Information loss in black hole, why is it a problem?

[OscarCP]

TL;DR Summary

AsI understand it, when an object falls into a black hole ,the information on it is lost outside the event horizon. But as seen by observers that never fall into the hole, it takes for ever for the falling object to get to the event horizon. If this is so, then why something that never happens is a problem?

If an observer never falls into a black hole, something it observes that does fall in takes an infinite time to reach the event horizon.
If an observer falls into a black hole along with an object, it will not lose information on the falling object, but will lose that from the outside of the black hole, except that it ill be able to observe the whole history of the Universe happening before the black whole closes the view of it because of time distortion working for this observer in reverse, as it were.
So when and how is information lost from all possible observers?

As a never-to-fall in the black hole observer sees it, the falling object will slow down constantly the nearer to the hole it gets, because of General Relativity time dilation in strong gravity fields. The falling object will also become redder, and when it reaches the event horizon will be finally utterly black throughout the electromagnetic spectrum and no longer observable, along with any information on it. But that will be at the end of eternity. So, for any non-eternal observer, it would never reach the event horizon. If one thinks of the eternal observer being the whole universe, then the information of the falling object is never lost in the universe.

So why something that never happens is a problem?

And what is wrong with my reasoning and conclusions here?

(Also I must explain that I am not a physicist, but an interested layman. Also I am new to this site.)

 

[PeroK]

But as seen by observers that never fall into the hole, it takes for ever for the falling object to get to the event horizon. If this is so, then why something that never happens is a problem?

The object does cross the event horizon in finite proper time. That event, however, cannot be observed by a distant observer.

If an observer falls into a black hole along with an object, it will not lose information on the falling object, but will lose that from the outside of the black hole, except that it ill be able to observe the whole history of the Universe happening before the black whole closes the view of it because of time distortion working for this observer in reverse, as it were.

This is wrong, and is a common misconception. The infalling object only receives light from a finite period before it crosses the horizon. This has been calculated here:

https://www.physicsforums.com/threa...into-a-black-hole.1012103/page-3#post-6599513

 

[OscarCP]

PeroK, I agree the falling observer will see the object fall through the event horizon and already wrote that is what happens. But most observers in the universe are not going to fall in that particular black hole, which was my point: for all those observers it will take for ever for the object to reach the event horizon.

As to the falling observer not seeing the whole remaining story of the universe from the moment it crosses the event horizon, I appreciate your answer, because it corrects my understanding of that side of the story.

 

[PeroK]

PeroK, I agree the falling observer will see the object fall through the event horizon and already wrote that is what happens. But most observers in the universe are not going to fall in that particular black hole, which was my point: for all those observers it will take for ever for the object to reach the event horizon.

The point of the paradox is that what eventually comes out does not depend on what went in. Also, if the BH evaporates, then the distant observer eventually sees the BH evaporate. As I understand it, in numerical terms, the number 6 falls into a BH and the number 123 comes out. Or, if the number 5 falls into the BH, the number 123 also comes out. The information about whether a five or a six went in is lost.

The ins and outs of Hawking radiation at the event horizon probably require a quantum theory of gravity to be understood fully.

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

 

[OscarCP]

PeroK, thanks for taking so much time with me.

I suspect that we are describing different things:

I am considering that for a non-falling into a black hole observer, whether close or far from the black hole (it could be passing relatively close by, but going too fast to fall into it) the time an object watched by such an observer takes to reach the horizon is infinite. This does not mean that things that fall in do not cross the event horizon in a finite time by their own clocks (if things carry clocks).

I am confused by one thing in the discussion on black holes in the thread you gave me the link to: the statements that light coming from outside to an observer at or near the event horizon just before or after falling through it is red shifted, because looking up a gravity well, clocks up there are seen to run faster than clocks down here, although all actually run just fine, be them high or be them low. I have done a lot of work with clocks in GPS satellites, so I know that.
By the same token, shouldn't the frequency of light coming down be blue shifted? And even blue shifted so much that it becomes very hard radiation when reaching the falling observer, whatever it was at its source? And when observed from below, outside clock speeds and radiation frequencies shouldn't become infinite (except, perhaps for quantum physics?) when the falling observer crosses the event horizon?
In other words: the exact opposite of what, observed from outside, is seen to happen to an object falling through the event horizon.

 

[PeroK]

I am considering that for a non-falling into a black hole observer, whether close or far from the black hole (it could be passing relatively close by, but going too fast to fall into it) the time an object watched by such an observer takes to reach the horizon is infinite.

That depends on what coordinates are used. Schwarzschild coordinates, which I expect you are assuming, have a coordinate singularity at the event horizon, so cannot be used to describe the event of crossing the horizon. But, other coodinates can be, such as the Eddington-Finkelstein that I used in the above thread.

You are reading too much into coordinate dependent statements. Saying that that event takes infinite time is actually a meaningless statement.

The thing that is independent of coordinates is that light from the object at the event horizon never reaches the distant observer. That is a meaningful statement.

I am confused by one thing in the discussion on black holes in the thread you gave me the link to: the statements that light coming from outside to an observer at or near the event horizon and falling through it is red shifted, because looking up a gravity well, clocks up there are seen to run faster than clocks down here, although all actually run just fine, be them high or be them low.

I suspect you are confusing an observer hovering near the event horizon (who would see incoming light blue-shifted) with an infalling observer, who would see incoming light red-shifted.

 

[OscarCP]

PeroK, you wrote: "You are reading too much into coordinate dependent statements. Saying that that event takes infinite time is actually a meaningless statement.

The thing that is independent of coordinates is that light from the object at the event horizon never reaches the distant observer. That is a meaningful statement."

I meant the latter: I expressed it differently and not rigorously. but that is what I was tried to express. And it harks back to my original question. What something that can never be seen to happen by most observers presents a problem? (Meaning by "problem" the loss of information, whether there actually is a Hawkins radiation or not).

As to blue or red shift, it looks like it depends on the motion of the observer: so it is blue for an observer hovering at a constant distance, red for one falling into the black hole. Is that because at that point the special relativity red shift overcomes the gravitational blue shift?

 

[PeroK]

For a calculation of the red-shift see:

https://www.physicsforums.com/threa...nt-horizon-of-black-hole.653237/#post-4174007

 

[PeroK]

I meant the latter: I expressed it differently and not rigorously. but that is what I was tried to express. And it harks back to my original question. What something that can never be seen to happen by most observers presents a problem? (Meaning by "problem" the loss of information, whether there actually is a Hawkins radiation or not).

I've already explained that. It's the Hawking radiation coming out (relative to what went in) that is the problem.

No Hawking radiation or BH evaporation, then no information problem.

 

[OscarCP]

PeroK: Thank you so much, you answer completes the necessary explanation I needed and now I have all the answer I was after.
This is a problem that has mildly bugged me for years. I have asked about it several times several people whose work involves some aspects of black holes, and the answers have been always something like: "Well, I am not really an expert on black holes, I just look for the equations that might be of some use to me and that's it. Sorry."
I don't know if you are "an expert on black holes", but you do know your Relativity.

 

[PeroK]

PeroK: Thank you so much, you answer completes the necessary explanation I needed and now I have all the answer I was after.
This is a problem that has mildly bugged me for years. I have asked about it several times several people whose work involve some aspects of black holes, and the answers have been always something like: "Well, I am not really an expert on black holes, I just look for the equations that might be of some use to me and that's it. Sorry."
I don't know if you are "an expert on black holes", but you do know your Relativity.

I'm not an expert on black holes, nor the information paradox. I only know what I know!

You can see from the Wikipedia page that there is not a consensus among the experts on whether there is a paradox and if so the resolution to it.

There are a number of useful Insights on this forum about relativity and black holes in particular. These are something of an antidote to the over simplifications you find in popular science sources.

There are, for example, many high quality YouTube videos peddling the misconceptions you had in this thread. I.e. High quality production, but physically wrong!