Effect before Cause:absolute horizon

[Naty1]

Kip Thorne says the following in his book BLACK HOLES AND TIME WARPS,1994, page 417,

Little attention was paid to the absolute horizon because of our cherished notion that an effect should not precede it's cause...When matter falls into a black hole, the absolute horizon starts to grow (effect) before the matter reaches it (cause). The horizon grows in anticipation that the matter will soon be swallowed...this seeming paradox has a simple origin. The very definition of the absolute horizon depends on what will happen in the future: on whether or not signals will ultimately escape to the distant universe...it forces the horizon's evolution to be teleological...

It may be "simple", but that explanation sounds flimsy at best...can anyone help me understand it? How did effect precede cause in classical general relativity or does this have some other origin? It sounds more like quantum mechanics of some sort.

 

[atyy]

Think of a bottle enclosing some coke. Is the bottle capped or not? You start at the bottom, and you don't find out that it's capped until you get to the top. But if it is capped, then it was capped when you were at the bottom.

 

[xantox]

can anyone help me understand it? How did effect precede cause in classical general relativity or does this have some other origin? It sounds more like quantum mechanics of some sort.

The standard definition of the event horizon according to Hawking and Ellis 1973 is the boundary of $$J^-(\mathcal{I}^+)$$, where $$\mathcal{I}^+$$ is future null infinity and $$J^-$$ its causal past. Since it is defined over the entire spacetime (eg "eternally"), it has some counterintuitive non-local features, as it describes the horizon in terms of events happening in the infinite future, not of events happening in the past.

 

[DrGreg]

The standard definition of the event horizon according to Hawking and Ellis 1973 is the boundary of $$J^-(\mathcal{I}^+)$$, where $$\mathcal{I}^+$$ is future null infinity and $$J^-$$ its causal past. Since it is defined over the entire spacetime (eg "eternally"), it has some counterintuitive non-local features, as it describes the horizon in terms of events happening in the infinite future, not of events happening in the past.

To translate this into less technical language, to decide whether an event is inside or outside the absolute event horizon, consider all the photons passing through that event. If any of those photons eventually "escape to infinity", you are outside the horizon. The problem is you have to wait an infinite time to be absolutely sure a photon reaches infinity. And whether a photon gets there or not depends on events that lie in the future of the event you are trying to categorise. So, from practical point of view, you can only determine where the horizon was in the past, you can't actually measure where it is now. But you can say where it is now if you believe you can successfully predict the future of escaping photons.

That maybe isn't quite so strange as it at first sounds. Even in special relativity, you can't actually find out what is happening now anywhere, you can only retrospectively determine when events occurred some time after their occurrence.

 

[xantox]

But you can say where it is now if you believe you can successfully predict the future of escaping photons.

Interestingly, the event horizon has a causal behavior if you pretend time is flowing in reverse, starting from future infinity.

 

[MeJennifer]

Little attention was paid to the absolute horizon because of our cherished notion that an effect should not precede it's cause...When matter falls into a black hole, the absolute horizon starts to grow (effect) before the matter reaches it (cause). The horizon grows in anticipation that the matter will soon be swallowed...this seeming paradox has a simple origin. The very definition of the absolute horizon depends on what will happen in the future: on whether or not signals will ultimately escape to the distant universe...it forces the horizon's evolution to be teleological...

Perhaps Kip should have been a bit clearer about black holes which, except in cases of exotic cosmological constant constructions, only occur in closed spacetimes.

 

[Naty1]

That maybe isn't quite so strange as it at first sounds. Even in special relativity, you can't actually find out what is happening now anywhere, you can only retrospectively determine when events occurred some time after their occurrence.

Oh I think I'll stiick with "yea, it's pretty strange"! I'm amazed anybody could interpret all that from mathematical formulations! Good input, thanks.

 

[JesseM]

Perhaps Kip should have been a bit clearer about black holes which, except in cases of exotic cosmological constant constructions, only occur in closed spacetimes.

That certainly isn't true, black holes are typically modeled in asymptotically flat spacetimes which are spatially infinite. Where did you get this idea? From a source by a physicist like a textbook or a paper, or through your own chain of reasoning?

 

[JesseM]

It may be "simple", but that explanation sounds flimsy at best...can anyone help me understand it? How did effect precede cause in classical general relativity or does this have some other origin? It sounds more like quantum mechanics of some sort.

The absolute horizon is an abstract entity defined in terms of the infinite future of the spacetime (it's the boundary between the set of events where all light from those events would in the arbitrarily distant future end up hitting the singularity, and events where at least some light from the events would escape and never hit the singularity), it's not something that can actually be measured locally, so there's no issue of any measurable physical effects preceding their causes here. It's like if I defined my "-10th deathday" as the point on my worldline that occurs exactly 10 years before I die according to my own proper time, there'd be some objective truth about where on my worldline the -10th deathday occurs but there'd be no way to discover it until I actually died.

 

[Naty1]

Thorne also makes these statements about relative and absolute horizons:

The apparent horizon is a relative concept, not an absolute one. It's location depends on the observers reference frame. When matter falls into a black hole the apparent horizon can jump suddenly...(discontinuously)

Hawkings absolute horizon by contrast was...the same in all reference frames...(it) changes shape and size in a smooth continuous way...

Hawking was well aware the choice of definition of a horizon...could not influence in any way predictions for the outcome of experiments..but could strongly influence the ease with which the properties and behaviors of black hole.s (are deduced)...

So what can be measured locally and what cannot is not entirely obvious to me. But the apparent ambiguity emerging from classical general relativity sure begins to seem more like the uncertainty underpinning quantum mechanics than I had previously realized ...///

 

[DrGreg]

So what can be measured locally and what cannot is not entirely obvious to me.

JesseM's birthdays be measured locally but his deathdays (as defined in post #9) can't. I wouldn't liken that to quantum uncertainty.