Is information ever actually lost in a black hole?

[RJBeery]

The Information Paradox arises in the subject of black holes because it appears that once information (matter/energy) crosses the event horizon there is no way to retrieve it. The information has essentially been removed from existence (or at least theoretical access), and this violates a conservation of information.

I'd like to start a discussion whether information is ever actually lost in a black hole; specifically, I'd like to analyze the statement:

Is there information, which existed in the past, that is theoretically unavailable to external observers today due to falling through the event horizon of a black hole?

I'd like to restrict this thread to GR, and limit the discussion to the above specific statement and subject matter.

I'm open to suggestions on how to analyze this question, but my thoughts are to follow. To the external observer an infalling object is never lost. He could continue to study such an object for all time, taking readings and measurements of the object, albeit from an asymptotically redshifted and time dilated view of it. The external observer could adjust his measurements to account for such redshifting and time dilation and record perfectly accurate data (with perfect instrumentation).

Does this answer the question? There does seem to be a view in the community that reality contains some sort of a physical disconnect between what the observer sees and what has "really happened". How can we probe this? One thought I had was to launch a mirror towards the event horizon, and let the external observer watch his own clock in that mirror. It seems to me that if there is a point of last communication (from the perspective of the mirror) then there would be a terminating time T after which the external observer could no longer see his own clock.

I do not believe this is the case. From Reflections on Relativity:

Having discussed the prospects for hovering near a black hole, let's review the process by which an object may actually fall through an event horizon. If we program a space probe to fall freely until reaching some randomly selected point outside the horizon and then accelerate back out along a symmetrical outward path, there is no finite limit on how far into the future the probe might return. This sometimes strikes people as paradoxical, because it implies that the in-falling probe must, in some sense, pass through all of external time before crossing the horizon, and in fact it does, if by "time" we mean the extrapolated surfaces of simultaneity for an external observer. However, those surfaces are not well-behaved in the vicinity of a black hole. It's helpful to look at a drawing like this:

This illustrates schematically how the analytically continued surfaces of simultaneity for external observers are arranged outside the event horizon of a black hole, and how the in-falling object's worldline crosses (intersects with) every timeslice of the outside world prior to entering a region beyond the last outside timeslice.

If it's true that there exists no time T on an external clock which cannot be observed from that clock's location, after having been reflected on an infalling mirror, then I believe the answer to the question in this thread is NO and information has never yet been lost to a theoretical event horizon. We could replace any infalling candidate from the past whose existence is in question with a mirror; we could then send a pulse of light in the direction of that object today with the anticipation of reading back that pulse of light at some point in our finite future.

Thoughts?

 

[RJBeery]

There may be a problem here concerning what the infaller (mirror) sees of the outside world. It's supposedly a net redshifting when SR and GR effects are considered, and I don't believe that jibes with the Reflections on Relativity graph. The infalling worldline is finite and the book indicates that each point on that worldline has an extrapolated surface of simultaneity for the external observer. In order to fit an infinite number of points (i.e. the external observer's time) on to a finite length (i.e. the infaller's worldline) I don't see how a blueshifting is not required. I think I'm going to post this to PhysicsForums...

 

[Farsight]

Thoughts?

Yes: it's all bollocks. Information doesn't exist in any real sense. It isn't like energy. Energy is conserved. Information is just some pattern, and patterns can be scrambled. Conservation of information isn't physics. See how the Wikipedia Information Paradox article refers to Hawking radiation, the holographic principle, and AdS/CFT duality? It's all hypothesis. It isn't in line with Einstein's GR. He described a gravitational field as a place where the speed of light varies:

So something else that isn't in line with Einstein's GR is falling through the event horizon of a black hole. That's a place where the "coordinate" speed of light is zero. According to remote observers, the speed of light at that location is zero. So how is falling body at some location going to move faster than the speed of light at that location?

To the external observer an infalling object is never lost. He could continue to study such an object for all time, taking readings and measurements of the object, albeit from an asymptotically redshifted and time dilated view of it.

Not so. Think about it. You drop the object from a safe distance, and it falls faster and faster and faster. Because a gravitational field is a place where the speed of light varies. This is why that object falls down. Not for any other reason. Now think about the halfway point. The object is falling at the speed of light at that location. And you might think it would keep on falling even faster, but the wave nature of matter means an object can't move faster than light. Something's got to give, hence Friedwardt Winterberg's gamma ray bursters. The object is destroyed. The information is destroyed too.

It seems to me that if there is a point of last communication (from the perspective of the mirror) then there would be a terminating time T after which the external observer could no longer see his own clock.

There is a point of last communication, but not what you were thinking. Instead, think BOOM! And let's hope the external observer was at a safe distance.

I do not believe this is the case. From Reflections on Relativity: "Having discussed the prospects for hovering near a black hole, let's review the process by which an object may actually fall through an event horizon. If we program a space probe to fall freely until reaching some randomly selected point outside the horizon and then accelerate back out along a symmetrical outward path, there is no finite limit on how far into the future the probe might return. This sometimes strikes people as paradoxical, because it implies that the in-falling probe must, in some sense, pass through all of external time before crossing the horizon, and in fact it does, if by "time" we mean the extrapolated surfaces of simultaneity for an external observer. However, those surfaces are not well-behaved in the vicinity of a black hole. It's helpful to look at a drawing like this:"

There's a lot wrong with this. Worldlines do not exist in any real sense. They aren't infalling, the probe is infalling. And whilst it is, that probe moves through space, not through time. And even if there was no gamma-ray burst, the probe does not "pass through all of external time before crossing the horizon". Instead it hasn't crossed the horizon yet, and it never ever will.

If it's true that there exists no time T on an external clock which cannot be observed from that clock's location, after having been reflected on an infalling mirror, then I believe the answer to the question in this thread is NO and information has never yet been lost to a theoretical event horizon. We could replace any infalling candidate from the past whose existence is in question with a mirror; we could then send a pulse of light in the direction of that object today with the anticipation of reading back that pulse of light at some point in our finite future.

IMHO you're missing the trick here. Objects don't cross the event horizon. The frozen-star black hole grows from the inside, like a hailstone. It's a place where the speed of light is zero. That's why the black hole is black. So whatever "information" was in the original star is gone forever.

There may be a problem here concerning what the infaller (mirror) sees of the outside world. It's supposedly a net redshifting when SR and GR effects are considered, and I don't believe that jibes with the Reflections on Relativity graph. The infalling worldline is finite

It's a fairy tale. A worldline is an abstract thing. And that infalling mirror hasn't crossed the horizon yet, and it never ever will. The finite proper time is an integral too far. It's what Fednis called an improper domain extension.

and the book indicates that each point on that worldline has an extrapolated surface of simultaneity for the external observer. In order to fit an infinite number of points (i.e. the external observer's time) on to a finite length (i.e. the infaller's worldline) I don't see how a blueshifting is not required. I think I'm going to post this to PhysicsForums...

I imagine you'll get the same old guff that doesn't hold water and which appeals to Einstein's authority whilst flatly contradicting the guy. The more I learn the more I come to appreciate that the stuff peddled by the likes of Hawking and Penrose is just woo.

 

[PhysBang]

I imagine you'll get the same old guff that doesn't hold water and which appeals to Einstein's authority whilst flatly contradicting the guy.

Says the asshole who refuses to learn any of Einstein's mathematics or science, yet demands to be recognized as the only person on the entire planet who understands Einstein.

 

[RJBeery]

Yeah I'm pretty familiar with your stance on black holes, Farsight. We agree that something is amiss but we don't agree on quite a few things. In this particular thread, though, if you don't consider Conservation of Information to exist or even have any value or meaning I'm not sure that this is the best thread for you to participate in.

 

[Fednis48]

I keep going back and forth on the question of the point of last communication. You're right that no matter how far an object falls (short of the event horizon), it should always be able to climb back out. But my understanding of the point of last communication is slightly differet: it's the point after which, as long as the mass remains in freefall, no new signal from the observer will ever catch up with it. In your mirror example, the image of the clock will just get frozen in freefall along with the mirror, rather than bouncing off it and eventually escaping. Like I said, I keep going back and forth on whether such a point actually exists.

Inspired by the Zhang paper that paddoboy posted on the other thread, I think it might also be productive to consider a case with two infalling objects. If there's just one object, you're right that it asymptotically approaches the horizon, although the point of last communication introduces a potential wrinkle. With two objects, my current understanding is that the even horizon can expand to approach the outer object, potentially swallowing the inner object in the process.

 

[RJBeery]

In my experience there are folks on PhysicsForums who are more inclined to include a math analysis so I'm hoping for that. I can't say for sure that the image of the clock would get frozen in free fall, but if it does then we would have the termination time I'm looking for. There are some tricky things going on with infinities which make this difficult to internalize.

 

[Farsight]

What conservation of information? I can burn a book. I can render a planet full of books down to atoms, then throw them into a black hole and watch the gamma ray burst. Then all the information in those books is just random noise, like what you see on a detuned TV. And if I somehow trapped that light and threw it into a black hole, it's gone forever. Conservation of information isn't physics, it's a conjecture. Like all those other popscience conjectures associated with the "black hole information paradox". Which certain celebrity quacks peddle in order to promote themselves. Take a look at the associated physical information article on Wikipedia:

"Information itself may be loosely defined as "that which can distinguish one thing from another". The information embodied by a thing can thus be said to be the identity of the particular thing itself, that is, all of its properties, all that makes it distinct from other (real or potential) things."

When you grind down that planet full of books not just to atoms, not just to electrons and protons and neutrons, but to photons (and presumably neutrinos), identity is definitely lost. And it's doubly lost once you throw the photons into the black hole. Because the black hole isn't some teeming pot of photons, or anything else. Not when the speed of light is zero. Hawking radiation totally ignores this. So does the mooted conservation of angular momentum. How can that apply in a place where the speed of light is zero, when nothing can move faster than light? How does conservation of charge apply if you can rip an electron into photons? On top of that photons can superpose, and the black hole is thought to comprise some kind of difficult-to-describe state of matter/energy/space, see [URL='https://www.google.co.uk/#q=black+hole+state+of+matter]']google. It could be like one big boson. All identity lost. All information gone. Forever.[/URL]
[URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter']
[URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter']As for [URL='https://en.wikipedia.org/wiki/Hawking_radiation#Overview']Hawking radiation riding to the rescue, forget it. It demands virtual particles that pop into existence when actually they're field quanta that only exist in the mathematics of the model, it requires negative-energy particles that don't exist, it ignores the little issue of vacuum energy feeding the hole, and it ignores gravitational time dilation. It's a fairy tale. It ignores GR.[/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL]
[URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter'][URL='https://www.google.co.uk/#q=black+hole+state+of+matter']
Anyway, in order to understand the situation, I recommend you start with a single photon. You send it into the black hole. As it descends, it moves slower and slower and slower. Eventually it stops, and that's that. It's that simple.[/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL][/URL]

 

[przyk]

The Information Paradox arises in the subject of black holes because it appears that once information (matter/energy) crosses the event horizon there is no way to retrieve it.

I don't follow this so much but my impression is that the real concern only arises when quantum physics is brought into the picture and you ask what effect black holes have. For instance: if you have two entangled particles A and B, what happens if you toss A into a black hole that later evaporates? The "paradox", as I understand it (or at least one version of it), is that:

1. The Schrödinger equation predicts that quantum states evolve in a way that is deterministic and invertible (i.e, if $$\lvert \psi(t_{0}) \rangle \neq \lvert \phi(t_{0}) \rangle$$ then $$\lvert \psi(t_{1}) \rangle \neq \lvert \phi(t_{1}) \rangle$$ for any times $$t_{0}$$ and $$t_{1}$$).
2. If you have two particles A and B, there are different (and experimentally distinguishable) initial entangled states they could be in that become completely indistinguishable if you only have access to (say) the B particle.

...so if you toss A into the black hole then either half of the entangled state is lost (a situation that the Schrödinger equation doesn't accommodate, so some of our ideas about quantum physics are wrong) or it gets transferred somewhere else that survives the black hole (so some of our ideas about black holes are wrong).

 

[brucep]

I keep going back and forth on the question of the point of last communication. You're right that no matter how far an object falls (short of the event horizon), it should always be able to climb back out. But my understanding of the point of last communication is slightly differet: it's the point after which, as long as the mass remains in freefall, no new signal from the observer will ever catch up with it. In your mirror example, the image of the clock will just get frozen in freefall along with the mirror, rather than bouncing off it and eventually escaping. Like I said, I keep going back and forth on whether such a point actually exists.

Inspired by the Zhang paper that paddoboy posted on the other thread, I think it might also be productive to consider a case with two infalling objects. If there's just one object, you're right that it asymptotically approaches the horizon, although the point of last communication introduces a potential wrinkle. With two objects, my current understanding is that the even horizon can expand to approach the outer object, potentially swallowing the inner object in the process.

That's not what GR predicts. This conversation was about what GR predicts. Stephen Hawking predicts the actual horizon position coordinates constitute what he named the apparent horizon. I'm convinced that is a coherent prediction. This prediction means the lightlike barrier separating what we can know from what we can't know is dynamic. It's coordinates can change. In either direction depending on changes in black hole total energy. The local proper speed of matter as it crosses this lightlike barrier is c. Between the lightlike barrier and the center of the black hole the average proper speed is predicted to be 3/2c. So what do you think the likelihood is that a change in apparent horizon position coordinates will actually transform the position of an in falling stone from inside the lightlike barrier to outside the lightlike barrier? How fast does the position of the barrier change? I'm thinking at the local speed of light? I review the theoretical prediction as certainly possible but somewhat unlikely as a common occurrence. Using remote coordinates for analyzing the local spacetime of an apparent horizon just doesn't seem to be the best choice.

 

[paddoboy]

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html

The article concludes.....
Two notes to finish off. First, you might think that the thermal nature of the black hole is inevitable since it is radiating, but you would be wrong. In most of these quantum radiation calculations, the spectrum of the radiation does not have a Planck spectrum. If that had been the case for black holes, too, then we would not be able to assign a temperature or an entropy to black holes. In that case, people probably still would not believe Bekenstein and instead of the information loss paradox we'd still be wondering how to reconcile black holes with the second law. The thermal spectrum of Hawking radiation is one of the most serendipitous results in modern physics, in my opinion, which is another way of saying that something deep and not understood is going on.

The second is an interesting sidelight. While it's true that the Gibbs law gives the correct Bekenstein-Hawking entropy from the calculated temperature, no one has been able (until a few months ago) to explain the entropy directly from quantum mechanical / statistical mechanical grounds. In fact, it has been proven that semiclassical gravity is insufficient to account for this entropy. This is a profound result, since the thermodynamical entropy is obtained at a semiclassical level (in fact, due to some quirks that I suspect are related to the non-linearity of gravity, it is essentially classical). Thus, we are faced with the disconcerting choice that A) thermodynamical entropy does not always have a statistical mechanical basis or B) gravity is not a fundamental interaction, but rather a composite effect of some more fundamental underlying theory. Option B is not disconcerting to superstring theorists, however, it is exactly their point of view. Interestingly, since about the beginning of the year, the superstring people have jumped into the "origin of black hole entropy" fray. It turns out that by using some old result about monopoles in certain types of field theories they have been able to count the string states that would contribute to a certain (unphysical) class of a black hole of a given mass. The entropy is exactly that given by the Bekenstein area formula. The experts assure me that this will be extended to more physical models in the future. An exciting prospect indeed, if it pans out.

 

[brucep]

I don't follow this so much but my impression is that the real concern only arises when quantum physics is brought into the picture and you ask what effect black holes have. For instance: if you have two entangled particles A and B, what happens if you toss A into a black hole that later evaporates? The "paradox", as I understand it (or at least one version of it), is that:

1. The Schrödinger equation predicts that quantum states evolve in a way that is deterministic and invertible (i.e, if $$\lvert \psi(t_{0}) \rangle \neq \lvert \phi(t_{0}) \rangle$$ then $$\lvert \psi(t_{1}) \rangle \neq \lvert \phi(t_{1}) \rangle$$ for any times $$t_{0}$$ and $$t_{1}$$).
2. If you have two particles A and B, there are different (and experimentally distinguishable) initial entangled states they could be in that become completely indistinguishable if you only have access to (say) the B particle.

...so if you toss A into the black hole then either half of the entangled state is lost (a situation that the Schrödinger equation doesn't accommodate, so some of our ideas about quantum physics are wrong) or it gets transferred somewhere else that survives the black hole (so some of our ideas about black holes are wrong).

In the end the classical predictions will be wrong but I don't think the quantum solution will predict information loss. It's interesting to read about some of the quantum predictions such as the firewall or predictions that put the final shell outside the position coordinates of the apparent horizon. Or the Hawking thought experiment about what the manifold will look like after all the black holes evaporate. And of course the physics associated with the holographic principle. About the entangled states. Why would we consider the information is lost for A when we know the status of B and subsequently the state of the system? Both particles.

 

[brucep]

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html

The article concludes.....
Two notes to finish off. First, you might think that the thermal nature of the black hole is inevitable since it is radiating, but you would be wrong. In most of these quantum radiation calculations, the spectrum of the radiation does not have a Planck spectrum. If that had been the case for black holes, too, then we would not be able to assign a temperature or an entropy to black holes. In that case, people probably still would not believe Bekenstein and instead of the information loss paradox we'd still be wondering how to reconcile black holes with the second law. The thermal spectrum of Hawking radiation is one of the most serendipitous results in modern physics, in my opinion, which is another way of saying that something deep and not understood is going on.

The second is an interesting sidelight. While it's true that the Gibbs law gives the correct Bekenstein-Hawking entropy from the calculated temperature, no one has been able (until a few months ago) to explain the entropy directly from quantum mechanical / statistical mechanical grounds. In fact, it has been proven that semiclassical gravity is insufficient to account for this entropy. This is a profound result, since the thermodynamical entropy is obtained at a semiclassical level (in fact, due to some quirks that I suspect are related to the non-linearity of gravity, it is essentially classical). Thus, we are faced with the disconcerting choice that A) thermodynamical entropy does not always have a statistical mechanical basis or B) gravity is not a fundamental interaction, but rather a composite effect of some more fundamental underlying theory. Option B is not disconcerting to superstring theorists, however, it is exactly their point of view. Interestingly, since about the beginning of the year, the superstring people have jumped into the "origin of black hole entropy" fray. It turns out that by using some old result about monopoles in certain types of field theories they have been able to count the string states that would contribute to a certain (unphysical) class of a black hole of a given mass. The entropy is exactly that given by the Bekenstein area formula. The experts assure me that this will be extended to more physical models in the future. An exciting prospect indeed, if it pans out.

That's a great discussion by Professor Baez. Both the leading quantum gravity models were able to make the prediction derived from the Bekenstein area formula.

 

[tashja]

Thoughts?

Hi, RJ! Good to see you posting again.

Here is a quick reply from Prof. Marolf:

Hi. Here is the short answer:

We could replace any infalling candidate from the past whose existence is in question with a mirror; we could then send a pulse of light in the direction of that object today with the anticipation of reading back that pulse of light at some point in our finite future.

This is not possible. At late enough times, no ingoing pulse can reach the infalling object. The situation is illustrated by e.g. the diagram at the bottom of page 248 of

http://web.physics.ucsb.edu/~marolf/MasterNotes.pdf .

A signal sent inward at late times starts near the top of the diagram. And since it can travel no faster than the speed of light, it will be described by a line more vertical than horizontal (slope greater than 45 degrees). If it starts late (high) enough, it cannot reach the purple line (a given bit of infalling matter) outside the black hole, or even before that matter reaches the singularity.

This is what is meant when we say that information is lost. Sure, some info near a black hole might happen to be heading outward and return to the region far away. But some (typically, most) will not. And there is no way to actively probe it to either read the info or change its trajectory.

Best,

Don

 

[paddoboy]

Hi, RJ! Good to see you posting again.

Here is a quick reply from Prof. Marolf:

Vinaka vakalevu again tashja!

 

[The God]

This is the thread !

What is this information paradox business ?

The first line of OP says..

The Information Paradox arises in the subject of black holes because it appears that once information (matter/energy)

He is equating information = matter / energy ?

wiki link on information paradox talks of Physical Information

The black hole information paradox[1] is an observational phenomenon that results from the combination of quantum mechanics and general relativity which suggests that physical information could permanently disappear in a black hole,

And what is Physical information .

In physics, physical information refers generally to the information that is contained in a physical system. Its usage in quantum mechanics (i.e. quantum information) is important, for example in the concept of quantum entanglement to describe effectively direct or causal relationships between apparently distinct or spatially separated particles.

and I am yet to talk of Quantum information....

The definition of Physical Information is not really matter / energy ? Farsight appeared to be right when he said that conservation of information is not akin to conservation of mass and energy. may be RJbeery can explain. Are we not being fooled here by Sir SH (surprisingly rhymes with BH).

 

[Write4U]

The definition of Physical Information is not really matter / energy ? Farsight appeared to be right when he said that conservation of information is not akin to conservation of mass and energy. may be RJbeery can explain.

I would certainly be very interested.

According to Bohm's experiment of a drop of ink in a turning container og glycerine, the inkdrop will slowly stretch into a fine continuous thread, until it is no longer visible. However when reversing the precise process the inkdrop reassembles itself to its original state.

Question: If we could precisely reverse the activities in a BH (I admit this is highly unlikely), could the original information be returned to its original state?

“Bohm proposes that the holomovement consists of two fundamental aspects: the explicate order and the implicate order. He illustrates the concept of the implicate order by analogy to a remarkable physical phenomenon.

Consider a cylindrical jar with a smaller concentric cylinder (of the same height) inside it that has a crank attached, so that the inner cylinder can be rotated while the outer cylinder remains stationary. Now fill the annular volume between the two cylinders with a highly viscous fluid, such as glycerin, so that there is negligible diffusion. If a droplet of ink is placed in the fluid, and the inner cylinder is turned slowly, the ink drop will be stretched out into a fine, thread-like form that becomes increasingly thinner and fainter until it finally disappears altogether. At this point it is tempting to conclude that the ink drop has been thoroughly mixed into the glycerin, so that its order has been rendered chaotic and random. However, if the inner cylinder is now rotated slowly in the opposite direction, the thin ink form will reappear, retrace its steps, and eventually reconstruct itself into its original form of the drop again. Such devices have been constructed, and the effect is quite dramatic.

http://www.halexandria.org/dward404.htm

 

[paddoboy]

Because the black hole isn't some teeming pot of photons, or anything else. Not when the speed of light is zero. Hawking radiation totally ignores this.

The only one ignoring scientific fact is the same one that has in the past, claimed to have a TOE, and that constantly quotes/misquotes, and takes out of context most of what the great man has said.
Let me tell you one up...The speed of light is always "c" despite your continued ranting to claim otherwise and attempt to mislead people........
https://en.wikipedia.org/wiki/Propagation_of_light_in_non-inertial_reference_frames
For example, at the event horizon of a black hole the coordinate speed of light is zero, while the proper speed is c.[1] The coordinate speed of light (both instantaneous and average) is slowed in the presence of gravitational fields. The local instantaneous proper speed of light is always c.

As for

Hawking radiation riding to the rescue, forget it.

The only thing this forum needs to forget is what you claim, including this TOE you have gone silent on.

Anyway, in order to understand the situation, I recommend you start with a single photon. You send it into the black hole. As it descends, it moves slower and slower and slower. Eventually it stops, and that's that. It's that simple.

No, not really: The photon is gradually gravitationally time dilated and at the same time red shifted to infinity. In actual fact from a distant FoR, it is never seen to be stopped, just eventually fading beyond the viewing capabilities of your eyes and/or instrumentalities. It's that simple.

 

[tashja]

Vinaka vakalevu again tashja!

You're welcome, Paddo.

RJ, Here's Prof. Baez's reply:

Hi-

Here is my reply:

If it's true that there exists no time T on an external clock which cannot be observed from that clock's location, after having been reflected on an infalling mirror, then I believe the answer to the question in this thread is NO and information has never yet been lost to a theoretical event horizon.

If you hold a clock and drop a mirror into a black hole, there is in fact a time T, such that you will never see a time after T reflected in the clock's face.

More precisely:

The mirror will quickly become redshifted as it falls in, and fade to invisibility. As it does so, the hands on the reflected image of the clock will slow down. If you could continue watching it forever - despite the fact that in practice it quickly becomes too faint - you would see the time on the clock approach some value T, but never reach this value.

It's easier to solve this kind of problem using Eddington-Finkelstein coordinates than Schwarzschild coordinates. It doesn't ultimately matter what coordinates you use - you always get the same answer - but Schwarzschild coordinates make this kind of problem more confusing. For a nice and detailed analysis of a related but slightly different problem, see Greg Egan's webpage "The Finite Fall":

http://gregegan.customer.netspace.net.au/SCIENCE/FiniteFall/FiniteFall.html

He uses Eddington-Finkelstein coordinates to answer the question "If a friend of yours is dropping into a black hole, how long can you wait before it's impossible to swoop down, grab him and return?" At the uttermost limit of what's possible, you'd be swooping down at the speed of light and returning at the speed of light. Then this problem is just like the problem of light going in towards a mirror that's falling into a black hole and bouncing back!

Best,
jb

 

[Farsight]

See Eddington–Finkelstein coordinates on Wikipedia:

"They are named for Arthur Stanley Eddington and David Finkelstein, even though neither ever wrote down these coordinates or the metric in these coordinates. Roger Penrose seems to have been the first to write down the null form but credits it (wrongly) to the above paper by Finkelstein, and, in his Adams Prize essay later that year, to Eddington and Finkelstein. Most influentially, Misner, Thorne and Wheeler, in their book Gravitation, refer to the null coordinates by that name".

These coordinates were invented by Penrose, then given false pedigree by Misner Throne and Wheeler. See what Greg Egan says:

"How can we compute this time interval? A convenient set of coordinates to use for this problem are the Eddington-Finkelstein coordinates. The space-time metric for a non-rotating black hole of mass M (using geometric units in which the gravitational constant and the speed of light are both equal to 1) is given in these coordinates by..."

Note how it uses units where the speed of light is 1? That flatly contradicts what Einstein said. What we have here is the same old schoolboy error. The optical clock goes slower and slower, and is stopped at the event horizon where gravitational time dilation goers infinite, because light stops at the event horizon. And yet we can gaily switch to some new neverland coordinate system where the clock somehow carries on ticking at the same old rate? It's nonsense.