Has information been lost to a black hole?

[rjbeery]

I'd like to understand if and when 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. It seems plausible, if not completely convincing, that the observer could proclaim information has been lost at time T.

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:

http://mathpages.com/rr/s7-03/7-03_files/image022.gif

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. However it's supposedly a net redshifting of what the infalling mirror sees of the outside world 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 all points on the external observer's infinite worldline. In order to fit an infinite number of points on to a finite length I don't see how a blueshifting is not required.

So does anyone have the answer? What I'd really like is the calculation for "when" an external observer could no longer see himself in the infalling mirror.

Thoughts?

 

[Jeff Rosenbury]

I think you are right. There is no limit if you restrict yourself to GR.

My guess is that the surface irregularities of the event horizon are due to other aspects of physics/mathematics. (Noether's theorem would seem to indicate a limit on redshift for example.) But you wanted a simpler model.

BTW, in geometry, any non-zero line segment has an infinite number of points. It is not clear to me that a line segment of a given (or even infinite) length is big O to the number of points on the smallest segment (less the zero length segment of course). Thus a mapping should be possible. (I could be wrong though.)

BTW, I'm not an expert

 

[rjbeery]

I think you are right. There is no limit if you restrict yourself to GR.

My guess is that the surface irregularities of the event horizon are due to other aspects of physics/mathematics. (Noether's theorem would seem to indicate a limit on redshift for example.) But you wanted a simpler model.

BTW, in geometry, any non-zero line segment has an infinite number of points. It is not clear to me that a line segment of a given (or even infinite) length is big O to the number of points on the smallest segment (less the zero length segment of course). Thus a mapping should be possible. (I could be wrong though.)

BTW, I'm not an expert

Right, I don't have a problem with mapping infinite points on to a finite length, I have a problem "experiencing" that finite length as a worldline and not "experiencing" those infinite points as being necessarily, infinitely, blueshifted away from their original signal.

 

[Chronos]

First, you need to consider what constitutes 'information', followed by what it means to be 'lost'. Can you deduce the last thing that passed through the mind a bug from the spatter on your windshield [other than 'crap!']? The black hole information paradox relies on too many poorly defined assumptions to be taken too seriously, IMO.

 

[rjbeery]

First, you need to consider what constitutes 'information', followed by what it means to be 'lost'. Can you deduce the last thing that passed through the mind a bug from the spatter on your windshield [other than 'crap!']? The black hole information paradox relies on too many poorly defined assumptions to be taken too seriously, IMO.

This doesn't bother me so much. Losing information to chaos is radically different from losing information to physical laws.

 

[Jeff Rosenbury]

I know the energy of information depends on temperature. So if we redshift enough we will lose the information in the cosmic background radiation as the energy value drops below the signal to noise ratio (by a lot).

Does that count as a physical law, or chaos? It seems both to me.