How is information lost if nothing passes the event horizon?

[greypilgrim]

Hi.

From an outside observer's view, any object approaching the event horizon of a black hole appears to slow down and never quite pass through the horizon. So information about those objects can always be retrieved (if you correct for the redshift). So what actually is the information paradox about?

 

[phinds]

Hi.

From an outside observer's view, any object approaching the event horizon of a black hole appears to slow down and never quite pass through the horizon. So information about those objects can always be retrieved (if you correct for the redshift). So what actually is the information paradox about?

It is about the fact that regardless of what you see, what matters is what HAPPENS, which is that the object doesn't even know the event horizon is there and just keeps falling to the singularity.

EDIT: to expand slightly, what you can "see" is just the information that is available from visible light. That doesn't tell you everything about the object. For example, what would photons from the object tell you about its charge?

EDIT #2: I should not have said "visible" light, I should have said "the electromagnetic spectrum". CrazyNinja's post directly below is perhaps a more straightforward explanation.

 

[CrazyNinja]

Lets split this into two cases:

1) The object (lets take it to be a radio source) is JUST about to fall into the event horizon. It sends out a pulse at this time t=0. We(the observers) CAN receive this signal. Hence we have information about the source falling through.

2) The radio has fallen beyond the event horizon (as @phinds says IT doesent know that it has fallen through) at t=T sec. Let's say it emits a pulse at t=T+1 sec. Now this pulse CANNOT reach us, for no radiation escapes the event horizon. Thus we have no information about the radio now. (or so we think).

 

[greypilgrim]

2) The radio has fallen beyond the event horizon (as @phinds says IT doesent know that it has fallen through) at t=T sec. Let's say it emits a pulse at t=T+1 sec. Now this pulse CANNOT reach us, for no radiation escapes the event horizon. Thus we have no information about the radio now. (or so we think).

Ok, but for the outside observer the emission of this second pulse never happens, or only in an infinite future. Why do we assume that he somehow needs to receive information about an event that doesn't even take place in his reality?

Also, wouldn't some of the proposed solutions to the information paradox violate causality? Let's say there is a way information about the second pulse can escape the black hole (e.g. through Hawking radiation). So we could measure it and conclude there is a second pulse from inside the event horizon, while at the same time observing the radio still being outside (since it never passes through in our outside reference frame).

 

[phinds]

Such an event were it possible would simply confirm what we already knew which was that the radio did in fact fall past the event horizon.

 

[greypilgrim]

I might have misunderstood something about black holes. I was under the impression that for any outside observer, the object DOES NOT actually pass the event horizon, because time dilation diverges. Is this wrong? Reading your posts, it sounds like also in the outside reference frame the object DOES pass the event horizon, we just can't observe it because the light gets more and more delayed.

EDIT: to expand slightly, what you can "see" is just the information that is available from visible light. That doesn't tell you everything about the object. For example, what would photons from the object tell you about its charge?

Is this really a problem? Pretty much all we know about the universe is obtained by EM measurements, i.e. (radio-)telescopes. Nobody would call this a paradox just because we cannot measure charge directly.

 

[PeterDonis]

information about those objects can always be retrieved

Information from a finite portion of the worldlines of those objects can be retrieved. But it's only a portion--the portion above the horizon. Information from events on the objects' worldlines that are at or below the horizon cannot be retrieved from outside the horizon.

for the outside observer the emission of this second pulse never happens

The outside observer can never see it, but that doesn't mean it doesn't happen. We have had many, many threads on this.

I was under the impression that for any outside observer, the object DOES NOT actually pass the event horizon, because time dilation diverges. Is this wrong?

Yes. The object actually passes the horizon; that is a geometric fact about spacetime and the object's worldline, independent of any observer. The outside observer cannot see the object pass the horizon because light rays from that event can't escape.

it sounds like also in the outside reference frame the object DOES pass the event horizon

Whether or not the object passes the horizon does not depend on any choice of reference frame. The outside observer's natural reference frame cannot describe the object passing the horizon. (Also note that this "natural" frame is not the only one the outside observer can adopt; he can choose others which can describe the object passing the horizon, even though he can't see light rays from it directly.)