Is there something behind a horizon?

[JohnStanton]

In flat space-time, an accelerated observer sees a horizon behind him. But any inertial observer sees the events behind that horizon.

Around a black hole, a distant observer sees a horizon, a freely falling observer sees none.

In all these cases, one observer can say "there is nothing behind the horizon" and the other says "of course there is something, I can see it".

Of course, the one who sees behind the horizon, in both cases, cannot tell the other what he is seeing. Does this mean that it is correct to say that "nothing is behind a horizon"? Or is it more correct that there is something behind it?

 

[xepma]

Welcome to relativity where some statements you can make are frame-dependent ;)

If the observer outside of the black hole says: "there is nothing behind the horizon", then I think what he really should say is: "from my point of view / frame I observe nothing behind the horizon". Nothing wrong with that statement, but keep in mind that it is frame-dependent (i.e. only valid for frames outside the horizon).

Another example is that of simultanious events. In one inertial frame you observe two events happening at the same time, and you could say that the two events happened simultaniously. But a different observer, a moving one, will disagree due to special relativitiy. So a statement about simultanious events is again an example of a statement which is frame dependent.

 

[JohnStanton]

Ok. The question is also whether there is space behind a horizon. Some people say that behind a horizon there is space (e.g. behind a black hole horizon, or behind the cosmic horizon) others say that behind them there is nothing.

Is the difference just a change of reference, or is more precise to say that there is always space behind a horizon?

 

[HallsofIvy]

Who says that?

Do you understand what "horizon" means? If you are on a boat on the ocean, you can see the horizon. Would it occur to you to ask "is there something behind the horizon"?

The "horizon" is simply what you can see from a particular viewpoint. It does NOT imply that what you can see, from that viewpoint, is all there is to the universe.

 

[javierR]

Spacetime geometry has an existence and structure that is independent of particular coordinate systems used, and therefore independent of different observers' points of view. Particular coordinatizations of spacetime may not "cover the whole spacetime", but there is a way of saying that we know the coverage is incomplete and that there are parts of spacetime that we haven't included in our coordinatization. You can try to find coordinates that cover more or all of the spacetime. So it is correct to say that there is spacetime on the other side of a horizon. Some observers will see this part of spacetime and some will not, but it is still there.

 

[jambaugh]

It is not that "there is nothing" behind the horizon. It is that the horizon is a point past which we cannot observe. For example at a given instant and point (event) the future light-cone forms an event horizon. We can't (at that time and place) see any events outside that cone. It is however a moving event-horizon (if you consider an observer moving through time) as opposed to the "stationary" event horizons of black holes and accelerated frames. But remember that motion is relative in SR and GR.

You can think of a black hole as where the future light-cones for events on the surface have been bent inward. In effect the horizon itself is a future light-cone bent into a "future light cylinder". The future of any event at the horizon is inside or at best on the surface. For simple black holes the futures of any event points inside all eventually lead to the space-time singularity at the center.

 

[JohnStanton]

All agree that there is something behind a horizon, The reason being that other observers do not have/share the same horizon and do see something there.

But if I summarize correctly, the observer that has the horizon could as well say that there is nothing behind the horizon, as long as he acknowledges that other observers will indeed see something there.

The question is thus whether "there is something" is an observer-invariant statement or an observer-dependent statement. It seems that most here agree that it is an observer-invariant statement.

 

[ernestpworrel]

How would you define horizon? Would it be the limit of our vision? That doesn't mean there's nothing there. Just something we haven't realized yet.

 

[JohnStanton]

How would you define horizon? Would it be the limit of our vision? That doesn't mean there's nothing there. Just something we haven't realized yet.

Well, I think it is fair to say: if something cannot be measured, it does not exist.
And behind a horizon, nothing can be measured. Thus nothing exists there, not even space.

 

[ernestpworrel]

It could be something we don't know that we can measure, something so fundamental that it escapes us.

 

[jambaugh]

Well, I think it is fair to say: if something cannot be measured, it does not exist.
And behind a horizon, nothing can be measured. Thus nothing exists there, not even space.

Be careful with your logic here. We can in principle observe events inside the horizon of a black hole by going inside the horizon. I agree with the positivist attitude but it should be stricter.

"If something cannot possibly be measured then its "existence" is meaningless in the context of science."

In a very real sense the event horizon of a black hole is similar to our inability to observe the future (while in the present). There is an event horizon separating future from past which is no different in quality than the event horizon separating events inside the BH from those outside. I can speak of Alpha Proxima presently existing because in the future, after I cross a specific event horizon, I can observe the light that is currently being emitted by Alpha Proxima. That event horizon is the future light-cone of the event located at Alpha Proxima and occurring "now" in my inertial frame.

I extrapolate the current existence of Alpha Proxima by projecting forward what I know about the dynamics of matter from my observations of Alpha Proxima's condition 5 years ago when it emitted the light I have been seeing over the last few months.

Just so we can extrapolate events beyond the event horizon of a black hole (events we could potentially observe by diving into see them) base on the known dynamics of matter and space-time outside the black hole.

 

[jambaugh]

Let me add to the black hole business this:
The inability to communicate what we see inside the event horizon to others in the outside world is no different than our inability to go back and tell others in the past what we have observed in the future.

It is in fact exactly the same issue. Once I cross the event horizon of a black hole all events no matter how far into your future are in my past. This is why you, watching me fall in, will see my time appear to come to a stop. Past that point of my time all your future events are in my past. (Though not necessarily in my past light-cone. I may have to wait a short time to see a signal your great grandson sends me.)

Actually I'm not being quite specific enough in my "past" "future" descriptors. I should be more precise. Consider me now at this instant and place. I have a future light-cone, a past light-cone, and the region outside both.

By causal-past I mean the interior of my past light-cone.

By causal-future I mean the interior of my future light-cone.

By actual-past/actual-future I mean an event on my past/future world-line.

Note that my light-cones are independent of my inertial frame at this instant so I can define any event-point in the exterior region as occurring "now" by boosting to a suitable frame. Likewise I can place this point in my "past" or "future".
So I can speak of my potential-past as everything but my causal-future and my potential-future as everything but my causal-past. However this is assuming flat space-time. We may suppose the possible existence of black-holes, white-holes, and worm-holes into separate "universes". Hmmm... I need to think about this some-more but as it applies to this thread I'll rephrase my statements:

Once I cross the event horizon of a black hole and assuming you never do, all events in your causal-future are in my potential-past...
and
... All events in my causal-future are outside the causal-past of any of your actual futures. (here the assumption that you don't dive in later is important and this is a statement that no observer outside the event-horizon can receive a signal from someone inside.)

Whew. That will take some parsing but the problem is that our past-present-future tense structure evolved under assumptions of absolute time. I'll have to ponder this more to see if I can polish up this extension to tenses.