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Imagine that 2 million light years from our current location is a collapsing shell of radiation, headed towards us. Two million years from now (minus a little bit) that shell will pass within its Schwarzschild radius and a blackhole will reside where we once stood.
But we don’t know that yet. We can’t know that yet. The shell of radiation is well outside our past lightcone. Still, despite our blissful ignorance of the doom that awaits us, an event horizon has already formed here on Earth. Light signal from our present location will never escape to infinity. The existence of this event horizon is a global geometrical statement. When, exactly, it formed depends on the total “mass” of that shell of radiation. And … we don’t know what that is.
Penrose diagram for a blackhole formed by a collapsing shell of radiation. The horizon forms before any knowledge of the collapsing shell reaches the hapless observer.
For you and me, the horizon is undetectable. There are no local measurements that we can make that will allow us to determine whether the statements of the first paragraph of this essay are correct.
George Chapline, of Livermore National Lab (along with his apparent partner in crime, Bob Laughlin), however, can tell. He claims that when you and I cross the horizon, we can observe all sorts of weird quantum-mechanical phenomena. And the thickness of the region over which these phenomena take place is a function of the mass of the blackhole that will ultimately form.
George’s chums in the Andromeda galaxy can send him superluminal signals by manipulating the “strength” of that collapsing shell (and hence the size of the region over which one observes this quantum criticality).
Normally, I wouldn’t belabour this sort of thing. But I just sat through a Harvard Physics Colloquium by the aforementioned gentleman. It was the most surreal hour I ever spent in Jefferson Laboratory.
Luboš, in his own inimitable style, has more to say on the subject.
Posted by distler at March 14, 2005 8:40 PM
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The apparent horizon, at least, can be defined by a local criterion. So the assertion that something funny happens there is not prima facie absurd.
Altering the known laws of physics at the apparent horizon would be pretty radical in itself. But he wants to fix the “paradoxical” behaviour of blackholes. That ambitious goal requires that something funny happen at the event horizon.
On the other hand, we believe in things like unitarity and Hawking radiation which all seem to indicate that something funky is going on somewhere.
Mathur, if you believe him, has the horizon never forming, so something must happen to your sphere of infalling dust.
And, because it’s late at night and I have a cold, I can make half-assed guesses. Assuming you don’t mess with the GR lagrangian too much and you believe the null energy condition (both of which have issues, I suppose), then you better not ever create a trapped surface. Being about to create a marginally trapped surface seems to me to be as good a guess for a local criterion as any.
I completely agree with your picture and conclusion but I would like to point out two issues with your configuration:
1) In order to make your point you require “sharp” edges of your shell which would result in discontinuities.
2) the asymptotics of your example is a bit funny (your space is not flat at infinity)
We could smooth the edges of the shell so that the leading edge (observable today) is weaker than the background radiation impinging on the earth.
I only had the shell extending out to past null-infinity to ensure that it could never have been in causal contact with us today. Alternatively, it could have been created yesterday by Chapline’s chums in the Andromeda Galaxy. If our telescopes were sufficiently powerful, we would be able to observe their arboreal ancestors coming down from the trees, and know that, in the future, their descendants would construct a “Doomsday Machine” and train it upon us.
I leave it you you to decide whether that modified scenario should induce quantum criticality here today.
Now I’m not a hot-shot physicist like all of you (in fact, I haven’t even passed Quantum Mechanics 1 yet), so excuse my ignorance please.
If an event horizion formed and Chapline’s friends in Andromeda can send him a FTL signal warning him, why can’t he start an explosion, change the distribution of energy inside shell (altering how it collapses) or do something that causes the singularity not to form in a million or so years? There’s probably something I’m missing.
You have, indeed, discovered one of the many, many reasons why any theory that allows faster-than-light signalling is necessarily crap.
Thanks for spelling that out. As a “hot shot physicist,” I tend to assume that as soon as I explain that “X implies faster-than-light signalling”, my audience immediately apprehends the implication that “X is utter crap”.
“I tend to assume that as soon as I explain that “X implies faster-than-light signalling”, my audience immediately apprehends the implication that “X is utter crap”.”
Another diagnostic of Utter Crap is when the author of a paper writes that future historians will look back at his work as a turning point in the history of physics, as Chapline does. Sad.
I’m not sure I understand your question, but let me try to answer it anyways.
In a Penrose diagram, light (or, indeed, any massless propagating field, like gravitational waves) travels along 45° lines.
Massive particles propagate vertically, or, at least, at angles less than 45° from vertical.
“Past null-infinity” is the 45° line at the lower right of the figure. Signals can propagate in from there. “Future null-infinity” is the 45° line at the upper right. Signals can propagate out to there.
But there’s a region of spacetime (to the upper left of the dashed line marked “event horizon”) which cannot send signals out to future null-infinity. Indeed, that’s what the event horizon means It separates regions of spacetime which can send signals out to future null-infinity from those which can’t.
George Chapline thinks that the collapse of the massive stars, which was long believed to generate black holes, actually leads to the formation of stars that contain dark energy. “It’s a near certainty that black holes don’t exist,” he claims.
Re: The Blackhole of Chapline
Just to play devil’s advocate, what if you replaced `event horizon’ by `apparent horizon’?