Black hole information paradox

[ArthurDent]

I watched this documentary about an argument involving information loss in a black hole, Stephen Hawking managed to wind everybody up by claiming information was lost and therefore broke existing laws of physics.

Its an old recording so it may not be relevant anymore but one part of this argument has always puzzled me.

I think it was eventually resolved something like this, all the information about everything that fell into the black hole was stored holographically in the event horizon and this information was carried back into the universe by Hawking radiation as it evaporated.

My problem lies in the holographic information in the event horizon, it shouldn't be possible for the following reason. As a black hole's mass increases its event horizon expands. If information is stored in the event horizon then its traveling away from the singularity. The event horizon is supposed to be a point of no return.

 

[Bill_K]

You'll find a discussion of the various proposed answers to this question on the Wikipedia page "Black Hole Information Paradox".

EDIT: URL corrected! Thanks

 

[Crazymechanic]

@Bill your link appears to be not exactly correct i will put the right one.

https://en.wikipedia.org/wiki/Black_hole_information_paradox

 

[TheEtherWind]

Does anyone know the equation that Hawking came up with? It related entropy to area of the event horizon, Plancks constant, the speed of light, and Newton's gravitational constant. I've seen it before, just can't remember it.

 

[atyy]

Bekenstein-Hawking entropy

 

[kugbol]

There is no generally accepted solution to the black hole information paradox. On Wikipedia you'll see that all the proposed solutions raise other issues or are purely speculative. The paradox remains a conflict between two generally accepted theories.

 

[phinds]

There is no generally accepted solution to the black hole information paradox. On Wikipedia you'll see that all the proposed solutions raise other issues or are purely speculative. The paradox remains a conflict between two generally accepted theories.

Leonard Susskind is NOT going "like" you on facebook

 

[haael]

My problem lies in the holographic information in the event horizon, it shouldn't be possible for the following reason. As a black hole's mass increases its event horizon expands. If information is stored in the event horizon then its traveling away from the singularity. The event horizon is supposed to be a point of no return.

The information is not flowing from the singularity. It was stored in the horizon from the very beginning. You may imagine that when you fall into a black hole, the horizon "scans" you and stores the full information about you.

The horizon in this picture is not spherical. Rather, it is wrinkly. It stores information about you in local displacements. It is only spherical on average. In fact, information of the object falling into black hole is stored in waves moving along the horizon, just like the shape of an object falling into water is stored in the waves.

 

[kugbol]

The horizon of a black hole is not a special place, according to general relativity. If the horizon "scans" you and stores the full information about you, then I'm being scanned right now, in my non-special place. With no evidence to support it, the idea is indistinguishable from science fiction, like the baby universe proposed solution on Wikipedia.

 

[haael]

The horizon of a black hole is not a special place

It is special. It's the point from where you can not return. From your words one may deduce that the horizon doesn't exist at all.

You can not locally detect the exact horizon position. But that doesn't mean it doesn't exist.

If the horizon "scans" you and stores the full information about you, then I'm being scanned right now, in my non-special place.

In a sense, yes. If we are now falling into a black hole, or even if we are orbiting it (and we do), we are affecting the hole's horizon. We are in the process of "scanning". A part of our information is leaking onto the black hole surface.
When we completely submerge under the horizon, our scan would be completed.

It's all just a consequence of the fact, that our gravity affects the black hole's horizon shape.

It's Susskind's idea, by the way.

With no evidence to support it

It will still take few more years before we start making experiments with actual black holes. Until then, the only thing we have is theory.

 

[PeterDonis]

You can not locally detect the exact horizon position.

That's what I think kugbol meant by "the horizon is not a special place". You and others are saying that the horizon somehow "scans" objects as they fall through it. But how does the horizon know that it is a horizon? How does it know that it is supposed to do the scanning, if there is no way locally to detect the exact horizon position?

This is a key issue with the "horizon scanning" proposal (which Susskind supports, but it's not solely due to him). The responses to it basically involve invoking some sort of quantum phenomenon that *does* "know" where the horizon is; in other words, saying that classical GR is no longer valid close to the horizon, because quantum effects become non-negligible there even if the classical spacetime curvature *is* negligible (which it is for a large enough black hole).

 

[haael]

You and others are saying that the horizon somehow "scans" objects as they fall through it.

That was an analogy, lol.

But how does the horizon know that it is a horizon?

The position of the horizon is an objective thing. You are either under the horizon or over it, for all observers. If you dive into a horizon, there's no reference frame where you didn't.

It's the same for the equivalence principle. You can not locally distinguish between acceleration and gravity, but the gravity does exist, doesn't it? Earth generates it's own gravity and no reference frame can deny it. You just can't tell if you are falling on Earth when you are closed in a box.

How does it know that it is supposed to do the scanning, if there is no way locally to detect the exact horizon position?

There's no need for any physical entity to do the scanning. The only thing you need to understand is: the shape of the horizon depends on the mass distribution around the black hole. When some massive object approaches a black hole, the horizon deforms. Think of it: the object has it's own attractive force, so a particle sitting on the very edge of the horizon is attracted by it. If the object were a little closer, the particle would be attracted a little bit stronger. So, it could escape the black hole. That means, it was not on the horizon. In fact, the horizon backs off a little bit when a massive object approaches it.

Now, the key idea of Susskind: the horizon shape depends also on distribution of mass inside a black hole. When a massive object falls into a black hole, it gets a little bigger. Does it get bigger immediately, preserving its spherical shape? No, that would violate the speed of light limit. In fact, it gets a "bump" in the place where the object has fallen, just like a wave on water. The bump then flows all over the horizon and flattens. The hole becomes approximately spherical again, but the wave remains forever.

The position of a horizon when viewed globally, depends solely on the mass distribution of nearby objects. But when viewed alone, it looks exactly like a fluid surface. It's not just an analogy. The equations of horizon evolution are exactly the same as for fluid surface dynamics. Honestly I haven't actually seen them, but Susskind say so.

 

[PeterDonis]

The position of the horizon is an objective thing. You are either under the horizon or over it, for all observers. If you dive into a horizon, there's no reference frame where you didn't.

This is all true, but it doesn't explain how the states of infalling objects get stored at the horizon.

It's the same for the equivalence principle. You can not locally distinguish between acceleration and gravity, but the gravity does exist, doesn't it? Earth generates it's own gravity and no reference frame can deny it. You just can't tell if you are falling on Earth when you are closed in a box.

And for the same reason, you can't tell if you're at the horizon when you're falling past it. So how can your state get stored there? More precisely, why would your state get stored there, particularly, as opposed to anywhere else? Why isn't a copy of your state getting stored right now in the space you occupy? (Which it isn't, according to the model you're describing.)

There's no need for any physical entity to do the scanning.

Yes, there is. This discussion might be better in the Quantum Physics forum, though, since the "scanning" is a quantum phenomenon. According to the model you are talking about, there is some quantum process at the horizon (actually in the "stretched horizon", a boundary layer that extends for a Planck length above the horizon) that makes copies of the quantum states of objects falling through the horizon. But why should that happen only at the horizon?

The only thing you need to understand is: the shape of the horizon depends on the mass distribution around the black hole. When some massive object approaches a black hole, the horizon deforms. Think of it: the object has it's own attractive force, so a particle sitting on the very edge of the horizon is attracted by it. If the object were a little closer, the particle would be attracted a little bit stronger. So, it could escape the black hole. That means, it was not on the horizon. In fact, the horizon backs off a little bit when a massive object approaches it.

I'm not sure where you are getting this from. It's not wrong, exactly, but it's misleading. The horizon is not a "thing". It's the boundary of a region of spacetime that can't send light signals to future null infinity. Saying that the horizon "deforms" is just saying that that region of spacetime has an asymmetric shape, at least for some period of time.

Also, I think you are misunderstanding what happens to the horizon when a massive object is falling in; the horizon does not "back off" when that happens. It expands. The fact that the massive object pulls "upward" on an object close to the horizon is more than compensated for by the fact that the massive object is falling inward.

It would help if you would give a specific reference; I suspect that you are misinterpreting at least some of what you're reading about this topic.

Now, the key idea of Susskind: the horizon shape depends also on distribution of mass inside a black hole. When a massive object falls into a black hole, it gets a little bigger. Does it get bigger immediately, preserving its spherical shape? No, that would violate the speed of light limit.

Again, I think it would help if you would give a specific reference. I strongly doubt that Susskind has said what you're paraphrasing here, since it's wrong. When a massive object falls into a black hole, the horizon expands *before* the object reaches it.

In fact, it gets a "bump" in the place where the object has fallen, just like a wave on water. The bump then flows all over the horizon and flattens. The hole becomes approximately spherical again, but the wave remains forever.

This is not entirely correct either. The horizon does expand asymmetrically at first, and the asymmetry does turn into waves. But the waves (gravitational waves) are radiated away to infinity; they don't stay on the horizon. The horizon does settle down to a spherical state (at least, in the idealized case where the infalling mass adds no angular momentum to the hole).

There are, according to the quantum model that Susskind and others have proposed, wavelike quantum states in the "stretched horizon" (see above). But they don't make the horizon non-spherical or only approximately spherical. The waves are quantum waves; they are waves in Hilbert space, not waves in ordinary space.

The position of a horizon when viewed globally, depends solely on the mass distribution of nearby objects.

No, it doesn't. It depends on the massive object that originally collapsed to form the hole.

But when viewed alone, it looks exactly like a fluid surface. It's not just an analogy. The equations of horizon evolution are exactly the same as for fluid surface dynamics. Honestly I haven't actually seen them, but Susskind say so.

Again, can you give a specific reference? I suspect you are misinterpreting what Susskind says.

 

[kugbol]

Susskind's idea applies as well to the border between the Pacific and Indian oceans. I can design my equation for the border such that a bump flows over that border when a ship passes through it. But if you conducted a physical experiment where my equation says the border is, to find information about the ship encoded in the border, you wouldn't expect to find any.

 

[Crazymechanic]

Well as for what Peter said i would agree that logically the EH should expand a little when a massive body approaches it just like the water level rises when moon is close because two bodies with mass attract each other , I know that because I'm writing this from a laptop that just fell from the desk.:)

Now maybe I'm wrong with this but does the information necessarily needs to be conserved just like a book put into a cabinet and then taken out again in the same state with nothing changed or maybe it is more like when you burn wood or any other material,the material doesn't disappear instead it is transformed into different states of matter like solid to gas and one chemical to another.
But as long as speaking that information could be lost or is lost , well then the question goes can you pick up the smoke from the burning wood later and tell that it cam from an object that was round or rectangular or how big it actually was , I think you can't.
Just as after thousands of years the original Chernobyl reactor with all the buildings and town around it may long be demolished and recycled but the higher levels of radiation may still be there as to a reminder of what was the original state of the system years ago before changes happened.
What I want to say is that states are changing with time and under certain circumstances and the information is not always preserved in a classical way rather the consequences or the outcomes are determined by the input or by what was there so maybe the information or conserved only in that matter.
As if you would throw a dog into a black hole you could not get a dog out if it even if there would be a way to dissolve one and stop it from being a black hole.Just like you take a cd format audio recording then decode and compress it to a mp3, you cannot get back the original quality from the mp3 as some of the data is lost , some is transformed and some is overlapped in places where the coding algorithm found that they can be overlapped.

For information to be preserved at the event horizon aka scanned that would rather mean that the EH is some kind of a physical place full with information as basically information is a property of matter and cannot be without it.Like there is no mind without the physical neurological processes taking place in one's brain.
Rather the EH is just the barrier after which gravity is so intense that (the point of no return) not even light cannot escape or the escape velocity is higher than c , so that in falling matter is just broken up compressed , changed (in terms of atomic structure) .

To add to the general discussion not my personal thoughts the question would be, how does the EH scan and preserve something if it's not a physical thing itself rather a point or line or a border after which "we can't see" ?
There is no Event horizon from the viewpoint of the black hole nor for the observer falling into one , it's just a glimpse for us , then how come it store something?Like information? It's not even a glimpse as there are no reflections either as the light before the EH hasn't "seen" what's in it and after it does we can't see it anymore nor the story it would have to tell so...

 

[haael]

Well as for what Peter said i would agree that logically the EH should expand a little when a massive body approaches it just like the water level rises when moon is close because two bodies with mass attract each other

The opposite. The horizon contracts when an object approaches it. It then expands when an object has fallen into it. You may call it a repulsive force if you wish.

This is all true, but it doesn't explain how the states of infalling objects get stored at the horizon.

Imagine a world full of black holes. They are in such proximity one to each other, that they deform they own horizons. You can have a full description of that universe by writing down positions, masses and momentums of all black holes singularities.

Thesis: You can restore the full information of the universe from the shape of all horizons.

In other words, there is one-to-one correspondence between the set of all configurations of singularities and the set of all configurations of horizons. When you move one black hole into other place, it will affect other's horizons different way. You can restore the information of the shift by checking how all horizons changed shape.

You may call it a coincidence, but the dynamics of horizons closely resembles fluid dynamics. When the singularities are moving according to Einstein equation, the horizons are changing shape like a fluid surface.

Now imagine two colliding black holes. Their horizons will be severly distorted when it happens. After the two holes have finally merged, the horizon of the new big hole will not be still. It will be distorted as well.

Thesis: you can deduce the whole past history of a black hole from its horizon shape.

The spherical horizon of a Schwarzschild hole is a special case of a stationary hole that has existed from infinity and will exist for eternity. Any other black hole will have a different horizon shape. If you somehow get to know the exact shape of the horizon, you instantly know all the history of the hole, including the information about all objects that have fallen into it. Provided that the world is deterministic, you also know the future.

Black holes of different shapes affect their environment different way. That means - the information about the event horizon shape leaks away of it, despite it may be hard to measure directly. Since we know that the horizon shape holds all information about the hole past, we deduce, that the information of objects that have fallen into black hole leak away from it.

Now, let me repeat: You don't need the horizon to be a physical entity. You don't have to have any fabric that exists positively and builds the horizon. The horizon is just a place in the spacetime, with no special local properties. It has however special global properties. It is a border of a region of space, where you are destined to meet a singularity. It's the singularities positions that hold the actual information. The horizon only mirrors that information. But thanks to the mirroring, you can restore the information of the current, past and future (if the world is deterministic) configuration of singularities positions. This also allows you to fetch information about objects that have fallen into a hole.

This is the solution to the information paradox by Susskind. When an object falls into a hole, you loose information about it, since it disappears from our universe. But the information is still held in the horizon shape. This way, the information is preserved.

The position of a horizon when viewed globally, depends solely on the mass distribution of nearby objects.

No, it doesn't. It depends on the massive object that originally collapsed to form the hole.

Yes, I mean - it depends on the objects that have fallen into the hole and the objects that are outside it. The singularity is also "near" the horizon.

 

[PeterDonis]

The horizon contracts when an object approaches it.

No, it doesn't. Where are you getting your information from?

Imagine a world full of black holes. They are in such proximity one to each other, that they deform they own horizons.

No, their horizons will merge into one. It will not be a static situation.

You can have a full description of that universe by writing down positions, masses and momentums of all black holes singularities.

Reference, please?

Thesis: You can restore the full information of the universe from the shape of all horizons.

Is this something you just made up, or do you have a reference?

In other words, there is one-to-one correspondence between the set of all configurations of singularities and the set of all configurations of horizons. When you move one black hole into other place, it will affect other's horizons different way. You can restore the information of the shift by checking how all horizons changed shape.

Again, reference please?

You may call it a coincidence, but the dynamics of horizons closely resembles fluid dynamics. When the singularities are moving according to Einstein equation, the horizons are changing shape like a fluid surface.

The singularities don't move. They are spacelike surfaces; i.e., they are instants of time. They are not locations in space. Where are you getting all this from?

Now imagine two colliding black holes. Their horizons will be severly distorted when it happens. After the two holes have finally merged, the horizon of the new big hole will not be still. It will be distorted as well.

That depends on how the holes collide. If they started out with angular momentum relative to one another, then yes, the final hole will not be spherical; it will be oblate, because it's a rotating hole (i.e., a Kerr black hole, not a Schwarzschild black hole). But its shape will be exactly oblate; it won't be "distorted".

Thesis: you can deduce the whole past history of a black hole from its horizon shape.

The spherical horizon of a Schwarzschild hole is a special case of a stationary hole that has existed from infinity and will exist for eternity. Any other black hole will have a different horizon shape.

Incorrect. Any system with zero angular momentum that collapses to a black hole will form a precisely spherical hole. There are many different possible systems like that, and you can't tell from a spherical hole which one collapsed to form it.

Once again, where are you getting all this from?

If you somehow get to know the exact shape of the horizon, you instantly know all the history of the hole, including the information about all objects that have fallen into it. Provided that the world is deterministic, you also know the future.

Incorrect. Where are you getting this from?

Black holes of different shapes affect their environment different way. That means - the information about the event horizon shape leaks away of it, despite it may be hard to measure directly. Since we know that the horizon shape holds all information about the hole past, we deduce, that the information of objects that have fallen into black hole leak away from it.

Reference?

Now, let me repeat: You don't need the horizon to be a physical entity. You don't have to have any fabric that exists positively and builds the horizon. The horizon is just a place in the spacetime, with no special local properties. It has however special global properties. It is a border of a region of space, where you are destined to meet a singularity.

No, it's the boundary of a region of *spacetime* that can't send light signals to future null infinity. That's the definition. The fact that there must be a singularity inside is an *additional* statement, that will hold if certain conditions are met. It is not equivalent to the statement that there is a horizon.

It's the singularities positions that hold the actual information.

Singularities don't have positions; they are spacelike surfaces.

The horizon only mirrors that information. But thanks to the mirroring, you can restore the information of the current, past and future (if the world is deterministic) configuration of singularities positions. This also allows you to fetch information about objects that have fallen into a hole.

Reference?

This is the solution to the information paradox by Susskind. When an object falls into a hole, you loose information about it, since it disappears from our universe. But the information is still held in the horizon shape. This way, the information is preserved.

Once again, I think you are seriously misinterpreting what Susskind says. Can you give any actual references? If you can, do so. If not, stop making statements that you can't support.

Yes, I mean - it depends on the objects that have fallen into the hole and the objects that are outside it. The singularity is also "near" the horizon.

Incorrect. The singularity may or may not be "near" the horizon, depending on your definition of "near" and on how massive the hole is. Also, "near" in this connection means "near in time", *not* "near in space". The singularity is not a "place in space"; it is an instant of time.

(Technically, if the black hole is rotating, it's more complicated than that; but you don't appear to even understand the idealized non-rotating spherical case, so there's no point in going into the further complications of the idealized rotating case. Most black hole physicists don't believe the rotating Kerr black hole interior is physically reasonable anyway.)

 

[PeterDonis]

Well as for what Peter said i would agree that logically the EH should expand a little when a massive body approaches it just like the water level rises when moon is close because two bodies with mass attract each other

This logic only holds if the horizon is a "thing". It's not. It's a global phenomenon, not a local one. The reason it expands *before* an infalling massive object reaches it is that the infalling massive object is going to reach it. In other words, to know the exact location of the horizon, you have to know the entire future of the spacetime; you have to know all the objects that will fall into the hole in the future, and when they will fall in.

Now maybe I'm wrong with this but does the information necessarily needs to be conserved just like a book put into a cabinet and then taken out again in the same state with nothing changed or maybe it is more like when you burn wood or any other material,the material doesn't disappear instead it is transformed into different states of matter like solid to gas and one chemical to another.

In the first case, there is no change in entropy (at least in the idealized case where we assume that putting the book into the cabinet is perfectly reversible--in real life it wouldn't be because you would need to expend energy to move the book back and forth, which would increase entropy). In the second case, there is. When an object falls into a black hole, entropy increases, so it's more like the second case.

However, when physicists talk about the "information loss problem" of black holes, they are talking about something different. In your second case, where a material burns, at the atomic level (at least according to our best current understanding) the process is completely reversible; if you could keep track of the exact states of all the atoms, you could reverse the process exactly and "unburn" the wood. (Of course, you would also have to make sure you did everything in a closed box so none of the atoms would escape.) The reason we say that entropy increases when the wood burns is that we *can't* keep track of all the states. But that doesn't mean the "information" is destroyed; it just means it's not accessible to us. I.e., the information is still there in principle, but for practical purposes we can't make use of it.

When an object falls into a black hole, something different happens; when the atoms in the object hit the singularity at the center, they are destroyed, and all the information they carry is destroyed along with them. In other words, there is *no* way to reverse the process, even if you could keep perfect track of all the atoms' states up to the point where they hit the singularity. Once they hit the singularity, it's irreversible *in principle*, not just for practical purposes.

At least, that's the classical prediction. However, in quantum mechanics there is something called "unitarity", which basically says that nothing like that can happen to a quantum system. So dropping a quantum object into a black hole and having it hit the singularity would violate unitarity. Physicists like Susskind believe that violating unitarity is a worse problem than violating classical General Relativity, so they believe that something must happen at the quantum level to prevent unitarity from being violated. The "scanning at the event horizon" model (that's not really a good name for it, see below) appears to be the best current hypothesis for *how* unitarity is preserved.

For information to be preserved at the event horizon aka scanned that would rather mean that the EH is some kind of a physical place full with information as basically information is a property of matter and cannot be without it.

Yes, this is one of the objections to the "scanning" model: how does whatever-it-is that stores the information at the horizon "know" that it is at the horizon? The alternative is that information is being "scanned" everywhere, not just at the horizon. I'm not entirely sure what the current position is on questions like this; see further comments below.

Rather the EH is just the barrier after which gravity is so intense that (the point of no return) not even light cannot escape or the escape velocity is higher than c , so that in falling matter is just broken up compressed , changed (in terms of atomic structure) .

But it isn't; at least, classically it isn't. Classically, spacetime curvature at the horizon can be as small as you like, for a black hole of large enough mass; and therefore the atomic structure of an object falling through can remain perfectly intact.

One of the possibilities for resolving this is that there are quantum corrections to the classical behavior that become large near the horizon. In other words, when you add quantum fields to the spacetime, the horizon is no longer just a globally defined boundary; there is now actual local physics going on that makes the horizon seem like it's filled with hot gas, even to an observer that is freely falling inward. However, I don't think this possibility is widely accepted, since it is open to the same question as above: how does the quantum field "know" that it is near the horizon?

To add to the general discussion not my personal thoughts the question would be, how does the EH scan and preserve something if it's not a physical thing itself rather a point or line or a border after which "we can't see" ?

Yes, as I said above, this is the question, how does whatever is storing copies of infalling quantum states "know" that it is at the horizon? I have read quite a bit of what Susskind and others have written and I'm not sure what their answer is.

There is no Event horizon from the viewpoint of the black hole nor for the observer falling into one

Yes, there is. The horizon is not frame-dependent. But there is no way to know exactly where it is without knowing the entire future of the spacetime, as I said above.

 

[Naty1]

In these forums we usually discuss absolute/true and apparent horizons. Susskind utilizes another, the 'stretched horizon' described below. Whatever is 'right' or 'wrong' Susskind says in his book that Hawking came to agree with him.

Note the very interesting pg 434 claim!


I've posted the following before on this topic:

Leonard Susskind, THE BLACK HOLE WAR (his arguments with Stephen Hawking)

Black Hole Complementarity

In this view, all the information ever accumulated by a BH is encoded on a stretched horizon...a Planck length or so outside the event horizon and about a Planck length thick. This is a reflection of the Holographic principle: all the information on the other side of an event horizon is encoded on the surface area of that event horizon...

[pg 434] Of every 10,000,000,000 bits of information in the universe, all but one
are associated with the horizons of black holes. [So if you can lose information via black holes, it a really,really,really big deal….]


(p238) Today a standard concept in black hole physics is a stretched horizon which is a layer of hot microscopic degrees of freedom about one Planck length thick and a Planck length above the event horizon. Every so often a bit gets carried out in an evaporation process. This is Hawking radiation. A free falling observer sees empty space.

(p258) From an outside observer’s point of view, an in falling particle gets blasted apart….ionized….at the stretched horizon…before the particle crosses the event horizon. At maybe 100,000 degrees it has a short wavelength and any detection attempt will ionize it or not detect it!

(p270)…. eventually the particle image is blurred as it is smeared over the stretched horizon and….and the image may (later?) be recovered in long wavelength Hawking radiation.



Here are two descriptions of horizons which I like:


Two 'simple' ones first:
from Roger Penrose:

There is no mass as we know it (inside); inside all particles have been destroyed and gravitational effects remain outside the event horizon along with a few characteristics (electric charge, spin, etc).

Mitchell Porter posts: [from a forums discussion]

... the idea is that the interior of the black hole has a dual (holographic) description in terms of states on the horizon; a lot like AdS/CFT, with the horizon being the boundary to the interior. So when someone crosses the horizon from outside, there's a description which involves them continuing to fall inwards, until they are torn apart by tidal forces and their degrees of freedom redistributed among the black hole's degrees of freedom, all of which will later leak away via Hawking radiation; but there's another description in which, when you arrive at the horizon, your degrees of freedom get holographically smeared across it, once again mingling with all the black hole's prior degrees of freedom (also located on the horizon), which all eventually leak away as Hawking radiation

and another more technical description:

https://www.physicsforums.com/showthread.php?t=631987&page=3...:

The event horizon of a black hole is actually lightlike. This follows from it being a null surface, and you can even think of the event horizon as being "trapped light". “the EH is a null surface--more precisely, it has two spacelike and one null dimension.”

PAllen & PeterDonis…… the event horizon is a 3-surface whose tangent space at each point can be given a basis that has two spacelike basis vectors and one null basis vector…the EH is not a "thing". It's just a boundary between two regions of the spacetime.,,,, The strictly correct way to state it would be to say "looking at the spacetime as a whole, as a 4-dimensional geometric object, this particular null surface is an event horizon"…..The technical definition of black hole event horizons cannot be satisfied in a closed universe. There is no infinity to escape to…

I am unsure of the source for the following explanation...but I have seen multiple explanations which are generally similar:


The technical definition of black hole event horizons cannot be satisfied in a closed universe. There is no infinity to escape to…

An apparent horizon avoids the future dependency problem precisely because it forms later and is generally inside the true event horizon. By virtue of forming later and being smaller, it responds to events which are quasi-locally committed, and not to things like a star interacting with a black hole in the future…An event horizon's definition is not causal. It is a feature of a complete spacetime manifold, which is the complete history of some hypothetical universe.

[] enclosed my additions

For a collapsing [mass?] shell, the true horizon starts forming while the shell is still a little beyond its SC radius, and it starts at a point. The apparent horizon forms a little later, when the shell is at the point of no return, and it can jump [discontinuously] into existence at a finite radius. It is still true that there is no matter at the center and no singularity when the apparent horizon has formed….The event horizon doesn't exist for a free falling observer. This is the same as a Rindler horizon - it only exists for accelerating observers, not for inertial observers.


In other sections of his book Susskind explains the stretched horizon and Hawking radiation in terms of STRINGS:...he envisions the stretched horizon as composed of strings and from time to time quantum fluctuations cause a section of a string to lump up..and these can break from the main string an escape...'radiation' is born.

 

[PeterDonis]

The technical definition of black hole event horizons cannot be satisfied in a closed universe. There is no infinity to escape to…

Yes, correct. More precisely, there is no future null infinity in a closed universe that recollapses.

An apparent horizon avoids the future dependency problem precisely because it forms later and is generally inside the true event horizon. By virtue of forming later and being smaller, it responds to events which are quasi-locally committed, and not to things like a star interacting with a black hole in the future…

The apparent horizon is local because it has a local definition: it is a surface at which outgoing light rays don't move outward. This is locally measurable. It has nothing to do with the apparent horizon forming "later" than the event horizon or being inside it; those are global features, not local ones. IIRC there are cases in which an apparent horizon can form outside the event horizon.

An event horizon's definition is not causal. It is a feature of a complete spacetime manifold, which is the complete history of some hypothetical universe.

I agree with the second sentence, but it doesn't imply the first. An event horizon is a causal boundary, like any null surface.

The event horizon doesn't exist for a free falling observer.

The EH is a global feature of the spacetime; it is not observer-dependent.

This is the same as a Rindler horizon - it only exists for accelerating observers, not for inertial observers.

This is one way in which the analogy between the EH and the Rindler horizon breaks down. There are different Rindler horizons for different accelerating observers, so the Rindler horizon is observer-dependent. But in any given spacetime with an event horizon, the EH is the same for all observers.

 

[Naty1]

PeterDonis posts:

Quote by Naty1
An apparent horizon avoids the future dependency problem precisely because it forms later and is generally inside the true event horizon. By virtue of forming later and being smaller, it responds to events which are quasi-locally committed, and not to things like a star interacting with a black hole in the future…

Peter explains:
The apparent horizon is local because it has a local definition: it is a surface at which outgoing light rays don't move outward. This is locally measurable. It has nothing to do with the apparent horizon forming "later" than the event horizon or being inside it; those are global features, not local ones. IIRC there are cases in which an apparent horizon can form outside the event horizon.

Yes to the first two sentences of yours, am unsure I understand the significance of the rest...

I think a clearer description than the one I posted [and I would have used, but I could not find in my notes and so had to type again from my notes, arggghhhh!] is this from Kip Thorne's book "Black Holes and Time Warps", Box 12.1...

It provides some context for 'later'...and strongly suggests apparent horizons are generally 'smaller'...but I am unsure just why...

The absolute horizon is created at the star's center well before the star's surface shrinks through the critical circumference. The absolute horizon is just a point when created,but it then expand smoothly...and emerges through the star's surface precisely when the surface shrinks through the critical circumference. It then stops expanding and thereafter coincides with the suddenly created apparent horizon...

Hawking could see... that the areas of absolute horizons [but not necessarily apparent horizons] will increase not only when black holes collide and coalesce but also when they are being born, when matter or gravitational waves fall into them..and when rotational energy is being extracted from the swirl of space just outside their horizons...

Hawking was well aware that the choice of definition of horizon, absolute or apparent, could not influence in any way predictions for the outcomes of experiments. However the choice of definition could strongly influence the ease with which theoretical physicists deduce...the properties and behaviors of black holes.

 

[PeterDonis]

I think a clearer description than the one I posted [and I would have used, but I could not find in my notes and so had to type again from my notes, arggghhhh!] is this from Kip Thorne's book "Black Holes and Time Warps", Box 12.1...

The thing about this description of apparent horizons is that the details only apply to the case where a massive object is collapsing to form a black hole, or where a massive object is falling into an already formed black hole. It doesn't cover any other cases; in particular, it doesn't cover black hole evaporation. (It also, I believe, doesn't cover rotating black holes, at least not without complications; but I haven't seen a lot of discussion of that case.) So I don't think you can make general assumptions about how apparent horizons work from this description.

Also, for extra fun, the notion of an apparent horizon is actually not invariant. There was a thread about this some time back, IIRC. (The absolute horizon is, of course, invariant.) The key is that the definition of an apparent horizon, that outgoing light rays no longer move outward, depends on the definition of "outgoing" light rays; but that definition is frame-dependent.

 

[Crazymechanic]

I was away for a while came back saw that the discussion has continued, well some responses from me...

@PeterDonis Now I understand this is not your personal theory but you say that when atoms from an object hit the singularity they are destroyed now destroyed can mean a lot of things , a crashed car , a broken computer , a tv that just hit the pavement from the fifth floor.
But how does one destroy an atom?
I mean you can have huge pressures and temperatures and fuse atoms and make new elements and radiation and heat and etc but in a black hole none of that ever gets released so to me it looks more like a 100% tight hermetically sealed blender you throw some things (matter) in it and it just blends and blends and everything inside is vaporized or so but those vapor never get to escape.
I mean you do have interactions and elements turning into different ones but how do you destroy something? Or maybe in the case of BH the word destroy suddenly has a totally new meaning , totally non classical?
Now if the information is destroyed in the sense that after matter has gone inside and underwent rapid interactions it has turned to different states which if suddenly released would not turn back into the ones that fell in then yes that sounds logic.

 

[Naty1]

when atoms from an object hit the singularity they are destroyed...But how does one destroy an atom?

that's beyond GR and QM, but I can think of a few possibilities...

MAYBE an approximate way to think about what MIGHT happen along the way: if all particles are point like, then you can compress a lot of them and the aggregate will remain pointlike...no dimension, no volume...unrecognizable...just squished together...
except that Heisenberg uncertainty means... "everything becomes unrecognizable in a quantum foam'...space,time,matter,force lose their meaning. [I just noticed Kip Thorne describes the singularity almost precisely this way.]We do know electrons get pushed into protons [electron degeneracy] and the nuclei get crushed [neutron degeneracy] ... on the way to a BH and even neutron stars and for those we have equations we believe are accurate. Degenerate electrons and neutrons are spaced much closer [and any separation likely diminishes further closer to a BH singularity] so the DeBroglie wavelength is much shorter...that's one intuitive way to try to think about 'matter converting to energy'...but I'm not sure anybody knows exactly what happens in such conversions...oh yeah there must be binding energy changes too...like fusion and fission...

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

edit: Another view is via topological mathematics...and I am completely blind here...but Thorne mentions [pg 465] briefly that a singularity may involve topological changes...and he says '..Roger Penrose triggered a revolution in our research...tools that are now called "global methods" in the early 1970's...

 

[Naty1]

Peter Donis:

The thing about this description of apparent horizons is that the details only apply to the case where a massive object is collapsing to form a black hole, or where a massive object is falling into an already formed black hole. It doesn't cover any other cases; in particular, it doesn't cover black hole evaporation...

Interesting point...

Oddly, the title of the chapter I quoted is BLACK HOLES EVAPORATE...which I forgot to post...but once Thorne explains what I summarized, he goes on to describe Hawking, Beckenstein at al and their descriptions of Black Hole Evaporation...he never mentions horizons of any sort again in that chapter...he never describes horizon behavior during evaporation...

edit" Also, for extra fun, the notion of an apparent horizon is actually not invariant. There was a thread about this some time back.."

I think I know the one you mean and I recall that was consistent with descriptions I have seen...

 

[PeterDonis]

you say that when atoms from an object hit the singularity they are destroyed now destroyed can mean a lot of things , a crashed car , a broken computer , a tv that just hit the pavement from the fifth floor.
But how does one destroy an atom?

Actually "atom" is probably not the right word here since atoms can be broken up into their constituent parts by a temperature of thousands of degrees Celsius, which sounds hot but is very common because it occurs in every star.

A better word would be "fundamental particle" to make it clear that we're talking about *anything*, and that "destroyed" means something much more extreme than just dissociating an atom into plasma. At the singularity, worldlines *end*--anything hitting the singularity simply ceases to exist. The singularity is a boundary of spacetime; there is no spacetime beyond it, so spacetime itself ceases to exist at the singularity.

Or maybe in the case of BH the word destroy suddenly has a totally new meaning , totally non classical?

"Destroyed" does mean something extreme at the singularity (see above), but that meaning is not non-classical; what I described above is the standard classical prediction of General Relativity. In fact, quantum effects are expected (at least by what seems to be a majority of physicists who have looked at this) to make what happens *less* extreme, not more, by introducing new physical effects that change what happens where classical GR would predict a singularity.

Now if the information is destroyed in the sense that after matter has gone inside and underwent rapid interactions it has turned to different states which if suddenly released would not turn back into the ones that fell in then yes that sounds logic.

No, that's not what the classical prediction says: it says that the information literally ceases to exist (see above). However, as I noted above, quantum effects are expected, at least by many physicists, to change this.

 

[PeterDonis]

"everything becomes unrecognizable in a quantum foam'...space,time,matter,force lose their meaning. [I just noticed Kip Thorne describes the singularity almost precisely this way.]

He's talking about the quantum prediction, not the classical prediction. See my previous post.

Degenerate electrons and neutrons are spaced much closer [and any separation likely diminishes further closer to a BH singularity] so the DeBroglie wavelength is much shorter...that's one intuitive way to try to think about 'matter converting to energy'...but I'm not sure anybody knows exactly what happens in such conversions...oh yeah there must be binding energy changes too...like fusion and fission...

"Matter converting to energy" is a vague term, but one common meaning is particles with non-zero rest mass, like electrons and positrons, annihilating each other and producing particles with zero rest mass, like photons. This has nothing to do with De Broglie wavelengths being shortened.

It is also not quite true that particles get pushed closer and closer together as they approach the singularity (we are talking about the classical GR prediction now). What happens as particles approach the singularity is that tidal gravity increases without bound; but the tidal gravity includes stretching as well as compression, so some particles are being pushed closer together while others are being pulled farther apart.

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.

Thorne mentions [pg 465] briefly that a singularity may involve topological changes...and he says '..Roger Penrose triggered a revolution in our research...tools that are now called global methods.." in the early 1970's...

The tools he's talking about don't have anything to do with the (speculative) ideas about topological changes. The global methods are what were used to prove the standard singularity theorems, which are part of mainstream classical GR; Hawking & Ellis is the definitive reference. The topological changes Thorne talks about are part of speculations about what a quantum gravity theory might contain.

 

[PeterDonis]

Oddly, the title of the chapter I quoted is BLACK HOLES EVAPORATE...which I forgot to post...but once Thorne explains what I summarized, he goes on to describe Hawking, Beckenstein at al and their descriptions of Black Hole Evaporation...he never mentions horizons of any sort again in that chapter...he never describes horizon behavior during evaporation...

Just to note, black hole evaporation is also a quantum phenomenon; it isn't present in classical GR.

 

[Naty1]

PeterDonis

Just to note, black hole evaporation is also a quantum phenomenon; it isn't present in classical GR.

agreed,
So are the GR based horizons only for an accreting BH?? ...no horizon descriptions as black holes get smaller??
I've never seen one I can recall...and I just did a quick scan of three or four books on BH and did not see any...Hmmmmmmm.

 

[PeterDonis]

So are the only GR based horizons for an accreting BH?? ...no horizon descriptions as black holes get smaller??

In the context of classical GR, yes, black holes can only get larger, not smaller, so horizons can only increase in area, not decrease. This follows from the area theorems that were proved in the early 1970's using the global methods that have been referred to before.

The reason quantum effects can cause black holes to get smaller is that quantum effects can violate the assumptions used to prove the area theorems: specifically, they can violate one of the energy conditions (IIRC the null energy condition).

 

[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.