an "elementary particle", would eventually be crushed or stretched out of existence by the increasing curvature.

Thirdly elementary particles probably get very compressed at the singularity and something happens to them but what exactly we don't know.

Or they get stretched; as I said in a previous post, there is both tidal stretching and tidal compression. But you're correct that we don't know exactly what happens to elementary particles under these conditions. We don't know enough about what elementary particles are to know that, because we haven't probed them on small enough length scales, as I said in a previous post.

I guess the debate about the Event horizon and the question what's behind the doors is really a dead end for now on atleast because physics itself forbids us from exploring such places

No, it doesn't forbid us from exploring them. It just forbids us from sending our results back out to be published in a journal.

even a quantum gravity theory no matter how good would not be the total answer because how do we know a theory is correct?

This is a good question too. Some physicists seem to think that when we discover the correct "theory of everything", we will somehow be able to prove mathematically that it *is* the theory of everything. Hawking, for example, likes to take that position in his popular books. I'm not sure how many other physicists believe that.

 

[Crazymechanic]

Well i think physics itself consists of many branches , ones theorize others experiment on theory , another ones experiment on "thin air" and other ones create new theories so that the ones before them wouldn't have to experiment on "thin air" anymore.
Now you said that we can explore black holes just can't get a peer review paper back on the front page on "Nature"
Well saying that we could explore a black hole is like saying that one can explore the "underworld" or life beyond death.
In both cases it is a one way road.Turning back is not only forbidden it is impossible.The problem with mathematics especially in the case of BH is that mathematics can only work for 100% for something we can measure or atleast have a grasp about.
In the case of a BH math become a predictive tool rather than a empirical one.

The thing I maybe don't quite understand is that information is basically a given count and parameters of a particle or a system in a given state in a moment "X"
Now as time goes these states can change and we don't need a black hole even to do that it happens on daily basis.
The atoms of air and this world and the molecules were different some 1000 years ago.I mean not physically different but the atoms that made up oxygen back then could now very well be in a different state in a different material, now theoretically (philosophically) we could track them back but in real life I don't think so.
Now for the BH the matter that goes in now we say that when it would come out (if it would be possible) it would be different than when went in but on daily basis atoms fuse , decay , elementary particles like electrons emit photons and so and we don't worry about that , I guess in the case of a BH we are so worried about the so called information ceasing to exist bcause our current math tells us this scenario , now if we would suddenly come to understand the working of a singularity I think there would be a great chance for the information paradox to be cleared away.

 

[PeterDonis]

The atoms of air and this world and the molecules were different some 1000 years ago.I mean not physically different but the atoms that made up oxygen back then could now very well be in a different state in a different material, now theoretically (philosophically) we could track them back but in real life I don't think so.

This is basically the reason for the second law of thermodynamics: we can't keep track of the exact state, we can only keep track of statistical aggregates. You're correct that the presence of a black hole doesn't fundamentally change this.

if we would suddenly come to understand the working of a singularity I think there would be a great chance for the information paradox to be cleared away.

I think this is true; in fact it is basically the one thing that everyone appears to agree on. What they disagree on is their opinions about what this understanding of the working of a singularity will entail. But you're right that all that is speculation at this stage.