(Also posted this at
Physicsforums.com but I don't think that's against the rules)
Over the years I've watched Science try to deal with the Information Paradox regarding black holes.
http://news.sciencemag.org/physics/2015/12/physicists-figure-out-how-retrieve-information-black-hole
I've always been curious how we got to the point where we see this as a problem in need of a solution. In order for information to be "in" a black hole, and theoretically unavailable to us, it must have crossed the event horizon
from our perspective, correct?
We talk about the existence of black holes as a matter of fact, in
present tense, but present tense existence of spatially distant objects (i.e. events) are space-like separated by any definition, and I don't think anyone will disagree with this. The temporal order of space-like separated events is ambiguous, and can be changed based on the frame of the observer. Now, follow this logic:
Let's denote an event a "growth event" when matter crosses an event horizon. In order for a black hole to presently exist with a non-zero radius for an observer, that observer must have "growth events" in his or her past light cone. The claim that a black hole currently exists
for us fails on two counts: firstly because no such black hole growth events have occurred in any of our past light cones and, secondly, because there
are no frames which can claim otherwise for us or themselves.
The typical response to this point is frame jumping by imagining ship A free-falling across an event horizon E with sufficiently low (survivable) tidal forces; however, this
requires the existence of a black hole in the first place! We cannot use an imaginary black hole to prove the existence of theoretical black holes unless we are able to provide a theory of how they came to be in the first place. The problems faced by us on Earth would also exist for ship A; the existence of E could not be explained by any events in A's past light cone.
At this point, Kruskal (or some other) coordinates are dragged out. Again, there is no point to this. Kruskal coordinates are only needed to analyze an
existing black hole, and are not needed to discuss the birth of one. Additionally, no valid coordinate system (including Kruskal) can put growth events into the past light cone of any observer.
I don't mean to have a contentious tone, but I am frustrated by my inability to find someone who can convince me that black holes aren't a grand example of the Emperor having no clothes.
Oh, and MERRY CHRISTMAS!